Optical and Magnetization Studies
on Europium Based Iron Pnictides
Von der Fakultät Mathematik und Physik der Universität Stuttgart
zur Erlangung der Würde eines Doktors der Naturwissenschaften
(Dr. rer. nat.) genehmigte Abhandlung
Vorgelegt von
Sina Maria Ute Zapf
aus Offenbach am Main
Hauptberichter: Prof. Dr. M. Dressel
Erster Mitberichter: Prof. Dr. B. Keimer
Zweiter Mitberichter: Prof. Dr. D. N. Basov
Tag der mündlichen Prüfung: 18.12.2014
1. Physikalisches Institut der Universität Stuttgart
2015

Expect problems
and eat them for breakfast.
A. A. Montapert

ABSTRACT
Understanding the interplay of magnetism and superconductivity is one of the central top-
ics in contemporary condensed matter research: while those are traditionally antagonistic
phenomena, there is growing experimental evidence that unconventional superconductiv-
ity - for instance in cuprates, heavy fermion or organic materials - is closely linked to
magnetism [1–3]. Among all these material classes, the cuprates garnered the most at-
tention because for more than two decades, they were the only known “high-temperature
superconductors”. Only recently, they lost this monopoly position due to the discovery of
relatively high critical temperatures in iron pnictides [4, 5].
One obvious common feature of cuprates and iron-based superconductors is an antifer-
romagnetic parent phase. While undoped cuprates are Mott insulators, the magnetism
in iron pnictides is usually considered as rather itinerant with a metallic spin density
wave ground state. Chemical substitution or external pressure continuously suppress the
magnetic transition temperature, until superconductivity emerges. Thus, magnetic fluc-
tuations are widely debated as a key ingredient for high-temperature superconductivity.
Recently, however, another similarity has moved into the focus of interest: at the nematic
phase transition, electronic interactions break the rotational symmetry of the crystal,
accompanied by strong fluctuations [6]. Compared to the antiferromagnetic phase, this
transition usually takes place at slightly higher temperatures. Unfortunately, the exper-
imental access to this exotic phase is challenging, as crystals usually appear twinned,
meaning that domains mask the intrinsic anisotropy.
The investigations carried out in the framework of this thesis mainly concentrate on
europium based iron pnictides. These are a peculiar member of the 122 family as they
develop at low temperatures (∼ 20K) an additional magnetic order of the local rare earth
moments (see Fig. 0.1). The Eu2+ spin structure is a so-called “A-type” antiferromag-
netism, meaning that spins of one layer are ferromagnetically aligned (along the a-axes),
while neighbouring planes are coupled antiferromagnetically. Furthermore, neutron mea-
surements revealed the possibility to detwin those compounds (i.e. to align the twinned
domains along one direction) at low temperatures in laboratory-scale magnetic fields [7],
a feat which is not possible in other iron pnictides and thus probably related to the rare
iv Abstract
earth magnetism. Therefore, europium based iron pnictides provide a unique platform
to study the interplay of structural, magnetic and electronic effects in high-temperature
superconductors. For this challenging purpose, we have employed SQUID magnetometry
and Fourier-transform infrared spectroscopy on EuFe2(As1−xPx)2 single crystals; the main
results are summarized as followed.
Figure 0.1: Magnetic struc-
ture of EuFe2As2 at 2.5K [8].
Fe2+ moments (brown ar-
rows) align antiferromagnet-
ically along the a- and the
c-axis, but ferromagnetically
along the b-axis. Eu2+ mo-
ments (blue arrows) align
within one europium layer
ferromagnetically along the
a-axis, and neighbouring ab-
planes are coupled antiferro-
magnetically.
By systematic studies of the in- and out-of-plane magnetic properties of a series of
EuFe2(As1−xPx)2 single crystals, we derived the complex magnetic phase diagram of eu-
ropium based iron pnictides (see chapter 7, Ref. [9] and Ref. [10]). As depicted in Fig. 0.2,
the Eu2+ magnetic ordering involves two steps for all phosphorus substituted compounds.
The transition at a higher temperature TN is characterized throughout the whole phase di-
agram by an antiferromagnetic interlayer coupling. One should note, however, that phos-
phorus substitution induces a ferromagnetic out-of-plane component, leading to canted
A-type antiferromagnetism. This canting develops rather quickly at low substitution lev-
els, similar to the suppression of TN and the spin density wave transition temperature.
These observations imply that the Eu2+ spin orientation is notably influenced by the spin
density wave anisotropy. Thus, our measurements demonstrate significant interactions
between the local Eu2+ and the (quasi-) itinerant spin density wave magnetism, which is
consistent with theoretical calculations [11].
The second magnetic transition in the europium subsystem displays glass-like dynamics,
affecting the coupling between the planes. As its transition temperature Tglass is lower
than the onset of magnetic order, it is referred to as “re-entrant” spin glass phase. With
increasing phosphorus substitution, Tglass rises quickly until it approaches TN, leading
to successive transitions that are separated by ∼ 2K. Thus, only measurements with
rather small temperature steps are able to resolve both phases. Nevertheless, we find
indications for similar dynamics when reviewing published data of other europium based
Abstract v
compounds (see chapter 6). Therefore, we suggest that the re-entrant spin glass phase
is the key to understand how bulk superconductivity can coexist with the usually strong
Eu2+ magnetism.
Figure 0.2: Phase Dia-
gram of EuFe2(As1−xPx)2.
TN (red dots) indicates a
canted A-type antiferro-
magnetic transition, Tglass
(blue triangles) a spin
glass transition, and Tc,on
the onset of supercon-
ductivity (grey squares).
Closed symbols correspond
to transition temperatures
deduced from magneti-
zation, open ones from
resistivity measurements.
Shadowed lines are guides
to the eye. The light grey
area indicates the onset of
superconductivity, while
bulk superconductivity is
fully developed in the dark
grey regime.
Despite the interactions of local and itinerant magnetism revealed by our magnetization
studies, the electrodynamic response of EuFe2As2 is surprisingly unaffected by the Eu2+
magnetic transition - the infrared spectra basically do not change when passing TN (see
chapter 8). By comparing several fitting approaches, we find that the most realistic results
are obtained with a model that contains two Drude components (probably representing
electron and hole bands) and a Lorentzian around 1000 cm−1, which can be attributed to
interband transitions involving Fe hole pockets [12]. Importantly, we are able to extract
trends that are independent from the fitting method. For instance, we conclude that the
spin density wave transition affects not only both Drude components, but also the spectral
weight transfer, which appears in iron pnictides usually up to very high energies. These
observations provide interesting insights into the relation of this transfer to the localization
of itinerant carriers driven by correlation effects.
Combining our expertise obtained from magnetization and optical studies on europium
compounds, we have also performed magneto-optical measurements on EuFe2As2 (see
chapter 9, [13]), which revealed a much more complex detwinning process than expected.
vi Abstract
At temperatures below the local Eu2+ ordering, the detwinning occurs in two steps, mean-
ing that the crystal gets already partially detwinned with b ‖ H at ∼ 0.1T, followed by
a reverse reorientation of structural domains with a ‖ H at ∼ 0.6T. Above TN, only the
latter process takes place. We ascribe these observations to an indirect magneto-elastic
coupling of the Eu2+ ions via the Fe2+ spins, which was - to our best knowledge - not pro-
posed before. Moreover, we give a simple model for the two-step detwinning process based
on the competition between magneto-crystalline anisotropy, antiferromagnetic exchange
coupling and Zeeman energy (see Fig. 0.3).
a a a
a a a a
b b b
bbbb
H
twin BII
twin AII
(d) H ≥ H2 (c) H = HSF (b) H ≈ H1 (a) H = 0T
Figure 0.3: Sketch of the twin distribution of EuFe2As2 dependent on an (from left to right
increasing) external magnetic field H ‖ [110]T at T < TEu. (a) For H = 0T, the zero-field
crystal is twinned and the domains are equally distributed. The Eu2+ spins are ordered A-
type antiferromagnetically with the spin direction along the a-axis. (b) With external field,
twin variant B‖ (red, bottom) with b ‖ H gets energetically favoured and therefore grows
on the expense of variant A‖ (green, top), as soon as the energy difference exceeds the twin
boundary pinning energy. (c) With further increasing field, Eu2+ spins in the remaining
type A‖ twins flip along the field direction. Energetically, twin B‖ is still more favourable.
(d) At slightly higher fields, twin A‖ is favoured and the crystal is detwinned with a ‖ H.
Most importantly, the induced detwinning is persistent, meaning that a significant im-
balance of twin domains remains when the magnetic field is switched off and the tempera-
ture is raised up to the nematic and spin density wave transition. Such strongly hysteretic
behaviour is surprising from a very fundamental point of view, as the detwinning that is
induced at low temperatures with very small magnetic fields persists up to much higher
temperatures, i.e. energy scales. Thus, our whole studies on europium based pnictides
reveal a remarkable interdependence between magnetic, electronic and structural effects
that might be very important to understand the unconventional superconductivity in these
fascinating materials.
ZUSAMMENFASSUNG
Eines der zentralen Themen der heutigen Festkörperforschung ist es, die Wechselwirkungen
zwischen Supraleitung und Magnetismus besser zu verstehen. Obwohl diese Phänomene
traditionell nicht miteinander vereinbar sind, mehren sich die Hinweise, dass unkonventio-
nelle Supraleitung, die beispielsweise in Kupferoxiden, Schweren Fermionen oder organi-
schen Materialien vorkommt, überraschenderweise sehr eng mit Magnetismus verbunden
ist [1–3]. Dabei stellen die Kupferoxide vermutlich die am meisten untersuchte Material-
klasse dar, da sie mehr als 20 Jahre die einzigen bekannten Vertreter der “Hochtempera-
tursupraleiter” waren. Tatsächlich ging diese Monopolstellung erst kürzlich verloren, als
Supraleitung mit überraschend hohen Übergangstemperaturen in Eisenpniktiden entdeckt
wurde [4, 5].
Vergleicht man verschiedene Hochtemperatursupraleiter, so ist eine offensichtliche Ge-
meinsamkeit, dass Antiferromagnetismus eine wichtige Rolle im Phasendiagramm spielt:
während undotierte Kupferoxide Mott-Isolatoren sind, geht man bei Eisenpniktiden in
den meisten Fällen von einem metallischen Spindichtewellen-Grundzustand aus. Durch
chemische Substitution oder das Anlegen von externem Druck wird dessen Übergangs-
temperatur kontinuierlich verringert, bis schließlich Supraleitung einsetzt. Deshalb liegt es
nahe, antiferromagnetische Fluktuationen mit dem Auftreten von Hochtemperatursupra-
leitung zu assoziieren. Aktuell rückt allerdings eine weitere Gemeinsamkeit immer mehr
in den Fokus der Forschung: bei dem sogenannten “nematischen” Übergang wird die Ro-
tationssymmetrie des Kristalls durch elektronische Wechselwirkungen gebrochen; dabei
treten sehr starke Fluktuationen auf [6]. Verglichen mit der antiferromagnetischen Phase
findet dieser Übergang im Normalfall bei einer leicht höheren Temperatur statt. Leider ist
seine Erforschung relativ kompliziert, da die resultierende strukturelle und elektronische
Anisotropie durch Domänenbildung maskiert wird.
Die im Rahmen dieser Arbeit durchgeführten Untersuchungen konzentrieren sich auf
Europium-haltige Eisenpniktide. Diese entwickeln zusätzlich zur Spindichtewelle bei tie-
fen Temperaturen (ca. 20K) eine lokale magnetische Ordnung. Hierbei sind die Eu2+ Spins
innerhalb einer Ebene ferromagnetisch, aber benachbarte Ebenen antiferromagnetisch ge-
koppelt - auch “A-typ” Antiferromagnetismus genannt (vgl. Abbildung 0.4). Desweiteren
viii Zusammenfassung
ging aus Neutronenstreuungs-Experimenten hervor, dass in EuFe2As2 relativ niedrige Ma-
gnetfelder ∼ 1T ausreichen, um bei Temperaturen unterhalb der Eu2+-Ordnung alle Do-
mänen gleich auszurichten [7]; in anderen Eisenpniktiden ist dies nicht möglich. Aus diesem
Grund bieten Europium-haltige Eisenpniktide die außergewöhnliche Möglichkeit, struktu-
relle, magnetische und elektronische Effekte, sowie deren Wechselwirkungen in Hochtem-
peratursupraleitern zu untersuchen. Dafür wurden im Rahmen dieser Arbeit Magnetisie-
rungsmessungen und Fourier-Transform-Infrarotspektroskopie an EuFe2(As1−xPx)2 Ein-
kristallen durchgeführt. Die wichtigsten Ergebnisse werden im Folgenden vorgestellt.
Abbildung 0.4: Magnetische
Struktur von EuFe2As2 bei
2.5K [8]. Die Fe2+ Spins (brau-
ne Pfeile) sind antiferroma-
gnetisch entlang der a- und
c-Achse, aber ferromagnetisch
entlang der b-Achse ausgerich-
tet. Die Eu2+ Spins (blaue Pfei-
le) einer Ebene sind ferroma-
gnetisch gekoppelt und zeigen in
Richtung der a-Achse; benach-
barte Ebenen sind antiferroma-
gnetisch gekoppelt.
Auf der Basis von richtungsabhängigen Untersuchungen der magnetischen Eigenschaften
von EuFe2(As1−xPx)2 Einkristallen konnte das komplexe magnetische Phasendiagramm
von Europium-haltigen Eisenpniktiden bestimmt werden; dieses ist in Abb. 0.5 zu sehen (s.
Kapitel 7, Ref.[9] und Ref. [10]). Man stellt fest, dass die lokale Eu2+-Ordnung tatsächlich
schrittweise abläuft. Betrachtet man zunächst den Übergang bei höherer Temperatur TN,
so bleibt die Kopplung zwischen den Ebenen durch das gesamte Phasendiagramm antifer-
romagnetisch. Allerdings entwickelt sich mit steigender Phosphor-Substitution rasch eine
ferromagnetische Komponente entlang der c-Richtung; man spricht von “gekantetem” A-
typ Antiferromagnetismus. Da die Zunahme dieser Komponente mit einer Unterdrückung
der Ordnungstemperatur von Spindichtewelle und lokalem Eu2+-Magnetismus verbunden
ist, liegt es nahe, dass die beiden magnetischen Ordnungen sich gegenseitig beeinflussen;
dies wird auch durch theoretische Berechnungen unterstützt [11].
Der zweite magnetische Übergang bei tieferen Temperaturen Tglass ist glasartig und be-
trifft die Kopplung zwischen den Ebenen. Da er einer magnetischen Ordnung folgt, spricht
man auch von einem “re-entrant” Spin-Glas. Betrachtet man den Verlauf der Übergangs-
temperatur Tglass, so steigt sie bei niedrigen Phosphor-Konzentrationen schnell an und
Zusammenfassung ix
Abbildung 0.5: Pha-
sendiagramm von Eu-
Fe2(As1−xPx)2. TN (rote
Punkte) ist die Übergangs-
temperatur des gekanteten
A-typ Antiferromagnetismus,
Tglass (blaue Dreiecke) die des
Spin-Glas Übergangs, und
Tc,on die der Supraleitung
(graue Quadrate). Geschlos-
sene Symbole wurden aus
Magnetisierungsmessungen,
offene aus Widerstandskur-
ven extrahiert. Transparente
Linien zeigen die wichtigen
Trends; während die hell-
graue Fläche das Einsetzen
von Supraleitung markiert,
entspricht die dunkelgraue
Region der voll entwickelten
Supraleitung.
folgt dann TN im Abstand von etwa 2K. Aus diesem Grund kann dieses ungewöhnli-
che Verhalten nur in Messungen mit sehr kleinen Temperaturschritten aufgelöst werden.
Nichtsdestrotrotz wurden ähnliche Beobachtungen auch bei anderen Europium-haltigen
Eisenpniktiden gemacht (s. Kapitel 6). Deshalb ist dieses glasartige Verhalten vermut-
lich der Schlüssel, um die Koexistenz von Europium-Magnetismus und Supraleitung zu
erklären.
Trotz der Wechselwirkungen zwischen den magnetischen und elektronischen Subsyste-
men, die durch diese Magnetisierungsmessungen nachgewiesen werden konnten, ist das
optische Spektrum von EuFe2As2 überraschend unbeeinflusst von der lokalen Eu2+ Ord-
nung (s. Kapitel 8). Der Vergleich mehrerer Modellierungsansätze ergibt, dass die rea-
listischsten Ergebnisse durch eine Analyse mit zwei Drude- und einer Lorentzkomponen-
ten (bei 1000 cm−1) erhalten werden. Dabei repräsentieren erstere vermutlich Elektronen-
und Lochbänder, letztere Interbandübergänge in die Eisen-Lochtaschen [12]. Vor allem
aber können durch diesen Vergleich Trends bestimmt werden, die unabhängig vom Mo-
dellierungsansatz sind: der Spindichtewellen-Übergang beeinflusst nicht nur beide Drude-
Komponenten, sondern auch den Transfer von spektralem Gewicht, der in Eisenpniktiden
üblicherweise bis zu sehr hohen Energien auftritt. Diese Beobachtungen liefern interessante
Informationen, inwiefern dieser Transfer mit der Lokalisierung von freien Ladungsträgern
aufgrund von Korrelationseffekten zusammenhängt.
x Zusammenfassung
Die Erfahrungen mit magnetischen und optischen Messungen wurden schließlich ge-
nutzt, um eine Reihe von magneto-optischen Untersuchungen an EuFe2As2 durchzuführen
(s. Kapitel 9 und Ref. [13]). Dabei konnte aufgedeckt werden, dass dem Ausrichten der
Domänen im Magnetfeld ein wesentlich komplexerer Prozess zu Grunde liegt, der jedoch
durch ein relativ einfaches Modell erklärt werden kann (s. Abb. 0.6). Bei Temperaturen
unterhalb von TN verläuft diese Ausrichtung in zwei Schritten: zunächst wird ein Großteil
der Domänen schon bei sehr niedrigen Feldern von ∼ 0.1T mit der b-Achse parallel zum
Magnetfeld H ausgerichtet; dem folgt eine Ausrichtung mit der a-Achse parallel zu H bei
Feldern von etwa 0.6T. Oberhalb von TN findet nur letzterer Prozess statt. Dieses Verhal-
ten deutet auf eine bis dahin unbekannte indirekte magneto-elastische Kopplung hin, bei
denen die Eu2+-Spins über die Fe2+-Momente mit dem Gitter wechselwirken können.
a a a
a a a a
b b b
bbbb
H
twin BII
twin AII
(d) H ≥ H2 (c) H = HSF (b) H ≈ H1 (a) H = 0T
Abbildung 0.6: Schematische Darstellung der Domänenverteilung in EuFe2As2 in Abhän-
gigkeit eines (von links nach rechts zunehmenden) externen magnetischen Feldes H ‖ [110]T
bei Temperaturen T < TEu. (a) Bei H = 0T sind die Domänen (“twins”) gleichmäßig verteilt,
wenn der Kristall im Nullfeld abgekühlt wurde. (b) In einem externen Feld werden zunächst
die Domänen B‖ (rot, unten) mit b ‖ H energetisch begünstigt, weswegen ihr Anteil auf Kosten
der Domänen A‖ (grün, oben) steigt, sobald die Energie die der Haftung der Domänenwände
übersteigt. (c) Wird das externe Feld weiter erhöht, kommt es zu einem Eu2+ Spin-Flip in
den verbleibenden A‖-Domänen; energetisch sind jedoch noch die anderen bevorzugt. (d) Dies
ändert sich erst bei leicht höheren Feldern und alle Domänen werden mit der a-Achse entlang
von H ausgerichtet.
Die vermutlich wichtigste Beobachtung bei diesen Studien ist, dass das magnetfeldin-
duzierte Ungleichgewicht der Domänen bestehen bleibt, auch wenn das Feld ausgeschaltet
und die Temperatur bis zum Spindichtewellen- und nematischen Übergang erhöht wird.
Berücksichtigt man die relevanten Energieskalen, so ist eine solch robuste Hysterese tat-
sächlich sehr überraschend. Somit konnten die im Rahmen dieser Arbeit durchgeführten
Studien an Europium-haltigen Eisenpniktiden ein bemerkenswertes Zusammenspiel von
magnetischen, elektronischen und strukturellen Effekten aufdecken, welches einen wichti-
gen Einblick in die faszinierenden Zusammenhänge unkonventioneller Supraleiter gibt.
PUBLICATIONS
Some results of this work have been already published:
• S. Zapf, D. Wu, L. Bogani, H. S. Jeevan, P. Gegenwart, and M. Dressel
Varying Eu2+ magnetic order by chemical pressure in EuFe2(As1−xPx)2
Phys. Rev. B 84, 140503(R) (2011).
• S. Zapf, B. Gorshunov, D. Wu, E. Zhukova, V. S. Nozdrin, S. Haindl, K. Iida, and
M. Dressel
Intra-gap absorption in superconducting Ba(Fe1−xCox)2As2 thin films studied by a
Fabry-Pérot resonant technique
J. Supercond. Nov. Magn. 21, 1557 (2013).
• S. Zapf, H. S. Jeevan, T. Ivek, F. Pfister, F. Klingert, S. Jiang, D. Wu, P. Gegenwart,
R. K. Kremer, and M. Dressel
EuFe2(As1−xPx)2: reentrant spin glass and superconductivity
Phys. Rev. Lett. 110, 237002 (2013).
• A. S. Prokhorov, E. S. Zhukova, A. A. Boris, I. E. Spektor, B. P. Gorshunov, V. S.
Nozdrin, E. A. Motovilova, L. S. Kadyrov, S. Zapf, S. Haindl, K. Iida, M. Dressel,
K. V. Chizh, M. S. Storozhevykh, L. V. Arapkina, V. A. Chapnin, O. V. Uvarov, V.
P. Kalinushkin, and V. A. Yuryev
Submillimeter quasioptical spectroscopy of multilayer conducting and superconduct-
ing systems
Radiophys. Quant. Electr. 56, 620 (2014).
• A. E. Karakozov, S. Zapf, B. Gorshunov, Y. G. Ponomarev, M. V. Magnitskaya,
E. Zhukova, A. S. Prokhorov, V. B. Anzin, and S. Haindl
Temperature dependence of the superfluid density as a probe for multiple gaps in
Ba(Fe0.9Co0.1)2As2: Manifestation of three weakly interacting condensates
Phys. Rev. B 90, 014506 (2014).
• A. E. Karakozov, B. P. Gorshunov, Y. G. Ponomarev, A. S. Prokhorov, M. V.
Magnitskaya, E. Zhukova, K. Iida, M. Dressel, S. Zapf, and S. Haindl
xii Publications
Studying the structure of the superconducting state in Co doped multiband BaFe2As2
compounds
JETP Letters 100, 328 (2014).
• S. Zapf, C. Stingl, K. W. Post, J. Maiwald, N. Bach, I. Pietsch, D. Neubauer, A.
Löhle, C. Clauss, S. Jiang, H. S. Jeevan, D. N. Basov, P. Gegenwart, and M. Dressel
Persistent detwinning of iron pnictides by small magnetic fields
Phys. Rev. Lett. 113, 227001 (2014).
• S. Zapf, D. Neubauer, A. Kadau, K. Post, H. S. Jeevan, P. Gegenwart, D. N. Basov,
and M. Dressel
Electronic scattering effects in Europium based iron pnictides
in preparation.
Additional scientific publications which are not presented in this thesis:
• B. Gorshunov, E. Zhukova, V. I. Torgashev, L. Motovilova, L. S. Kadyrov, F. Fis-
chgrabe, V. Moshnyaga, T. Zhang, R. Kremer, U. Pracht, S. Zapf, and M. Dressel
Boson peak in overdoped manganites La1−xCaxMnO3 (0.5 ≤ x ≤ 1)
Phys. Rev. B 87, 245124 (2013).
• B. P. Gorshunov, E. S. Zhukova, V. I. Torgashev, L. S. Kadyrov, E. A. Motovilova,
F. Fischgrabe, V. Moshnyaga, T. Zhang, R. Kremer, U. Pracht, S. Zapf, and M.
Dressel
Boson peak in manganites
J. Phys.: Conf. Ser. 486, 012001 (2014).
• S. Haas, E. Heintze, S. Zapf, B. Gorshunov, M. Dressel, and L. Bogani
Direct observation of the discrete energy spectrum of two lanthanide-based single-
chain magnets by far-infrared spectroscopy
Phys. Rev. B 89, 174409 (2014).
• L. S. Kadyrov, B. P. Gorshunov, E. S. Zhukova, V. I. Torgashev, A. S. Prokhorov,
E. A. Motovilova, F. Fischgrabe, V. T. Moshnyaga, T. Zhang, R. K. Kremer, U.
Pracht, S. Zapf, J. Pokorný, G. Untereiner, S. Kamba, and M. Dressel
Terahertz-infrared electrodynamics of overdoped manganites La1−xCaxMnO3
Phase Transitions 87, 1050 (2014).
Contents
1 Introduction 1
2 Magnetism 5
2.1 Basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Magnetic interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Types of magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Superconductivity 17
3.1 BCS theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Unconventional high-temperature superconductivity . . . . . . . . . . . . . 18
3.2.1 Cuprates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.2 Iron-based superconductors . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.3 Magnetic fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Superconductivity and Magnetism . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Type I and II superconductors . . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Magnetization of a superconductor . . . . . . . . . . . . . . . . . . . 28
3.3.3 Upper critical field(s) . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.4 Exotic phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Electrodynamic properties 33
4.1 Basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Broken symmetry states in metals . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.1 General quantum mechanical description . . . . . . . . . . . . . . . . 39
4.3.2 Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Iron-based superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Spectral features of the normal state . . . . . . . . . . . . . . . . . . 46
4.4.2 Analysis methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4.3 Antiferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4.4 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4.5 Unconventional normal state properties . . . . . . . . . . . . . . . . 53
5 Materials and methods 59
5.1 FTIR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 SQUID magnetometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3 Investigated samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
xiv Contents
6 Eu based iron pnictides 67
6.1 EuFe2As2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.1 Pressurized systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.2 Electron doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2.3 Eu dilution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.3 Electronic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.3.1 Normal state properties . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.3.2 Superconducting properties . . . . . . . . . . . . . . . . . . . . . . . 91
7 Magnetization studies on EuFe2(As1−xPx)2 95
7.1 Canted A-type antiferromagnetism . . . . . . . . . . . . . . . . . . . . . . . 95
7.2 Re-entrant spin glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.3 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8 Optical properties of EuFe2As2 117
8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
8.2 Multi-component analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9 Magnetic detwinning of EuFe2As2 131
9.1 Magneto-optical measurements . . . . . . . . . . . . . . . . . . . . . . . . . 132
9.2 Magnetization measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 139
9.3 Detwinning mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
9.4 Other techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
9.5 Detwinning fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9.6 Further infrared studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9.7 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
10 Summary and outlook 153
A THz investigations on Ba 122 thin films 157
A.1 Fabry-Pérot resonant technique . . . . . . . . . . . . . . . . . . . . . . . . . 158
A.2 Superfluid density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
A.3 Irradiation studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
B Acknowledgements 167
Bibliography 171
1
INTRODUCTION
The discovery of high temperature superconductivity in cuprates as well as iron-based
pnictides and chalcogenides unified two conventionally antagonistic fields of solid state
physics: magnetism and superconductivity. While magnetic interactions were fascinat-
ing already the ancient Greeks, superconductivity is a relatively “young” phenomenon,
discovered only in 1911 [2, 14].
Conventional superconductors exhibit two characteristic properties below a critical tem-
perature Tc: zero-resistivity and the expulsion of any external magnetic field. Both charac-
teristics have a huge potential for applications, such as non-dissipative power lines, energy
storages and levitating transport vehicles. Accordingly, enormous efforts were made to un-
derstand the microscopic origin of superconductivity. Nevertheless, it took almost 50 years
until Bardeen, Cooper and Schrieffer solved this puzzle by introducing a coherent ground
state formed out of electron pairs with opposite spin and momentum [15]. As internal or
external magnetic fields directly act on those properties, it is evident that magnetism and
superconductivity are traditionally competing phenomena.
One of the main drawbacks for applications is that the “glue” which holds those electron
pairs together consists conventionally of electron-phonon interactions [16, 17], which re-
quire very low temperatures to manifest [18]. Therefore, the discovery of high temperature
superconductivity (up to 164K [19]) in cuprates [20] and iron-based superconductors [4]
shook the scientific world and attracted tremendous interest even in the general public.
2 1 Introduction
Interestingly, the phase diagram of both material classes contains a magnetically ordered
phase that can be suppressed upon doping, chemical substitution or mechanical pressure,
until superconductivity emerges [3]. While the parent compounds of cuprates are antifer-
romagnetic Mott insulators, those of iron pnictides are metals that exhibit a spin density
wave phase. A similar situation can be found in a variety of other superconductors with
unconventional properties, such as heavy fermion or organic materials [1]. Therefore, the
idea developed that magnetic fluctuations might be the “pairing glue” of unconventional
superconductors.
It turned out, however, that a uniform description of high-temperature superconduc-
tors is much more complicated than expected. One reason is that a close inspection of
their phase diagrams reveals a number of exotic phases that appear in the vicinity of the
superconducting dome; it is not clear whether these additional phases support or com-
pete with superconductivity [21]. One example that attracted recently a lot of attention
is the nematic phase, which is the breaking of the rotational C4 symmetry driven by
electronic interactions [6]. This means that additionally to a tetragonal-to-orthorhombic
structural transition, an electronic in-plane anisotropy sets in, whose magnitude is much
larger than one would expect from the lattice distortion. Unfortunately, the experimental
investigation of this exotic phase is challenging, as the induced orthorhombic distortion is
so small that crystals usually appear twinned, meaning that domains mask the intrinsic
anisotropy. While in cuprates, mechanical clamps and magnetic fields were found to detwin
single crystals [22, 23], in the case of iron pnictides, the effect of laboratory magnetic fields
on the twin domain distribution is typically rather weak [24] and thus, only mechanical
clamps are commonly used [6]. However, this introduces an explicit symmetry breaking
by uniaxial pressure, meaning that one disturbs the anisotropy which one actually wants
to measure [25].
EuFe2As2 is a peculiar parent compound of the iron pnictides, since, in addition to
the spin density wave in the FeAs layers (∼ 190K), it exhibits long-range magnetic or-
der of the Eu2+ local moments at low temperatures (∼ 19K) [26–28]. Nevertheless, bulk
superconductivity up to ∼ 30K can be induced by mechanical pressure [29], isovalent
substitution [30, 31] and doping [32–34]. Furthermore, neutron studies revealed that mag-
netic fields in the range of 1T are able to detwin EuFe2As2 [7], allowing the study of
the electronic in-plane anisotropy at typical laboratory-scale fields. Thus, Eu based iron
pnictides offer the extraordinary possibility to investigate the interplay of unconventional
electronic properties, superconductivity, itinerant and local magnetism. Therefore, sys-
tematic (magneto-)optical and magnetization studies of EuFe2(As1−xPx)2 single crystals
were performed in the framework of this thesis.
3The following text is organized as follows: first, the basic concepts of magnetic and
superconducting materials are summarized (see chapters 2 and 3), focusing on high-
temperature superconductivity and the interplay of magnetism and superconductivity.
Subsequently, the electrodynamic properties of metals, broken symmetry phases, and in
particular iron pnictides are reviewed (see chapter 4), which is followed by a brief sum-
mary of the investigated materials and chosen methods (see chapter 5). The experimental
part of this thesis is introduced in chapter 6 with a review of Eu based iron pnictides.
This paves the way for the magnetic phase diagram of EuFe2(As1−xPx)2 that is gained by
our magnetization studies presented in chapter 7; from the comparison with literature, we
discuss further implications for other Eu based materials.
Despite the peculiar local magnetic order, EuFe2As2 displays typical electrodynamic
properties of correlated materials. Therefore, we use it in chapter 8 as a model system
to compare various fitting approaches that are commonly applied to iron pnictides. Fi-
nally, magneto-optical measurements on EuFe2As2 are presented that reveal a much more
complicated magnetic detwinning mechanism than expected (see chapter 9), uncovering
a unique possibility to study the intrinsic in-plane anisotropy of iron pnictides without
the application of any symmetry-breaking external force. All those findings are concluded
in chapter 10, evidencing a remarkable interplay of magnetic, electronic and structural
effects in Eu based iron pnictides.

2
MAGNETISM
Magnetism in condensed matter contains a wide variety of phenomena: the response of a
solid on an external magnetic field depends delicately on whether its magnetic moments
are interacting or basically isolated from each other. In this chapter, a sound basis should
be established to understand the complex magnetic order(s) in Eu based iron pnictides.
Therefore, important magnetic quantities are introduced, followed by a brief introduction
of magnetic interactions in solids. Finally, different types of magnetism are categorized
and phenomenologically described. If not declared explicitly, explanations follow Ref. [14].
2.1 Basic definitions
In free space, a magnetic field with strength H leads to a magnetic flux density B of:
B = µ0H (2.1)
with the permeability of free space µ0.
6 2 Magnetism
However, if H acts on a magnetic solid, one has to account also for the magnetization
M of this solid and equation 2.1 transfers into1:
B = µ0(H + M). (2.2)
The magnetic susceptibility χ describes, how much a material gets magnetized by a
magnetic field and is generally defined (along a certain direction) as:
χ = dM
dH
. (2.3)
For a so-called “linear material”, equation 2.2 can be rewritten as:
B = µ0(1 + χ)H = µ0µrH (2.4)
with the relative permeability of the material µr = 1 + χ.
When analysing experimental data, one further has to take into account that in magnetic
solids, the internal magnetic field strength Hint is reduced with respect to the external
one, Hext:
Hint = Hext −NM (2.5)
with the demagnetization factor N , which depends on the geometry of the sample and
varies 0 ≤ N ≤ 1.
An intuitive picture for this field reduction is the following [35]: in a magnetized sam-
ple, the magnetic moments are preferentially aligned along one direction. Imagining these
magnetic moments as miniature magnets with north and south poles (see Fig. 2.1a), neigh-
bouring poles will cancel each other out; only poles at the surface will be left (see Fig. 2.1b).
The latter will cause an internal magnetic field, which is opposed to the magnetization
and therefore called “demagnetization field”. Its strength Hd will be very sensitive to the
shape of the material. For a very thin sample and an in-plane magnetic field, there is basi-
cally no place for the formation of these surface poles, causing negligible demagnetization
effects (N → 0). For the out-of-plane direction, however, the situation is vice versa and
the demagnetization factor approaches unity.
Thus, the experimentally determined susceptibility of a linear material is actually:
χexp =
M
Hext
= M
Hint +NM
= χintrinsic1 +Nχintrinsic
(2.6)
1 With a relative permeability of µr ≈ 1.
2.2 Magnetic interactions 7
Figure 2.1: Schematic drawing to explain the demagnetization field (adapted from Ref. [35]).
(a) In a magnetized sample, magnetic moments depicted as miniature magnets with north (N)
and south (S) poles are preferentially aligned. (b) As neighbouring poles will cancel each
other out, only poles at the surface will be left. These cause an internal magnetic field
(“demagnetization field” with strength Hd) opposed to the magnetization M.
with the intrinsic susceptibility:
χintrinsic =
M
Hint
(2.7)
As usually χintrinsic  1, demagnetization effects are often negligible. However, sample
shape effects might determine the measured susceptibility in ferromagnets (see section 2.3),
causing χexp → 1/N .
2.2 Magnetic interactions
In order to describe magnetic long range order, one has to understand the underlying
interactions between the magnetic moments. Usually, magnetic dipolar interactions are
negligible, and the dominant mechanism can be described by exchange interactions via
the Heisenberg Hamiltonian:
H = −2
∑
i>j
JijSiSj (2.8)
with the exchange constant Jij between the ith and jth spin, whose sign determines the
magnetic ground state.
If the overlap between neighbouring magnetic atoms is high enough, direct exchange
interaction is possible. However, this is often not the case, for instance for the 4f -orbitals
of rare earth elements, and indirect exchange has to be considered. In metals, conduction
electrons can mediate the exchange between local moments via spin-polarization. This is
known as “RKKY-exchange”, named after the discoverers Ruderman, Kittel, Kasuya and
Yosida [36]. Depending on the details of the Fermi surface and the distance between the
magnetic moments, the RKKY-exchange constant oscillates between positive and negative
sign.
8 2 Magnetism
2.3 Types of magnetism
In this section, different types of magnetism are phenomenologically described. Starting
with the behaviour of non-interacting moments in a magnetic field, diamagnetism and
paramagnetism are introduced. In contrary, ferro-, antiferro-, and helimagnetic materials
show long-range magnetic order, where the involved magnetic moments act cooperatively.
Finally, also glassy short-range dynamics are discussed.
Diamagnetism
All materials exhibit diamagnetism: due to the orbital motion of the electrons, an external
magnetic field induces a magnetic moment opposed to the direction of the applied field.
This process is rather temperature-independent (see Fig. 2.2a). However, the induced
negative susceptibility (see Fig. 2.2b) is usually much smaller than other magnetic contri-
butions. One exception are superconductors which are “perfect diamagnets”, as will be
discussed in more detail in chapter 3.3.1.
Figure 2.2: Typical (a) temperature- and (b) field-dependent magnetization of a diamagnetic
material. The susceptibility is temperature-independent and negative.
Paramagnetism
The key ingredient for paramagnetism are unpaired, non-interacting electrons: while their
magnetic moments do not have any preferred orientation in zero field, they can be aligned
by an external magnetic field. The degree of alignment depends on the strength of the
external field as well as on the temperature, as thermal fluctuations counteract the field-
enforced order.
2.3 Types of magnetism 9
Figure 2.3: Typical (a) temperature- and (b) field-dependent magnetization of a paramag-
netic material. (a) The temperature-dependent magnetization can be described by the Curie
law χ ∝ 1/T . (b) The magnetization follows with increasing field a Brillouin function, which
is almost linear at low fields (as can be seen by the red line, a guide to the eye).
From a quantum mechanical description of non-interacting electrons with total angular
momentum J = L + S (L: orbital momentum, S: spin momentum), one can derive the
magnetic field dependence of a paramagnet as (see Fig. 2.3b):
M = MsBJ
(
gJµBJB
kBT
)
(2.9)
with the saturation magnetization:
Ms = ngJµBJ, (2.10)
the Brillouin function:
BJ(x) =
2J + 1
2J coth
(2J + 1
2J x
)
− 12J coth
(
x
2J
)
, (2.11)
the Landé g-factor:
gJ =
3
2 +
S(S + 1)− L(L+ 1)
2J(J + 1) , (2.12)
the number of spins per unit volume n, the Bohr magneton µB, the Boltzmann constant
kB, and the temperature T .
In typical paramagnetic materials, except for very high fields and very low tempera-
tures, the magnetization shows a linear field dependence and the temperature-dependent
susceptibility follows the Curie law (see Fig. 2.3a):
χ = nµ0µ
2
eff
3kB
1
T
(2.13)
10 2 Magnetism
with the effective magnetic moment:
µeff = gJµB
√
J(J + 1). (2.14)
Ferromagnetism
Due to exchange interactions, a ferromagnet exhibits below the Curie temperature TC -
even in the absence of any external field - a spontaneous magnetization, as all magnetic
moments align along one direction. The corresponding Hamiltonian (including an applied
magnetic field) can be written as:
H = −2
∑
i>j
JijSiSj + gµB
∑
j
SjB (2.15)
with the first term expressing the Heisenberg exchange energy with Jij > 0 (see equa-
tion 2.8) and the second term giving the Zeeman energy in an external field (g: the
electron’s g-factor). This Hamiltonian can be solved using a mean field approach.
It follows that at low temperatures, the magnetic order is even in the absence of any
external field self-sustaining, meaning that the alignment of moments causes an internal
(molecular) field, that in turn favours the parallel alignment of the spins. This results in
a spontaneous magnetization. At elevated temperatures, thermal fluctuations counteract
this process until any order is destroyed at the Curie temperature. The transition itself is
a second-order phase transition, as the derivative of the spontaneous magnetization (and
thus the second derivative of the system’s free energy) shows a discontinuous jump at TC.
However, the transition smears out for a finite external magnetic field and thus, no more
“true” phase transition takes place.
In magnetization measurements, three characteristic observations are commonly used
to identify ferromagnetic order (see Fig. 2.4):
• For temperatures T > TC, the susceptibility follows at small external fields the
Curie-Weiss law:
χ ∝ 1
T − TC . (2.16)
• At T < TC, the field-dependent magnetization resembles that of a paramagnet,
however, the saturation fields are much lower.
• Most remarkably, irreversibility effects appear in the temperature- and field-dependent
magnetization at temperatures T < TC. One has to distinguish whether the crystal
was cooled down through TC with or without external magnetic field.
2.3 Types of magnetism 11
Figure 2.4: Typical (a) temperature- and (b) field-dependent magnetization of a ferro-
magnetic material. (a) For T > TC, the temperature-dependent magnetization follows the
Curie-Weiss law χ ∝ 1/(T − TC). For T < TC, the magnetization increases with increasing
temperature if the crystal was cooled down in zero field (ZFC), and decreases if the crystal
was cooled down in an external field (FC). (b) The field-dependent magnetization shows at
temperatures T < TC a hysteresis, defined by the virgin curve, saturation magnetization Ms,
remanent magnetization Mr, and coercive field Hc.
These irreversibility effects are also known as “magnetic hysteresis”. They result, as
ferromagnets typically consist of many domains, which are energetically favourable as they
reduce the demagnetization fields introduced in section 2.1. Whereas in each domain, the
magnetic moments are uniformly aligned, different domains (separated by domain walls)
are randomly oriented with respect to each other. Thus, the total net magnetization in
the absence of any external field is zero.
An external magnetic field is in principle able to move domain walls. However, they
can be pinned due to strains or impurities. Thus, only if the magnetic field overcomes the
associated pinning energy, the domain wall can move further. At higher fields, it is also
possible that all spins of one domain rotate at once. In any case, one has to consider also the
magneto-crystalline anisotropy, meaning that crystals posses crystallographic directions
that are preferred (“easy axis”) or unpreferred (“hard axis”) in a magnetization process.
Thus, with increasing field, one single domain will be created where the magnetic moments
point along the easy axis closest to the direction of the external field. Only when the
magnetic field energy gets high enough, the moments will rotate away from the easy axis
to the direction of the external field. As in all those dynamics certain energy thresholds
need to be overcome, a magnetic hysteresis results.
The hysteresis in field-dependent magnetization measurements is defined by (see Fig. 2.4b):
• the initial magnetization curve after the crystal was cooled down in zero magnetic
field to temperatures T < TC, called “virgin curve”
• the saturation magnetization Ms
12 2 Magnetism
• the remanent magnetization Mr which stays after the sample was once fully magne-
tized and the field was switched off
• the coercive field Hc which needs to be applied to reduce the magnetization from
the remanent value to zero.
For temperature-dependent magnetization measurements (in a small magnetic field),
one has to distinguish below TC (see Fig. 2.4b):
• zero-field cooled (ZFC) curve: the magnetization increases (from zero) with increas-
ing temperature, as thermal fluctuations allow more and more domains to be oriented
along the field
• field-cooled (FC) curve: as the symmetry of the system was broken externally while
cooling through TC, a preferred spin direction was initialized; thermal fluctuations
are weakening the order and lead to a decrease of the magnetization with increasing
temperature.
Antiferromagnetism
For an exchange constant Jij < 0, neighbouring spins tend to align antiparallel. This leads
below the Néel temperature TN to antiferromagnetic order. For a theoretical description
following equation 2.15, an antiferromagnet can be considered to consist of two opposite,
interpenetrating ferromagnetic sublattices.
Antiferromagnetic behaviour can be usually identified by (see Fig. 2.5):
• For temperatures T > TN, the susceptibility follows at small external fields the
Curie-Weiss law
χ ∝ 1
T + TN
. (2.17)
• At T < TN and relatively small fields, the temperature-dependent magnetization is
strongly direction-dependent.
• At T < TN, the field-dependent magnetization along the spin direction shows a step
before achieving saturation.
• The temperature- and field-dependent magnetization does not display hysteretic
behaviour.
In order to understand the direction-dependence of the magnetization below the Néel
temperature, one should first consider the magnetization at small fields applied at 0K
2.3 Types of magnetism 13
Figure 2.5: Typical (a) temperature- and (b) field-dependent magnetization of an antifer-
romagnetic material. (a) For T > TN, the temperature-dependent magnetization follows the
Curie-Weiss law χ ∝ 1/(T + TN). For T < TN, the magnetization increases for the direction
parallel to the external field, and stays constant for the perpendicular direction. (b) The field-
dependent magnetization along the spin direction rises (at 0K) abruptly at the spin-flop field
HSF and increases further until saturation is reached at HS. For finite temperatures below
TN, this curve smears out due to thermal fluctuations. Brown arrows display schematically
the field-dependent spin alignment.
parallel (M‖) and perpendicular (M⊥) to the spin direction (see Fig. 2.5a): while for the
former case, small magnetic fields will not affect the antiparallel aligned spins and therefore
the net magnetization is zero, in the latter case, the spins will be tilted slightly out of
the balance position, leading to non-zero magnetization. With increasing temperature,
the thermal fluctuations counteract the exchange interactions. This does not notably
influence the effect perpendicular to the spin direction. Therefore, M⊥ is almost flat for
temperatures T < TN. However, for the field parallel to the spin direction, the field can
act on the thermally excited spins and thus M‖ increases with increasing temperature up
to TN.
In the case of high magnetic fields [37], it is clear that at one point the external field
must dominate over the internal exchange interaction, leading to a parallel alignment of
spins along the field direction. If the field acts perpendicular to the spin direction, this
will be a smooth process. However, the situation gets more complicated if the external
field is aligned parallel to the spin direction (see Fig. 2.5b). In this case, Zeeman energy,
exchange energy and magneto-crystalline anisotropy compete with each other, leading (at
T = 0K) to the total energy:
E = −MB(cosθ + cosφ) + JM2cos(θ + φ)− 12∆(cos
2θ + cos2φ) (2.18)
14 2 Magnetism
with the exchange coupling constant J and the magneto-crystalline anisotropy ∆. Thus,
the ground state energy of the antiferromagnetic configuration is independent of the ex-
ternal field:
E0 = −JM2 −∆. (2.19)
For higher fields, a “spin-flop” transition takes place: the spins rotate abruptly to a config-
uration where the angle between spins and external field is < 90◦ and the same (counted
clockwise and counter-clockwise) for both sublattices (see Fig. 2.5b). The energy of the
spin-flop phase is therefore:
E = −2MBcosθ + JM2cos2θ −∆cos2θ. (2.20)
Minimizing this energy with respect to θ and re-inserting the result in equation 2.20, yields
the minimum energy of the spin-flop phase:
E0,SF = −JM2 − M
2B2
2JM2 −∆. (2.21)
Comparing equations 2.19 and 2.21, the spin-flop takes place at:
BSF =
√
2J∆− (∆/M)2. (2.22)
The corresponding field-dependent magnetization is depicted in Fig. 2.5b. The magneti-
zation rises abruptly at the spin-flop field and increases afterwards steadily, as the spins
align gradually along the external field, until they are fully aligned.
One should also note that if the magneto-crystalline anisotropy is very strong, the spins
can directly rotate from the antiparallel to the parallel alignment (with respect to the
external field). This process is called “spin-flip”.
Helimagnetism
There exists a wide variety of other magnetic phases despite anti- und ferromagnetism,
often related to one of them or even both. One possible ground state of particular interest
for layered materials (such as several rare earth systems) is helimagnetism. In this case,
the spins are ordered ferromagnetically within one layer, however the magnetic moments of
neighbouring layers differ by a finite angle that is neither equal to zero (which would cor-
respond to ferromagnetism) nor equal to pi (which would correspond to antiferromagnetic
interlayer coupling). Thus, the spins will rotate along a spiral, which is not necessarily
commensurate with the lattice.
2.3 Types of magnetism 15
Spin glass
In materials where frustration and disorder play an important role, magnetic long-range
order is prohibited [38]. In particular the RKKY-interaction, which oscillates between
antiferromagnetic and ferromagnetic coupling, often leads to competing interactions. In
these materials, one can distinguish in principle four temperature ranges: at very high
temperatures, the spins are independent due to strong thermal fluctuations. When low-
ering the temperature, first local and then also long-range interactions will occur: the
system starts seeking its ground state. However, due to the competing interactions, it
gets stuck at the so-called “freezing temperature” Tf in a metastable state. As this “spin
glass” phase is only metastable, hysteretic and time-dependent behaviour can be observed.
There exist several types of spin glasses. Systems with dominant short range interactions
are sometimes called “mictomagnetic” or “cluster glass”, as the short range interactions
lead to magnetic clusters that freeze in at Tf. It is also possible that a magnetically ordered
state transforms at lower temperatures to a spin glass - although this is counterintuitive as
one would expect a more ordered state at lower temperatures. The low-temperature phase
resembles then a cluster glass, however, in order to make clear that this phase originates
from another state than paramagnetism, it is referred to as “re-entrant spin glass”. One
theoretical explanation for this behaviour is that only the transverse spin components
freeze at the glass transition [39].

3
SUPERCONDUCTIVITY
In the beginning of the 20th century, cryogenics was still in its early infancy. It was
not before 1908 that H. K. Onnes managed to liquify 4He, pushing the experimentally
accessible temperature range down to a few Kelvin. This opened a completely new world
in condensed matter research. Only three years later, he observed during his studies on Hg
at a critical temperature Tc ∼ 4.2K an abrupt resistivity drop to zero - superconductivity,
until then an unknown state of matter, was discovered.
More than twenty years later, W. Meissner and R. Ochsenfeld found out that a super-
conductor is not just an ideal conductor: it is also a perfect diamagnet, meaning that
magnetic fields can not penetrate into its bulk. Dubbed after its discoverers, this second
characteristic of a superconductor is known today as “Meissner Ochsenfeld effect”.
Although great progress was achieved in experiments and more and more superconduct-
ing compounds were found, a microscopic theoretical description was only developed in
1957 by J. Bardeen, L. N. Cooper and J. R. Schrieffer.
In the following chapter, a brief introduction in their “BCS theory” will pave the way to
distinguish between conventional and unconventional superconductivity. Particular focus
will be put on the discussion of high-temperature superconductors. Although magnetism
and superconductivity are usually antagonistic phenomena, magnetic fluctuations might
be the key to understand their extraordinary properties. This motivates some further
insights into the interplay of magnetism and superconductivity. If not given explicitly,
explanations follow Ref. [2] and [40] or references given at the beginning of a section.
18 3 Superconductivity
3.1 BCS theory
Early theoretical descriptions of superconductivity were based on macroscopic, phenomeno-
logical models. The success of those approaches can be still seen today, as hereby defined
characteristic quantities of the superconducting state such as the London penetration
depth and the Ginzburg-Landau coherence length are still widely used1.
In 1950, the observation of the so-called “isotope effect” introduced a relationship be-
tween the onset of superconductivity and the atomic mass of a superconducting com-
pound [41, 42], indicating that superconductivity arises from interactions between elec-
trons and lattice vibrations. A theoretical description of those interactions [16, 17] paved
the way for the microscopic BCS theory [15].
The fundamental idea behind BCS theory is that electrons of opposite spin and momen-
tum form pairs (so-called “Cooper pairs”), assuming an attractive potential due to weak
electron-phonon-coupling that exceeds the repulsive Coulomb interactions. Those Cooper
pairs condense in a coherent ground state, leading to a gap in the density of states. This
energy gap is the order parameter of the superconducting state; its squared absolute value
proportional to the Cooper pair density.
Originally, the effective attractive potential between electrons was assumed to be inde-
pendent of momentum, leading to an isotropic s-wave gap:
2∆0(T = 0) = 3.5kBTc (3.1)
with a temperature-dependence that can be well approximated by:
∆(T )
∆(0) = tanh
[
Tc
T
∆(T )
∆(0)
]
. (3.2)
The experimental verification of this energy gap, demonstrated by optical spectroscopy [43],
was one of the big successes of BCS theory.
3.2 Unconventional high-temperature superconductivity
Although BCS theory describes successfully a huge variety of superconductors, there exist
also some materials where it fails. Even in some elemental superconductors such as Pb and
1 The London penetration depth gives the distance where an (electro-) magnetic field inside a super-
conductor is screened to 1/e of its initial value; the Ginzburg-Landau coherence length describes the
length scale over which the superconducting order parameter varies due to a local distortion, such as a
vortex.
3.2 Unconventional high-temperature superconductivity 19
Hg, the observed behaviour slightly differs from BCS predictions. It turns out that the
latter compounds are still “conventional superconductors” with a strong electron-phonon
coupling and Eliashberg theory can achieve a proper description [44]. However, if the
coupling between electrons is not mediated via phonons, total spin or orbital momentum
are non-zero, superconductivity is inhomogeneous or magnetic interactions are observed,
the term “unconventional superconductivity” is used. Famous examples are heavy fermion
superconductors, ruthenates, cuprates, organic and iron-based superconductors [1].
One subclass of unconventional superconductors are high-temperature superconductors,
which have in common that (as their name already suggests) their critical temperature
exceeds any limit accessible by electron-phonon interactions [18, 45]. Up to now, only two
classes of high-temperature superconductors are known: the cuprates and the iron-based
superconductors, whose high critical temperatures were discovered in 1986 by G. Bednorz
and K. A. Müller [20] and in 2008 by the group of H. Hosono [4], respectively.
3.2.1 Cuprates
Cuprates are layered materials, where superconducting CuO2 planes alternate along the
crystallographic c-axis with spacer layers, resembling in total perovskite materials. Prob-
ably the most studied compounds are doped YBa2Cu3O7 (“YBCO”, [46]) and Bi2Sr2-
CaCu2O8 (“BSCCO”, [47]) which show maximum critical temperatures around ∼ 90K.
At present, the highest observed Tc is 164K for HgBa2Ca2Cu3O8 under pressure [19].
In the following, the generic phase diagram of cuprates is described (see Fig. 3.1), giving
a basis to elaborate similarities and differences to iron pnictides. Tuning through the phase
diagram results from electron or hole doping1; the spacer layers serve as charge reservoir.
Antiferromagnetic Mott insulator
The parent phase of cuprates is an antiferromagnetic Mott insulator that can be well
described by the Hubbard model: although the conduction band is half filled and thus
metallic behaviour would be expected, correlations (i.e. the Coulomb repulsion) between
electrons are strong enough to localize the electrons. With electron or hole doping, the
Mott phase gets suppressed.
d-wave superconductivity
While the Cooper pairs are conventional singlets, the superconducting order parameter
has unconventional dx2−y2-wave symmetry. This means that the gap changes sign along
1 The phase diagrams for electron and hole doping are slightly asymmetric: for electron doping, the Mott
phase is usually more robust and the superconducting dome narrower.
20 3 Superconductivity
Figure 3.1: Generic phase diagram of cuprates. The parent compounds are antiferromagnetic
Mott insulators (green). With doping, the magnetic long range order is suppressed and a
pseudogap phase (grey) appears, separating the Mott phase and the superconducting dome
(SC: blue). Above the superconducting dome, strange metal behaviour (red) is observed, with
a crossover to a Fermi liquid (yellow) in the overdoped range. This might indicate a quantum
critical point (QCP: red) buried by the superconducting dome.
the Fermi surface, leading to nodes in the order parameter at the diagonals of the Brillouin
zone, where the superconducting gap vanishes (see Fig. 3.2a,b). The maximum gap value
does not follow the BCS relation given in equation 3.1 and is typically much higher.
There is now broad consensus that the main pairing interactions take place between car-
riers within the CuO2 layers. As the coherence length is rather small, a three-dimensional
superconducting state appears due to Cooper pair tunneling along the c-axis. Thus,
cuprates display natural Josephson junctions.
Unconventional normal state properties
One of the main problems about a theoretical description of superconductivity in cuprates
is that the normal state from which superconductivity arises is still not understood: when
passing at high temperatures through the phase diagram, the Mott insulator gets replaced
by a “pseudogap” phase, which is followed by “strange metal” behaviour; conventional
Fermi liquid1 behaviour sets in only in the overdoped region.
In the pseudogap phase, a momentum-dependent gap appears [48]. While its absolute
value does not vary strongly with temperature, the gap opens for different momenta at
1 Landau’s Fermi liquid theory describes a system of interacting fermions by introducing long living
excitations. Those quasiparticles possess renormalized dynamical properties (such as an effective mass),
but can be described like a free electron gas. This results at sufficiently low temperature in a T 2- and
ω2-dependence of the scattering rate.
3.2 Unconventional high-temperature superconductivity 21
Figure 3.2: (a) Schematic Fermi surface of the cuprates. The grey shaded area marks the
occupied electron states. (b) Fermi surface superimposed with the dx2−y2 -wave symmetry of
the superconducting order parameter. Red and blue correspond to different signs of the order
parameter, which has nodes (white) along the diagonals of the Fermi surface. (c) Development
of the Fermi surface: the normal state Fermi surface (T > T ∗) is first reduced to Fermi arcs in
the pseudogap phase (Tc < T < T ∗), which develop until superconductivity sets in (T < Tc)
to nodes.
different temperatures. This leads to a reduction of the Fermi surface to arcs1, which
shrink further with decreasing temperature (see Fig. 3.2c). When superconductivity sets
in, almost the entire Fermi surface is already gapped: only the region at the nodes is still
occupied. Those nodes remain in the superconducting phase, consistent with the dx2−y2-
wave symmetry of the superconducting order parameter. Due to those (and many more)
similarities of the two gaps, the idea was developed whether the pseudogap phase is a
precursor of superconductivity, where non-coherent Cooper pairs form.
In contrast, recent results point more towards another explanation: the pseudogap seems
to be a separate phase. Indeed, ARPES and high-resolution STM measurements found a
small feature which they identified as a superconducting gap, with a smaller absolute value
than the pseudogap [52–54]. However, there is not yet consensus about the nature of the
pseudogap. To complicate this issue further, there are more and more additional phases
found by careful studies on cuprates such as (fluctuating) charge density waves [55–58]
and nematicity [59, 60]. Whether all those orders are competing with superconductivity,
1 Recent quantum oscillation measurements indicate that those arcs could be indeed small electron
pockets; charge order wave vectors that reconnect the remaining arcs might play a crucial role [49–51].
22 3 Superconductivity
a necessary key ingredient, or just appear due to an unknown “mother phase” needs to be
seen [21].
Another mystery in cuprates is the strange metal behaviour right above the supercon-
ducting dome. In this regime, the Mott-Ioffe-Regel limit is violated, meaning that the
mean free path of carriers is less than the interatomic distance [62, 63]. Thus, coherent
transport should not be possible and incoherent dynamics set in, as will be further dis-
cussed on the basis of optical measurements in chapter 4. Furthermore, the resistivity
displays over a wide temperature range linear behaviour, which might stem from spin
fluctuations or a quantum critical point1 [64].
3.2.2 Iron-based superconductors
Similar to cuprates, iron-based superconductors are layered materials [3, 5, 65]. Their
common ingredient are layers where Fe2+ is tetrahedrally surrounded by pnictogen or
chalcogen atoms. Thus, one differs between iron pnictides and iron chalcogenides. Further
classification results from the stoichiometric composition of the parent compounds.
According to this classification scheme, LaFeAsO1−xFx (which originally caused the
“iron age of superconductivity” [69]) belongs to the “1111”-family. Replacing La by other
rare earth elements increases Tc up to 56K in bulk materials; recent work on FeSe (“11”-
chalcogenide) monolayers indicated even higher accessible critical temperatures [67]. How-
ever, most research was done up to now on “122” iron pnictides due to the availability of
high quality single crystals, focusing on materials with BaFe2As2 as parent compound (see
Fig. 3.3a). Eu based iron pnictides also belong to this family; more detailed discussions
concerning their magnetic and electronic properties can be found in chapter 6. Here, the
focus is on the generic phase diagram of 122 iron pnictides (see Fig. 3.3b); tuning through
the phase diagram can be reached by electron or hole doping2, mechanical pressure, as
well as isovalent substitution.
Antiferromagnetism
Iron pnictides are multiband systems, where up to five Fe 3d-bands cross the Fermi energy.
This leads to a Fermi surface that consists usually of multiple quasi-two-dimensional hole
and electron pockets centered around the (0,0)-“Γ”- and (pi,0)/(0,pi)-“X”-points of the
1 A quantum critical point is a second order phase transition that takes place at absolute zero tempera-
ture. It leads to a divergence of several physical quantities.
2 In literature there is an ongoing debate, whether superconductivity is induced in iron pnictides and
chalcogenides due to doping or disorder [68]. However, this should not be in the focus of this thesis
and for simplicity, the expression “doping” is used.
3.2 Unconventional high-temperature superconductivity 23
Figure 3.3: Crystal structure (adapted from Ref. [8]) and generic phase diagram of 122 iron
pnictides. (a) Conducting Fe (beige) - pnictogen (green) planes are separated by spacer layers,
consisting of another element such as Eu, Ba, Sr or Ca (blue). In the antiferromagnetic phase,
the itinerant electrons of Fe order in a stripe-like configuration (brown arrows). (b) The an-
tiferromagnetic (AFM) phase (green) is found in the parent compounds. At slightly higher
temperatures, a nematic phase transition (grey) takes place, accompanied by a tetragonal-to-
orthorhombic structural transition. With doping, mechanical pressure or isovalent substitution
(“x”), those orders are suppressed and superconductivity sets in (SC: blue). Above the su-
perconducting dome, strange metal behaviour (red) is observed, with a crossover to a Fermi
liquid (yellow) in the overdoped range. This might indicate a quantum critical point (QCP:
red) buried by the superconducting dome.
unfolded1 Brillouin zone (see Fig. 3.4a). In general, the electronic system is more three-
dimensional than in the case of cuprates, visible in Fermi sheets that slightly warp along
the kz-direction and a less pronounced electronic anisotropy.
The ground state of the parent phase is an antiferromagnetic metal with a magnetic
moment per Fe atom of typically < 1µB. This value is much smaller than the possible
6µB for Fe2+. Indeed, it was found that the antiferromagnetic ordering vector is usu-
ally (pi,0) or (0,pi), matching the nesting vector between electron and hole pockets (see
Fig. 3.4a); the corresponding stripe-like spin order which is ferromagnetic in one direction
and antiferromagnetic in the others is depicted in Fig 3.3a. This points (at least for the
122 iron pnictides) towards a rather itinerant magnetism with a spin density wave ground
state. However, one should note that in some compounds, there are also indications for a
more local character of magnetism; one example are 11 chalcogenides, where the magnetic
order vector differs from the nesting vector. Therefore, magnetism in iron-based super-
1 The folded Brillouin zone is that of the actual lattice, considering Fe and pnictogen atoms; the unfolded
Brillouin zone arises when only the Fe atoms are considered. While the Γ -point is the same in both,
the X-point in the unfolded scheme corresponds to the M -point in the folded one.
24 3 Superconductivity
Figure 3.4: Schematic Fermi surface as well as superconducting gap symmetry and structure
of iron pnictides (adapted from Ref. [65, 71]). (a) The Fermi surface usually consists of
multiple hole (dark blue) and electron pockets (dark green) centered around the (0,0)-“Γ”-
and (pi,0)/(0,pi)-“X”-points of the unfolded Brillouin zone. Those pockets are nested by the
antiferromagnetic ordering vectors (dark red). (b) A superconducting order parameter with
s±-symmetry is isotropic and changes sign between electron and hole pockets. (c) For the
extended s±-symmetry, the order parameter might contain accidental nodes which can be
lifted by scattering [72].
conductors has probably a dual character with signatures of both, local and itinerant
magnetism.
Superconductivity
While it is consensus that the Cooper pairs are singlets, the symmetry of the supercon-
ducting order parameter of iron pnictides is still under debate. Mostly favoured is the
so-called “s±-symmetry”, where s-wave gaps at the different Fermi surface sheets have op-
posite sign (see Fig. 3.4b, [70, 71]). In the “extended s±-wave” scenario, those gaps may
have accidental nodes (see Fig. 3.4c) which are not given by symmetry and can be therefore
lifted by scattering [72]. This possibly explains the variety of contradictory measurements
concerning nodes in the order parameter, as their occurrence would be strongly affected
by scattering and thus the sample quality. Any analysis about gap sizes and symmetries
are further hampered by the multiband character of the iron pnictides, which causes the
opening of several superconducting gaps. Further details on this topic and a possible
smoking gun experiment to prove the s±-symmetry with the help of optical spectroscopy
are given in the attachment.
Despite the gap symmetry, another interesting difference between cuprates and iron-
based superconductors concerns the separation of superconductivity and long-range mag-
netic order in the phase diagram. In iron pnictides, the maximum Tc appears usually close
to the (extrapolated) end point of the antiferromagnetic phase transition. In some com-
pounds, even a coexistence region of spin density wave and superconducting order emerges
3.2 Unconventional high-temperature superconductivity 25
(in contrast to cuprates, where the Mott insulating phase and the superconducting dome
are separated by the pseudogap phase). The observation of competing order parameters
suggests that this coexistence appears on the microscopic scale [73, 74].
Unconventional normal state properties
Although the pseudogap phase governs the phase diagram of cuprates, it is either absent
or at least much less pronounced in the case of iron pnictides (see chapter 4.4.5). Never-
theless, the normal state above the superconducting dome is anything but conventional.
There is growing experimental and theoretical evidence for a “nematic phase” transition
that precedes or accompanies the antiferromagnetic ordering [6, 25, 75–80, 240]. The term
“nematic” is borrowed from liquid crystal theory and describes the breaking of the C4 rota-
tional symmetry. Interestingly, this does not only mean that a tetragonal-to-orthorhombic
phase transition takes place: an electronic in-plane anisotropy sets in, whose magnitude is
much larger than the orthorhombic lattice distortion. Furthermore, the b-axis resistivity
is higher than that along the a-direction, although one would expect the opposite1. In
other words, the itinerant electrons do not just follow the lattice anisotropy. Therefore,
the transition is generally believed to be driven electronically either by spin or orbital
fluctuations. Unfortunately, no matter which of those interactions is responsible, at the
transition one will always observe an anisotropy of all - structural, orbital and spin de-
grees of freedom - as they are strongly entangled. Thus, it is extremely difficult to decide
what is actually driving the nematic order. However, exactly this question is of particular
interest: the nematic phase in the iron pnictides phase diagram extends far above the
superconducting dome and appears also in cuprates. Therefore, it might be the essential
key ingredient for high-temperature superconductivity.
The experimental investigation of nematicity is challenging. In order to probe the
fluctuations above the transition, piezo elements can be used that induce some small
amount of strain on the sample [25, 81]. Those experiments uncovered a huge nematic
susceptibility that diverges at the transition temperature, independent of crystal type or
quality [81].
Below the nematic transition, as the orthorhombic distortion is only small, the forma-
tion of twin domains usually obscures the intrinsic anisotropy. In cuprates, mechanical
clamps and magnetic fields were found to detwin single crystals [22, 23]. In the case
of iron pnictides, the effect of typical laboratory magnetic fields on the Fe spins is rather
weak: 14T detwin BaFe2As2 only by ∼ 10% [24]. Thus, mechanical clamps are commonly
1 A stronger orbital overlap along the shorter b-axis as well as the ferromagnetic spin alignment should
both lead to a higher conductivity with respect to the a-axis.
26 3 Superconductivity
used [6]. However, this introduces an explicit symmetry breaking by uniaxial pressure,
which must be considered carefully [25]: similar to ferromagnets, where the magnetization
depends on the external magnetic field, the intrinsic nematic response can only be mea-
sured in the limit of zero external symmetry-breaking force. Indeed, mechanical clamps
were found to significantly enhance the transition temperatures in iron pnictides and even
induce additional anisotropy above [78].
In the framework of this thesis, it was uncovered that small magnetic fields are enough to
persistently detwin EuFe2As2. This provides the unique possibility to study the low tem-
perature electronic in-plane anisotropy of iron pnictides without applying any symmetry-
breaking external force. The corresponding results are discussed in chapter 9 and Ref. [13].
Despite the nematic phase, another similarity can be found between cuprates and iron
pnictides when looking at their normal state behaviour: a strange metal phase extends far
above the superconducting dome, accompanied by linear resistivity. In BaFe2(As1−xPx)2
- which is usually considered as a very clean material as P substitution does not induce
appreciable scattering - a diverging effective mass around the optimum substitution level
was verified [83, 84]. Therefore, similar to cuprates the existence of a quantum critical
point and its relation to unconventional superconductivity is discussed.
3.2.3 Magnetic fluctuations
Due to the proximity of high-temperature superconductivity to a magnetic phase in both,
cuprates and iron-based superconductors, it is intriguing to consider magnetic spin fluc-
tuations as a possible pairing glue for Cooper pairs. However, those interactions lead to
a repulsive pairing potential, opposite to the basic assumptions of BCS theory (see sec-
tion 3.1). Further insight how such a potential can still support superconductivity can be
found when looking at the BCS self-consistency gap equation for singlet pairing [85]:
∆(k) = −
∑
k′
V eff(k− k′)
2
√
∆2(k) + 2(k)
∆(k′) (3.3)
with the momenta k and k′, the energy gap∆, the effective two-particle pairing interaction
V eff, as well as the dispersion of the electrons in the normal state (k). Obviously, an
attractive pairing potential V eff < 0 (as assumed by Bardeen, Cooper and Schrieffer)
might support superconductivity, as left and right sides of equation 3.3 can obtain the same
sign. For V eff > 0, equation 3.3 can be only fulfilled for a strong momentum-dependent
potential that leads to gaps with opposite sign for the momenta k and k′. The simplest
solution for this problem is a d-wave gap, as indeed observed in cuprates. However, also
the s±-symmetry favoured in iron-based superconductors fulfils those conditions.
3.3 Superconductivity and Magnetism 27
In order to get experimental information about the importance of spin fluctuations,
inelastic neutron scattering has turned out to be a very powerful tool. It was found that
a resonance peak in the superconducting spin excitation spectrum is a unique feature of
unconventional superconductors [5, 65, 88]. This magnetic resonance appears at the same
wave vector as the static magnetism in the parent compounds: at temperatures T < Tc,
the antiferromagnetic neutron scattering signal gets depleted at lowest energies and a peak
appears at energies smaller than 2∆. Theory predicts such a peak if the superconducting
energy gap takes opposite values on different parts of the Fermi surface. Thus, it indicates
unusual repulsive electron pairing. In iron pnictides, such a resonance was demonstrated
for the first time for Ba0.6K0.4Fe2As2 [89].
One can further compare the spectrum of spin excitations with the Eliashberg spectral
function α2F (ω), where α denotes the electron-boson coupling strength and F (ω) the
frequency-dependent bosonic density of states [86, 87]. While the former can be measured
with inelastic neutron scattering, the latter can be extracted from tunneling or infrared
spectroscopy data. If spin fluctuations are responsible for Cooper pair formation, α2F (ω)
should be proportional to the imaginary part of the spin susceptibility. Indeed, both - iron
pnictides and cuprates superconductors - show that the resonance mode coincides with
features in α2F (ω) [5], further supporting the idea of magnetic fluctuations as pairing
glue.
3.3 Superconductivity and Magnetism
As the electrons forming a Cooper pair contain within the BCS theory opposite spin
and momentum, it is very clear that magnetism and superconductivity are conventionally
antagonistic phenomena. Their interplay is in the focus of the following sections.
3.3.1 Type I and II superconductors
A “type I” superconductor is a perfect diamagnet, meaning that an external magnetic
field gets shielded completely by supercurrents in a thin surface layer. Importantly, this
holds no matter whether the magnetic field is switched on below or above Tc, if the field
does not exceed a critical value Bc2 where superconductivity breaks down.
However, the detailed shielding mechanism depends on the cooling procedure. In the
case of zero-field cooling, shielding currents are induced that counteract the application of
the magnetic field; those currents do not decay, because the resistance is zero. As this is
nothing else than Lenz’s law, the same behaviour would also occur in an ideal conductor.
The difference between a superconductor and an ideal conductor lies in the field-cooled
behaviour: at temperatures T > Tc, magnetic flux can penetrate inside both specimen; for
28 3 Superconductivity
T < Tc, however, this flux is expelled only in the case of a superconductor. This additional
effect that can not be explained by Lenz’s law was discovered by Meissner and Ochsenfeld.
Therefore, the corresponding phase is called the “Meissner phase”.
High-temperature superconductors belong to another class of superconductors, the “type
II” superconductors, where an intermediate “Shubnikov phase” appears: above the critical
field Bc1, the external field can penetrate inside the material within “Abrikosov vortices”.
The Cooper pair density is zero at the core of such a vortex; it increases away from the
core within the Ginzburg-Landau coherence length. Correspondingly, the magnetic field
has a maximum at the core of the vortex; it decreases away from the core within the
London penetration depth. The ground state of the system is a triangular vortex lattice,
where each vortex contains a single flux quantum; higher magnetic fields lead to a higher
density of vortices, until superconductivity breaks down at Bc2.
3.3.2 Magnetization of a superconductor
Magnetization measurements are often used to characterize a superconductor, as a dia-
magnetic signal indicates bulk superconductivity. However, the interpretation of those
magnetization measurements can be very complex, as will be shown below.
Temperature-dependent magnetization
The first case that should be discussed are temperature-dependent magnetization mea-
surements [90, 91]. In the strictest sense, only a susceptibility of -1 that was gained in
a field-cooled measurement proves 100% bulk superconductivity. This can be understood
intuitively when considering a type I superconducting cylinder which has an axial hole,
where a magnetic field is applied parallel to the cylinder axis. For zero-field cooling, sur-
face currents will shield everything “inside”, also the hole - the whole specimen acts as a
perfect diamagnet. For field-cooling, however, the result is different: the magnetix flux
that could penetrate inside the specimen in the normal conducting phase needs to be ex-
pelled. This takes place only in the superconducting volume; the flux in the hole remains.
Therefore, only the superconducting volume acts as a perfect diamagnet. In summary,
the field-cooled susceptibility will be less negative than the zero-field cooled curve; only
the field-cooled response will give the true superconducting volume fraction.
Unfortunately, a less negative field-cooled signal does not mean necessarily a bad sam-
ple quality or a smaller superconducting volume fraction. For instance, granular super-
conductors have intergranular spaces that can trap flux. Another example are type II
superconductors, where vortex dynamics can lead to very complex hysteretic behaviour,
which will be discussed in more detail in the next section.
3.3 Superconductivity and Magnetism 29
Field-dependent magnetization
Real type II superconductors contain imperfections. Indeed, the system can win energy
when the vortices run through normal-conducting defects, as this effectively reduces the
vortex length. Thus, the vortices are “pinned” to those defects. If this pinning is strong,
the superconductor is characterized as “hard”, leading to interesting hysteresis effects due
to flux trapping.
The magnetization curves of such hard superconductors can be well described by Bean’s
critical state model [92]. While at B < Bc1, the penetration of the magnetic field is given
by the London penetration depth, at B > Bc1, vortices will start penetrating into the
material. Bean assumed that those vortices get pinned when entering through the surface,
leading below the surface to a broadened shielding volume with a homogeneous critical
current density jc. For external fields much smaller than the upper critical field, jc is
assumed as constant.
Figure 3.5: Development of an internal magnetic field Bint inside a hollow superconducting
cylinder (wall thickness d) when an external magnetic field Bext is applied (Bext > Bc1),
following Bean’s critical state model. The field distribution is schematically depicted in (a) for
increasing Bext and in (b) for decreasing Bext. (c) Bint dependent on Bext; fields displayed
in (a) and (b) are marked by symbols with the same colour. A distinct hysteresis results,
as vortices get directly pinned when entering the superconductor: with increasing field, the
cylinder gets gradually “filled” with vortices from the outside to the inside; with decreasing
field, opposite supercurrents cancel the vortices - again from the outside to the inside. Thus,
vortices are trapped inside the walls for a certain range of Bext.
30 3 Superconductivity
In order to understand the implications of those assumptions, a hollow superconducting
cylinder with thin walls of thickness d and neglectable small Bc1 can be considered, where
a magnetic field Bext is applied along the cylinder axis (see Fig. 3.5a). For small fields,
Bext gets completely shielded within the cylinder walls and the magnetic field at the center
of the cylinder Bint stays zero (see Fig. 3.5c). With increasing Bext, the volume where
vortices penetrate the superconductor increases until the cylinder walls are completely
filled. From this point, an increasing external field also leads to an increase of Bint. The
hysteretic effects get obvious when the external field is decreased (see Fig. 3.5c): due to the
decrease, an opposed critical current is induced at the surface, meaning that the density
of vortices decreases where this current flows. When decreasing Bext further, Bint does
not change until a homogeneous state is reached in the whole cylinder. At zero external
field, a finite internal field is trapped inside the hollow cylinder.
Indeed, the processes in a bulk sample are very similar [93], leading to characteristic
strongly hysteretic magnetization curves that appear also in iron pnictides [94]. Consid-
ering that jc should decrease when approaching the upper critical field, magnetization
curves of hard superconductors can be well described by Bean’s critical state model [95].
3.3.3 Upper critical field(s)
As already mentioned, superconductivity gets destroyed at the upper critical field Bc2.
In principle, there are two processes responsible for breaking up the Cooper pairs: spin
and orbital pair-breaking [96]. The first case only happens in spin singulett supercon-
ductors, where the Cooper pairs consist of electrons with opposite spin: As the magnetic
field induces an energy splitting between those (Zeeman effect), superconductivity gets
destroyed in the so-called “Pauli” or “Chandrasekhar-Clogston limit” [97, 98] as soon as
this difference exceeds the condensation energy of the Cooper pairs. In the case of orbital
or diamagnetic pair-breaking, the Cooper pairs are literally torn apart, as they possess
opposite momentum and thus the Lorentz force in a magnetic field will act in opposite
directions. While the upper critical field of most of the conventional superconductors is
determined by the orbital pair-breaking (described by the Werthamer-Helfand-Hohenberg
theory [99]), the Pauli limit plays a more important role in unconventional superconduc-
tors.
3.3.4 Exotic phases
Intuitively, one would not expect superconductivity in magnetic materials, as the magnetic
exchange field between spins creates usually very high internal fields. Nonetheless, in
some cases superconductivity is still energetically favourable, leading to exotic behaviour.
3.3 Superconductivity and Magnetism 31
Here, some of the effects that were discussed for Eu based 122 iron pnictides are shortly
introduced.
The first phenomenon that is observed in many of the Eu based iron pnictides is the
“re-entrant superconductivity”: for temperatures T < Tc, superconductivity is first de-
stroyed (Tn,re) and then re-enters at lower temperatures (Tc,re). This behaviour results
from temperature-dependent magnetic interactions and was initially predicted in 1971 for
materials that exhibit the Kondo effect [100]; in this case the pair-breaking first increases
with decreasing temperature due to the Kondo effect, until it decreases again at the coher-
ence temperature. Such a full cascade of transitions was experimentally verified in 1977
on La-Y-Ce alloys [101] with Tc = 0.55K, Tn,re = 0.27K and Tc,re = 0.05K.
Figure 3.6: Typical tem-
perature-dependent resistivity
of a re-entrant superconduc-
tor. Superconductivity that
sets in at Tc gets suppressed
at slightly lower temperatures
Tn,re due to competing mag-
netism. If the pair-breaking ef-
fects get weaker with decreas-
ing temperature, superconduc-
tivity can eventually re-enter
at Tc,re.
Nowadays, several rare earth materials are known to show re-entrant superconductivity.
One example are borocarbides [102], which have a similar crystal and magnetic structure
as EuFe2As2. In Ho(Ni2Co2)B2C, three different magnetic phases exist below Tc. In the
low temperature phase, spins within one layer are ferromagnetically coupled (with a small
out-of-plane component) and neighbouring planes are coupled antiferromagnetically. The
higher temperature phases are similar, but show slightly incommensurate spirals. It turns
out that the incommensurable magnetism is harmful to superconductivity, in contrast to
the commensurable phase. Theoretically, this behaviour is yet not well understood, but
leads to the characteristic temperature-dependence of a re-entrant superconductor, where
superconductivity is recovered when the commensurable magnetism sets in. The situation
is more clear in superconducting cluster glasses such as (Gd,La)Ru2 and (Nd,Th)Ru2 [102],
where the short-range ferromagnetic interactions compete with superconductivity, lead-
ing to re-entrant superconductivity. In this case, the superconducting state is probably
recovered, when larger ferromagnetic clusters become unstable at low temperatures.
32 3 Superconductivity
While the phenomenon of re-entrant superconductivity directly shows that superconduc-
tivity and magnetism compete, the question of how ferromagnetism and superconductivity
can coexist microscopically is more challenging to reply and several theoretical predictions
have been made.
In 1964, Fulde and Ferrell as well as Larkin and Ovchinnikov considered independently
from each other the effect of ferromagnetic moments on conventional singlet supercon-
ductors [103–105]. They found a stable phase, where the Cooper pairs contain non-zero
momentum, corresponding to the momentum difference of the Fermi surfaces of spin-up
and down electrons. This leads to a spatial modulation of the superconducting order
parameter, meaning that the Cooper pair density varies periodically in space. Although
it was yet not possible to verify this “FFLO-state” in ferromagnetic superconductors,
there are strong indications that such a spatially modulated state exists at high fields in
unconventional superconductors [106].
Another approach to this topic is that conventional ferromagnetism could be even ham-
pered to occur in a superconducting phase. In this spirit, it was suggested already in
1959, that in the superconducting phase only very small ferromagnetic domains will ap-
pear, which cancel each other out on the scale of the superconducting coherence length in
a “cryptoferromagnetic” alignment [107].
Furthermore, it was also predicted that in a ferromagnetic superconductor, spontaneous
vortices can occur, lowering the system’s energy similar to the Shubnikov phase in conven-
tional type II superconductors [108, 109]. At the moment, this effect is favoured to occur
in Eu based iron pnictides [31], although a direct experimental proof is still missing.
Finally, one should note that an external magnetic field can in principle also enhance
superconductivity if it acts against the internal magnetism. In rare earth materials such as
the Chevral-phase compound EuxSn1-xMo6S8 [111, 112], the appearance of a second super-
conducting dome at high magnetic fields was observed, while the original superconducting
dome was already suppressed at lower fields. This effect was theoretically explained in
1962 [110]: in those superconductors, the exchange field between conduction electrons and
local magnetic moments can be positive or negative, i.e. parallel or antiparallel to the
local moment direction. In the latter case, the exchange field is opposed to an external
magnetic field. Thus, for a certain field range, the external and internal magnetic fields
almost cancel each other out, significantly reducing the conduction electron polarization.
This leads to a re-appearance of superconductivity.
4
ELECTRODYNAMIC PROPERTIES
Optical spectroscopy is a powerful method to gather information about the electrodynamic
properties of materials, as it is able to resolve the energy scales of electronic interactions.
In this chapter, basic definitions and concepts to describe metals and broken symmetry
states are introduced, following Ref. [113] and [114]. Those concepts are then employed
to review the electrodynamic properties of 122 iron pnictides [115].
4.1 Basic definitions
In analogy to the relation of magnetic flux density and field strength discussed in chap-
ter 2.1, an electric displacement field D can be defined in free space as:
D = 0E (4.1)
with the permeability of free space 0 and the electric field E.
In a linear and isotropic dielectric material, an external electric field creates a polariza-
tion P and equation 4.1 needs to be extended:
D = 0E + P = 0rE (4.2)
34 4 Electrodynamic properties
with the relative dielectric constant (i.e. permittivity) r, which can be related to the
refractive index n˜ of the medium via:
n˜ = √r. (4.3)
In a dispersive medium, n˜ and r are both complex frequency-dependent quantities:
n˜(ω) = n(ω) + ik(ω) (4.4)
r(ω) = 1(ω) + i2(ω). (4.5)
Despite {n(ω), k(ω)} and {1(ω), 2(ω)}, there exist also two other pairs of optical
constants that are commonly used for describing the electrodynamic properties of solids.
The first is the frequency-dependent conductivity:
σ(ω) = σ1(ω) + iσ2(ω) (4.6)
that relates to the relative dielectric constant as:
r(ω) = ∞ + i
σ(ω)
0ω
(4.7)
with ∞ being the relative permittivity at ω →∞.
A common way to excess those optical constants are reflection measurements, where the
reflected wave displays a phase shift θ(ω) and an amplitude change r(ω) with respect to
the incident wave. In an experiment, the measured quantity is usually the reflectivity:
R(ω) = |r(ω)|2 = (n− 1)
2 + k2
(n+ 1)2 + k2 . (4.8)
Unfortunately, the phase shift
θ = arctan−1
[ 2k
n2 + k2 − 1
]
(4.9)
is accessible only by some measurement techniques such as ellipsometry or time domain
spectroscopy. However, as for all optical constants the causality condition holds, the
Kramers-Kronig transformation can be used to calculate the phase shift:
θ(ω) = −ω
pi
P
∫ ∞
0
lnR(x)
x2 − ω2dx (4.10)
4.2 Metals 35
where P denotes the Cauchy principle value. As usually the reflectivity is measured only
over a limited frequency range, R(ω) needs to be extrapolated properly to low and high
frequencies. Once this is done, one has obtained the last pair of optical constants from
which all the others: {n(ω), k(ω)}, {1(ω), 2(ω)} or {σ1(ω), σ2(ω)} can be calculated.
Indeed, Kramers-Kronig transformations connect all real and imaginary parts of optical
constants, and can be utilized to derive “sum rules”, which are powerful tools in the
analysis of spectroscopic measurements.
It should be noted that within this thesis, uniformly the SI system is used. However,
in optical spectroscopy often the CGS notation or even a mixture of unit systems can be
found. Most importantly, frequency and scattering rate are commonly given in [cm−1].
By using the conversion:
[cm−1]CGS ∗2pic−−−→ [1/s]SI (4.11)
the corresponding SI unit [1/s] can be obtained.
4.2 Metals
The electrodynamic properties of metals can be well understood considering the phe-
nomenological Drude and Lorentz model. While the former describes intraband interac-
tions, the latter accounts for interband transitions. In order to model the electrodynamics
in a real material, contributions from both models are included. While the reflectivity is
not additive, the conductivity is (according to Matthiessen’s rule).
Drude model
In the Drude model, a metal is described as a classical gas of electrons. Such an electron
interacts with its environment only in the form of collisions; the average time between
subsequent collisions is given by the relaxation time τ or the scattering rate Γ = 1/τ .
This leads in the presence of a time-dependent external field E(t) to the equation of
motion:
m
dr2
dt2 +
m
τ
dr
dt = qE(t) (4.12)
with mass m and charge q of the free carriers. By solving this equation, one obtains for
the real and imaginary part of the frequency-dependent conductivity:
σ1(ω) = σdc
1
1 + ω2τ2 = 0ω
2
pτ
1
1 + ω2τ2 (4.13)
σ2(ω) = σdc
ωτ
1 + ω2τ2 = 0ω
2
pτ
ωτ
1 + ω2τ2 (4.14)
36 4 Electrodynamic properties
with the frequency-independent prefactor given either by the dc conductivity
σdc =
Nq2τ
m
(4.15)
or the plasma frequency
ωp =
√
Nq2
0m
(4.16)
that depend on the density N of the free carriers.
The Sommerfeld extension of the Drude model accounts for the existence of a Fermi
surface, leading to a more realistic description with an effective massm∗ in equations 4.12 -
4.15 and a mean free path l given by the Fermi velocity vF:
l = vFτ. (4.17)
In Fig. 4.1a, the reflectivity R(ω) of a typical Drude response is displayed. For ω  1/τ ,
the electrodynamic properties of a metal depend mainly on the dc conductivity and the
reflectivity can be well described by the Hagen-Rubens relation:
R(ω) ≈ 1− 2
√
20ω
σdc
, (4.18)
as can be seen in the inset of Fig. 4.1a. With increasing frequencies, the reflectivity stays
close to unity, until it drops rapidly at ωp and the metal gets transparent.
Fig. 4.1b displays the corresponding complex conductivity. σ1(ω) is almost flat at low
frequencies with σ1 ≈ σdc and decreases at higher frequencies rather rapidly to zero, with
the inflection point of the curve at the scattering rate. In contrast, σ2(ω) vanishes at low
frequencies and has a maximum at 1/τ . One should note that the area below the real
part of the conductivity is a measure of the carrier density and effective mass. This can
be directly seen when integrating:
∫ ∞
0
σ1(ω)dω =
0pi
2 ω
2
p =
Nq2pi
2m (4.19)
Indeed, this so-called “f -sum rule” is valid independent from the Drude model.
Extended Drude model
In the Drude model, the scattering rate is assumed to be frequency-independent. However,
this assumption is invalid for many correlated materials, where the carriers couple to a
4.2 Metals 37
Figure 4.1: Typical (a) reflectivity and (b) conductivity of a metal according to the Drude
model. (a) R(ω) (brown line) is close to unity until it drops rapidly at ωp. The inset shows that
at low frequencies, the reflectivity can be well described by the Hagen-Rubens equation (red
dotted line). (b) σ1(ω) (green line) is close to σdc (red dotted horizontal line) and decreases
at higher frequencies with the inflection point of the curve at 1/τ , where σ2(ω) (blue dashed
line) displays a maximum.
bosonic mode. Therefore, an extended Drude model was introduced [116], where 1/τ got
replaced by a complex damping function:
M(ω) = 1
τ(ω) − iωλ(ω) (4.20)
with the frequency-dependent scattering rate 1/τ(ω) and the optical mass enhancement
factor λ(ω). Those parameters can be derived from the optical conductivity:
1
τ(ω) = 0ω
2
p
1
σ1(ω)
(4.21)
1 + λ(ω) = m
∗
mb
= −0ω2p
1
ω
1
σ2(ω)
(4.22)
with the band mass mb. This is of particular interest for unconventional superconductors,
as from 1/τ(ω) the Eliashberg spectral function α2F (ω) (introduced in chapter 3.2.3) and
the coupling strength to the bosonic mode λ (also called “mass renormalization factor”)
can be calculated.
38 4 Electrodynamic properties
Lorentz model
In many cases, resonant interaction of light with matter can be phenomenologically de-
scribed by the Lorentz model of damped harmonic oscillators. Typical examples are ionic
or phononic vibrations, as well as interband transitions. It follows for the real and imagi-
nary part of the frequency-dependent conductivity:
σ1(ω) = 0ω2p
ω2/τ
(ω20 − ω2)2 + ω2/τ2
(4.23)
σ2(ω) = −0ω2p
ω(ω20 − ω2)
(ω20 − ω2)2 + ω2/τ2
(4.24)
with the same definition of the plasma frequency ωp as in the Drude model; the damping
1/τ accounts for the energy loss of the oscillating dipoles due to collisions.
In Fig. 4.2a, the reflectivity R(ω) of a Lorentz oscillator is displayed. While the reflec-
tivity is rather flat at low frequencies, it increases strongly around ω0 due to the onset of
interband transitions. For higher frequencies, the reflectivity stays again rather constant,
until it drops similar to the Drude model at ωp.
Figure 4.2: Typical (a) reflectivity and (b) conductivity of a Lorentz oscillator. While R(ω)
(brown line) is rather flat at low frequencies, it increases around ω0, flattens again, and drops
finally similar to the Drude model at ωp. While σ1(ω) (green line) displays a maximum at ω0
with the FWHM = 1/τ , σ2(ω) (blue dashed line) has an inflection point at ω0 and extrema
at ω0 ± 1/2τ .
4.3 Broken symmetry states in metals 39
The corresponding conductivity can be seen in Fig. 4.2b. As the interband transitions
lead to strong absorption, σ1(ω) displays a maximum at ω0 with the full width at half
maximum (FWHM) given by 1/τ ; σ2(ω) is negative below ω0 and positive at higher
frequencies, with extrema at ω0 ± 1/2τ .
4.3 Broken symmetry states in metals
Electron-electron and electron-boson interactions might trigger in a metal a phase transi-
tion to an ordered, coherent ground state with broken symmetry. Examples are supercon-
ductivity and density wave states. While in the former case, gauge symmetry is broken
via the Higg’s mechanism, in the latter case, translational symmetry is broken due to a
periodic variation of spin or charge. Further differences can be found when considering
the pairing conditions: while for conventional superconductors1, electrons with opposite
momentum pair, in density waves electrons and holes pair with a total momentum of
Q = 2kF. Therefore, the latter process requires a substantial nesting of the Fermi surface,
meaning that parts of the Fermi surface can be mapped on top of each other by translation
with Q.
4.3.1 General quantum mechanical description
In the metallic phase, the interaction of light with matter can be described sufficiently
in the framework of the classical Drude and Lorentz model, as discussed in section 4.2.
For superconductors and density waves, however, a quantum mechanical description is
necessary.
According to Fermi’s golden rule, the net transition rate from an initial (occupied) to a
final (unoccupied) state (with energies E and E + ~ω, respectively) depends on:
• the energy of the external probe ~ω
• the number of occupied quasiparticle states, given by f(E)D(E) (with the energy-
dependent Fermi distribution f(E) and the density of states D(E))
• the number of unoccupied states, given by [1− f(E + ~ω)]D(E + ~ω)
• the transition matrix elementM
1 This section will focus on conventional superconductors with an isotropic energy gap.
40 4 Electrodynamic properties
and can be calculated in general as:
W ∝
∫
|M|2D(E)D(E + ~ω) [f(E)− f(E + ~ω)]dE. (4.25)
For broken symmetry states, one needs to consider some peculiarities about the density
of states and the transition matrix element that will be discussed below.
Single particle density of states
In the broken symmetry phase, a temperature-dependent energy gap appears in the single
particle excitation spectrum, as already discussed for a (conventional) superconductor in
chapter 3.1; the gap equation is the same for a density wave. The corresponding single
particle density of states is depicted in Fig. 4.3. Above the critical temperature where the
symmetry is broken (T > Tc), the density of states is basically flat and the occupation
of states follows the Fermi distribution. In the broken symmetry phase, states within the
energy gap can not be occupied. As the total number of states needs to be conserved, the
gapped states are reshuffled, leading to a divergent density of states at EF ±∆.
Figure 4.3: Single particle density of states for a metal that exhibits at Tc a transition to
a broken symmetry phase for (a) T > Tc, (b) 0 < T < Tc, and (c) T = 0; dark areas mark
occupied states, light colours unoccupied ones. (a) For T > Tc, the density of states follows
the Fermi distribution. (b,c) Below Tc, a temperature-dependent gap develops around EF,
leading to a divergence of the density of states at EF ± ∆. The absorption of photons with
~ω ≥ 2∆(T ) can break Cooper pairs (black solid arrow). (b) Only for T > 0, thermally
activated electrons are available to absorb photons (dashed black arrow).
The formation of an energy gap has important implications for the absorption of pho-
tons: while Cooper pairs can be broken only for energies ~ω ≥ 2∆(T ), thermally excited
4.3 Broken symmetry states in metals 41
electrons can also absorb photons with lower energies. This leads to two independent
absorption channels, whose properties will be discussed in the next sections.
Coherence effects
While transitions between different states are independent for a metal, the situation is
more complicated in the case of a broken symmetry phase where carriers are condensed
into a coherent ground state [40, 61]. As a quasiparticle of such a ground state consists
of two carriers with well-defined momentum- and spin-relation, it can be shown that one
will always find pairs of transitions that involve the same excitation states, although the
scattering process is different (for a typical example, see table 4.1).
Process State (k1, ↑) (−k1, ↓) (k2, ↑) (−k2, ↓)
1 initial 1 0 0 0
1 final 0 0 1 0
2 initial 1 0 1 1
2 final 1 1 1 0
Table 4.1: Two processes in a superconductor that lead to a scattering of an electronic
excitation from the initial state (k1, ↑) to the final state (k2, ↑). States that are occupied by
an electron are noted as “1”, unoccupied ones by “0”. Pairs of opposite spin and momentum
that form a Cooper pair are marked in blue; if in such a pair only one electronic state is
occupied, this is called electronic excitation (red). While the first process involves a scattering
of an electron from (k1, ↑) to (k2, ↑) (marked in bold signs), the second process involves
a scattering from (−k2, ↓) to (−k1, ↓). However, the initial and final states concerning the
electronic excitation are the same.
This needs to be considered when calculating the transition matrix elements, as equiva-
lent matrix elements have to be added coherently before taking the squared absolute value
in equation 4.25. It turns out that a proper mathematical description can be achieved via
so-called “coherence factors” F , transforming the transition matrix element as:
|M|2 → F|M|2 (4.26)
in the broken symmetry state. The absolute value of F depends on the type of perturbation
and varies between zero and one.
Fig. 4.4a displays the frequency-dependence (at T = 0K) of the electromagnetic absorp-
tion for a superconductor and a spin density wave system, calculated from equation 4.25
with considering the appropriate coherence factors. While for the latter case, the singu-
larity in the density of states is directly visible in the absorption spectrum, for a supercon-
ductor, the coherence factor approaches zero at the gap energy and cancels the singularity
42 4 Electrodynamic properties
in the density of states. This leads to a smooth increase of the absorption rate for ener-
gies above 2∆. In Fig. 4.4b, also the temperature-dependence of the absorption rate is
depicted for electromagnetic irradiation with small energies ~ω  2∆. In the case of a
superconductor, one can observe just below Tc a surprising enhancement of the absorption
rate. As this enhancement rises again from the coherence factor, this feature is usually
referred to as “coherence peak”.
Figure 4.4: (a) Frequency- and (b) temperature-dependent absorption of photons for a
superconductor (blue) and a spin density wave material (red) at T = 0 and ~ω  2∆,
respectively, as resulting from Fermi’s golden rule (adapted from Ref. [113]). (a) In both
cases, an energy gap appears below 2∆. While for the spin density wave, the singularity
in the density of states is directly visible in the absorption spectrum, for a superconductor,
coherence effects lead to a smooth increase of the absorption. (b) A coherence peak slightly
below Tc is only visible for a superconductor.
4.3.2 Superconductors
In the so-called “two-fluid” model, the electrodynamic properties of a superconductor
are approximated as a superposition of the response of superconducting and normal-
conducting electrons, neglecting any superconducting gap and coherence effects. For the
condensed electrons, such a classical descriptions transforms the Drude conductivity (see
equation 4.13) in the limit τ →∞ to:
σ1(ω) =
pi
2
Nq2
m
δ(ω = 0) = pi2
0
λ2L
δ(ω = 0) (4.27)
σ2(ω) =
Nq2
m
1
ω
= 0
λ2L
1
ω
(4.28)
4.3 Broken symmetry states in metals 43
with a delta-function in σ1(ω) at zero frequency δ(ω = 0), the London penetration depth:
λL =
√
m
µ0Nq2
= c
ωp,c
(4.29)
and charge and mass of a single electron, if N is defined as the density of superconduct-
ing electrons. When all electrons are condensed in the superconducting ground state,
the plasma frequency in the normal state ωp corresponds to that of the superconduct-
ing condensate ωp,c. One should note that despite λL, sometimes also a more general,
frequency-dependent penetration depth is defined:
λ =
√
0
σ2(ω)ω
. (4.30)
The 1/ω-divergence in σ2(ω) leads to a rapid, characteristic increase of the reflectivity
towards unity.
FGT sum rule
As the f -sum rule must hold also when passing from the normal to the superconducting
state, it follows that the missing spectral weight that appears in the superconducting
phase due to the opening of the gap is transferred to the delta-function at zero frequency.
This directly leads to the “FGT sum rule” (named after Ferrell, Glover and Tinkham
[117–119]), relating the conductivity in the normal state σn1 (ω), the conductivity in the
superconducting state σs1(ω), and the London penetration depth by:∫ ∞
0
[σn1 − σs1]dω =
0pi
2
c2
λ2L
. (4.31)
Dirty vs. clean limit
For a more detailed description of the electrodynamics, one has to consider the different
characteristic length scales; their relative magnitude determines the nature of the super-
conducting state. In particular, one has to distinguish between the dirty (local) and the
clean limit, 1/τ > ∆ and 1/τ < ∆, respectively. Thus, in the clean limit most of the
spectral weight of the Drude component lies below 2∆ and for T < Tc, almost all free
carriers collapse into the condensate. In contrast, in the dirty limit a significant amount
of Drude weight lies above 2∆. Therefore, only a fraction of the Drude spectral weight
collapses into the condensate, leading to a more pronounced gap feature in the optical
spectrum.
44 4 Electrodynamic properties
Mattis-Bardeen description
Based on the BCS theory, the electrodynamic properties of a superconductor were first
analytically calculated by Mattis and Bardeen [120], assuming τ → ∞, and extended
for finite scattering rates by Zimmermann et al. [121]. Fig. 4.5 displays the real and
the imaginary part of the conductivity for a superconductor in the dirty limit at T =
0.8 Tc, decomposed into contributions from Cooper pairs (broken by absorbed phonons)
and thermally activated electrons; Fig. 4.6 adds the temperature-dependence of σ1. The
general features that were discussed up to now, i.e. the non-diverging behaviour of σ1(ω ≤
2∆), the coherence peak in σ1(T ) (for ω  2∆) and the 1/ω-dependence of σ2(ω) are all
nicely visible.
Figure 4.5: Frequency-dependence of the (a) real and (b) imaginary part of σ(ω) (black
line) for a superconductor in the dirty limit at T/Tc = 0.8, decomposed into contributions
from Cooper pairs (blue dashed line) and thermally activated electrons (red dashed line)
(adapted from Ref. [122]). (a) The photon activated electrons contribute only for energies
~ω > 2∆(T ) to σ1(ω); coherence effects cancel the singularity in the density of states, leading
to a continuous increase of their response. The contribution of thermal electrons decreases
with increasing frequency, following the behaviour of the density of states. The sum of both
contributions displays a characteristic minimum at 2∆(T ). (b) The 1/ω-behaviour of the
phonon activated electrons dominates the response of σ2(ω); the contribution of the thermally
activated electrons is opposite, but negligible. At 2∆(T ), only a very weak kink is visible.
4.4 Iron-based superconductors
Optical spectroscopy revealed valuable information about correlations [123] and broken
symmetry states [124–127, 266] already within the first year after the discovery of iron-
based superconductors. Most of the relevant charge dynamics take place in the infrared
4.4 Iron-based superconductors 45
Figure 4.6: (a) Frequency- and (b) temperature-dependence of σ1(ω) for a superconductor in
the dirty limit for several temperatures and photon energies, respectively. (a) The pronounced
gap feature vanishes with increasing temperature. However, the response of thermally acti-
vated electrons at very low energies gets strongly enhanced close to Tc. (b) The latter is
consistent with a pronounced coherence peak at energies ~ω  2∆.
frequency range, as summarized in Fig. 4.7. This section provides an overview of great
achievements and open questions provoked by optical investigations on 122 iron pnictides.
Figure 4.7: Characteristic energy scales in iron-based superconductors. In order to study
the superconducting gap, terahertz (THz) and far-far-infrared (FFIR) frequencies have to
be covered. While itinerant dynamics are relevant in the far-infrared (FIR) energy range,
incoherent transport and interband transitions govern the mid- and near-infrared (MIR and
NIR, respectively). Ellipsometry measurements can be extended to very high energies.
46 4 Electrodynamic properties
4.4.1 Spectral features of the normal state
Similar to cuprates, the normal state in-plane reflectivity and optical conductivity of 122
iron pnictides do not show well-separated components, leading despite a zero-energy Drude
peak to a broad mid-infrared plateau that is rather untypical for a metal and often referred
to as “incoherent” region; no clear plasma edge is visible (see Fig. 4.8b, [128, 129, 266]).
At higher frequencies, humps characteristic for interband transitions appear.
Figure 4.8: Characteristic (a) reflectivity and (b) conductivity of 122 iron pnictides in the
normal state (adapted from Ref. [266]). (a) R(ω) (brown line) typically displays in the FIR
an overdamped metallic frequency-dependence; at higher frequencies, no clear plasma edge is
visible - only humps typical for interband transitions. (b) Correspondingly, σ1(ω) is slowly
decreasing at low frequencies with a long tail extending in the MIR region; it is followed by
a pronounced peak structure around 5000 cm−1. A cut-off separating itinerant Drude-like
behaviour (red area) from local and interband (Lorentz-like) dynamics (blue area) is often set
around 1500 cm−1. However, in reality a significant overlap exists.
With decreasing temperature, the response gets more metallic, meaning that spectral
weight is shifted within the mid- and far-infrared region to lower frequencies. However,
spectral weight shifts occur also at higher frequencies up to the visible spectral range, indi-
cating that correlation effects are of importance [130], as discussed further in section 4.4.5.
4.4 Iron-based superconductors 47
Along the c-direction, the flat MIR background dominates, which decreases with de-
creasing temperature1 [131]. However, lowering the temperature also uncovers a weak
Drude component, indicating interlayer coherence. Thus, iron pnictides display much less
electronic anisotropy than cuprates. Nevertheless, both families of high-temperature su-
perconductors share the broad plateau-like background in the mid-infrared, that is not a
simple Drude response.
4.4.2 Analysis methods
In the case of cuprates, two principal approaches exist that are commonly used to describe
the mid-infrared charge dynamics: one-component and multi-component models [116]. In
the former case, it is assumed that the low-frequency response originates from itinerant
carriers with a frequency-dependent scattering rate and mass. The formalism of this
extended Drude model was already introduced in section 4.2. In the multi-component
approach, the conductivity spectrum is described by a free-carrier Drude term and a set
of Lorentzian oscillators, accounting for example for interband transitions or impurity
states.
The debate which model describes better the charge dynamics in cuprates is yet not
solved. On the one hand, well-separated absorptions in lightly doped cuprates favour
the multi-component approach. On the other hand, the extended Drude formalism could
uncover a frequency-dependent scattering rate over a broad energy range and many inter-
esting aspects like the violation of Fermi liquid theory or the coupling to a temperature-
dependent bosonic mode, both consistent with other measurement techniques.
In the case of iron pnictides, the multiband character further complicates both, single-
and multi-component analysis. In principle, hole and electron bands with different scat-
tering rates should be considered. Furthermore, as five Fe d-bands are situated close to
the Fermi energy, low-lying interband transitions are plausible. Indeed, recent infrared
studies uncovered for Ba, Sr and Ca compounds two well-defined features around 1000
and 2300 cm−1 [12]. Due to its temperature- and doping-dependence, the former one can
be attributed (via a comparison to ARPES measurements) to interband transitions in-
volving Fe hole pockets. The origin of the second feature is yet not clear; the same holds
for another hump in the optical conductivity, that was observed in several compounds at
even lower energies (around 150 cm−1) [132–137]. Despite that, Dirac physics might also
play a certain role [139, 140].
1 Moon et al. demonstrate that a true c-direction response can be only obtained for cleaved samples, not
for polished specimen [131].
48 4 Electrodynamic properties
Disentangling all those processes in a multi-component analysis is almost impossi-
ble. Therefore, a “broad Drude” approach was suggested by Wu et al.: they modelled
the mostly temperature-independent background of eight different 122 compounds by a
very broad Drude and two high-frequency Lorentzians that account for interband tran-
sitions [128, 130]. The remaining temperature-dependent part of the spectrum can be
described by one narrow Drude. There is no spectral weight transfer between the different
subsystems. This model has the advantage that the coherent dynamics are described by
only a few parameters.
Nakajima et al. extended this approach, allowing the broad Drude component to vary
with temperature [129]. However, fitting the spectra was still possible without spectral
weight transfer between the different subsystems. In further publications, the broad back-
ground narrowed and was more and more attributed to the hole bands [141].
There exist also advocates of the conventional multi-component approach known from
cuprates, where one or a series of Lorentzians is used to model the mid-infrared plateau.
They argue that the mean free path of a very broad Drude would violate the Mott-Ioffe-
Regel limit, indicating that the conductivity in such a band is no longer metallic and
therefore better described by a bound excitation [142]. It turns out that in this case,
enough free parameters exist in order to fit the spectrum with only one Drude. In order to
account for electron and hole bands, one needs additional information, such as the relative
spectral weights of the Drude components which can be extracted from photoemission
experiments [143, 144].
The ambiguity of different modelling approaches is a serious drawback of optical spec-
troscopy on iron pnictides. Maybe one of the biggest problems is that usually one group
only publishes results using a single modelling approach. Thus, it gets not clear whether
(on the first view) contradictory studies result from different fitting approaches, sample
quality or have a physical meaning. As a direct comparison of different modelling ap-
proaches is still lacking, such a study was performed in the framework of this thesis and
is presented in chapter 9.
4.4.3 Antiferromagnetism
The early observation of energy gaps opening at the high-temperature phase transition in
iron pnictide parent compounds is one of the great achievements of optical spectroscopy:
already in 2008, Dong et al. proposed on the basis of optical measurements on polycrys-
talline LaOFeAs a spin density wave, driven by a nesting instability between electron and
hole Fermi surfaces [124]. Only six months later, Hu et al. reported more detailed studies
on single crystals of Ba- and SrFe2As2 [266].
4.4 Iron-based superconductors 49
At the spin density wave transition, the reflectivity develops a rather sharp edge in the
far-infrared, above which R(ω) gets substantially suppressed (see Fig. 4.9a). This is a typi-
cal signature of the formation of an energy gap. However, with decreasing temperature the
low-frequency reflectivity still increases, indicating that the Fermi surface is only partially
gapped. The remaining Drude response is dramatically narrowed, with the scattering rate
being decreased by ∼ 90%.
Figure 4.9: Characteristic (a) reflectivity R(ω) and (b) conductivity σ1(ω) of 122 iron pnic-
tides in the spin density wave state (solid curves) compared to the normal state (grey light
area) (adapted from Ref. [266]). The Fermi surface gets only partially gapped, visible in an
increase of R(ω) and σ1(ω) at low frequencies (red area). Spectral weight is shifted to higher
frequencies; σ1(ω) displays two bump-like features corresponding to two different gaps (purple
area). An additional spectral weight shift appears even in the range of interband transitions
(blue area), indicating correlations. The sharp peak around 260 cm−1 is the signature of an
FeAs phonon [145].
In the real part of the optical conductivity, the spin density wave becomes noticeable as
spectral weight is reshuffled from the far-infrared to higher frequencies, where it piles up
usually in the form of two well-separated peaks, corresponding to two different energy gaps
(see Fig. 4.9b). The peak position marks the gap energy; it is around 2∆/kBTSDW ∼ 3.5 for
the smaller and ∼ 10 for the bigger gap. As only spectral weight and peak position of the
lower gap follow the mean field temperature-dependence, it was suggested in accordance
with band structure calculations that this one has itinerant character, while the higher gap
50 4 Electrodynamic properties
appears due to local exchange splitting [146]. A different interpretation results from c-axis
measurements, where exclusively the smaller gap is visible [147]. From this, the authors
proposed that the larger gap is due to the nesting of 2D Fermi surfaces and the smaller
gap results from the backfolding of the magnetic Brillouin zone that cuts the 3D Fermi
sheet. Finally, also a magnon-assisted indirect spin density wave excitation was discussed
that could lead to the high energy gap [139].
4.4.4 Superconductivity
Optical signatures of a clear superconducting gap were first seen in 1111 LaFeAsO0.9F0.1−δ
and NdFeAsO0.82F0.18 polycrystalline samples [125, 126]. A more quantitative analysis
could be only achieved after 122 single crystals were available [127]. Since then, most
optical studies were carried out on (nearly) optimally Co doped Ba 122 compounds due to
the availability of high quality single crystals [128–130, 133, 134, 142, 154, 155] and thin
films [148–153].
Dirty vs. clean limit
It turned out that the in-plane optical response of Ba1−xKxFe2As2 and Ba(Fe1−xCox)2As2
is quite different in the superconducting regime: while the former displays over a broad
frequency range a quasilinear dependence of σ1(ω), the latter shows a steep onset of
absorption at energies corresponding to (one of) the smaller superconducting gap(s) [135].
Charnukha et al. demonstrated that both behaviours can be explained by using an effective
two-band Eliashberg theory with a strong coupling to spin fluctuations, if K substitution
leads to effective bands in the clean limit, while Co doped compounds are in the dirty
limit.
Superconducting gaps
The same calculations yield for Ba0.68K0.32Fe2As2 isotropic superconducting gaps with
2∆/kBTc ∼ 2.2 and ∼ 6, in quantitative agreement with other measurement techniques
such as ARPES, STM and specific heat. The situation is much more complicated in the
case of Ba(Fe1−xCox)2As2, where several reports exist which show neither consensus about
the gap sizes, nor about the number of gaps (see Fig. 4.10a). While most reports agree
on one directly visible gap at around the BCS mean field value, fitting approaches usually
need at least one more gap at significantly higher or lower energies for a satisfactory
description.
Similar to cuprates [116], an unexpected high intra-gap absorption was evidenced in the
superconducting state of Ba(Fe1−xCox)2As2, which cannot be accounted for by thermally
4.4 Iron-based superconductors 51
Figure 4.10: (a) Extracted superconducting gap sizes [128–130, 133, 134, 142–144, 148–155]
and (b) typical temperature-dependent conductivity in the THz frequency range for nearly
optimally doped Ba(Fe1−xCox)2As2 (adapted from Ref. [151]). (a) While most reports agree
on one directly visible gap at around the BCS mean field value (green dashed line / green
area), fitting approaches usually need at least one more gap at significantly higher or lower
energies for a satisfactory description (light blue areas). Black squares denote measurements
on single crystals, red points on thin films. (b) A coherence peak is commonly observed
below Tc at very low frequencies. However, the conductivity does not approach zero at lowest
temperatures, indicating an anisotropic gap or pair-breaking interband scattering.
broken pairs [134, 148, 150, 151]. It appears in films as well as single crystals. As it
can be fitted with a Drude peak (with an overall conserved spectral weight), a low-lying
impurity band is unlikely the reason [134]. Other explanations are an anisotropic gap [151]
or pair-breaking interband scattering1 [150, 156].
An important difference between K and Co doping is that in the former case, atoms
out of the FeAs planes are substituted, while in the latter case, the FeAs planes are
directly affected [156]. Therefore, stronger impurity scattering is expected for Co doping,
consistent with smaller residual resistivity ratios and superconductivity in the dirty limit.
It needs to be seen, whether this enhanced scattering is also responsible for the strong
intra-gap absorption. Proving this would be another very strong indication for the s±-
symmetry of the superconducting order parameter. Measurements on Ba(Fe1−xCox)2As2
1 In an s± superconductor, interband scattering by non-magnetic impurities is pair-breaking, as it mixes
hole and electron states that have superconducting order parameters of opposite phase [156].
52 4 Electrodynamic properties
thin films, where the impurity scattering gets step-wise enhanced by proton irradiation,
were performed and supervised within this thesis and are presented in the attachment.
Coherence peak
Optical spectroscopy on Ba(Fe1−xCox)2As2 thin films was able to resolve a well-pronounced
coherence peak in the THz frequency range (see Fig. 4.10, [148, 150, 151]). In general,
a coherence peak can arise when the portions of Fermi surface that are coupled by an
experimental probe have gaps of the same sign and magnitude [150]. As the momentum
transfer of light at THz frequencies is negligible compared to the reciprocal lattice momen-
tum, only parts of the same Fermi sheets are coupled. Therefore, the observed coherence
peak is consistent with an s±-symmetry of the superconducting order parameter. Further-
more, the position of the coherence peak can be used in multiband superconductors as a
quantitative measure of the lower superconducting gap, demonstrated by Dahm et al. for
MgB2 [157].
FGT sum rule
All infrared studies agree on a rapid recovery of the missing spectral weight in the FIR
frequency range, yielding in-plane London penetration depths (in accordance with the
extraction from σ2(ω)) between 200-400 nm. However, one very careful ellipsometry study
performed by Charnukha et al. on Ba0.68K0.32Fe2As2 uncovered a superconductivity-
induced suppression of an interband transition at energies well above the plasma edge [158].
Although the transferred spectral weight is only ∼ 0.5% and therefore too small to be
detected in infrared studies, it could have a big effect on reducing the kinetic energy of
the system, pointing towards an unconventional pairing mechanism. Such an effect was
already proposed for cuprates, however, is there still under debate [116].
Bosonic spectrum
As the extended Drude analysis accounts only for itinerant carriers, the contribution of all
interband transitions needs to be eliminated before any further data processing. Moreover,
one has to keep in mind that due to the multiband nature of iron pnictides, only an average
spectrum for bosonic excitations can be extracted.
Up to now, an extended Drude analysis was carried out mainly on K and Co doped
iron pnictides [130, 135, 142, 159–161]. In all cases, a frequency-dependent scattering
rate is observed at low frequencies, which increases linearly with frequency (at least) up
to ∼ 50meV. A further Eliashberg analysis reveals a strongly temperature-dependent
bosonic spectrum, which is inconsistent with phonon coupling. The mass renormalization
4.4 Iron-based superconductors 53
factor increases with decreasing temperature, reaching values between 3-41, much above
the electron-phonon coupling constant λ = 0.21. Both, the temperature-dependence of
the bosonic spectrum as well as the high coupling constant would be consistent with spin
fluctuations playing a key role for bosonic excitations in pnictides. This situation is very
similar to that in cuprates [116].
c-axis coherence
Measurements on cleaved Ba(Fe0.926Co0.074)2As2 crystals reveal not only interlayer coher-
ence in the normal state, but also a robust interlayer superconducting condensate with a
penetration depth of ∼ 1000nm [131]. This is in stark contrast to underdoped cuprates,
where normal state transport is incoherent along the c-axis, leading to Josephson coupling
of CuO2 layers in the superconducting phase [116].
4.4.5 Unconventional normal state properties
Optical spectroscopy is able to reveal important information on the unconventional nor-
mal state charge dynamics of high-temperature superconductors, as already demonstrated
impressively for cuprates [116]. Therefore, similar approaches were applied to iron-based
superconductors in order to identify (via a comparison to cuprates) key ingredients for
high-temperature superconductivity. It turned out that iron pnictides are moderately cor-
related materials, where (instead of Mott physics) Hund’s coupling plays an important
role. While the appearance of a pseudogap or a quantum critical point is yet not well
established, the nematic phase drew enormous attention - even giving a feedback effect
for research on cuprates. Important insights gained from infrared spectroscopy on iron
pnictides are summarized below.
Correlations
A comparison between the kinetic energy of electrons obtained by band structure calcu-
lations and optical measurements revealed that iron pnictides are moderately correlated
materials2 [123]. This indicates that coherent and incoherent processes play both a cer-
tain role in transport properties, in good agreement with the broad mid-infrared plateau
discussed above.
1 One has to keep in mind that the absolute value of the mass renormalization factor strongly depends
on the plasma frequency and thus on the model chosen for the analysis. This is probably the reason
why Tu et al. report smaller values than those given here [142].
2 A similar result can be obtained experimentally by comparing the spectral weight of coherent and
incoherent processes [162]. However, this method is very sensitive to the fitting approach.
54 4 Electrodynamic properties
In particular, LaFeAsO was found to be more correlated than LaFePO [165]. This
observation fits well with systematic room temperature studies performed by Nakajima
et al. on electron doped Ba(Fe1−xCox)2As2, hole doped Ba1−xKxFe2As2, and isovalently
substituted BaFe2(As1−xPx)2 [129, 141, 166]. They conclude that coherent transport is
enhanced by Co and P substitution, and slightly suppressed by K doping; incoherent trans-
port is basically not affected by Co doping, reduced by P substitution and enhanced by K
doping. Therefore, it seems that chemical substitution controls the Drude spectral weight
in quite different ways depending on dopant sites or type. The commonality found in
those studies is that superconductivity seems to be suppressed when the charge dynamics
become too coherent.
Hund’s coupling
The renormalization of electronic bands due to correlations does not only reduce the
Drude response (compared to band theory predictions), it also implies that additional
spectral weight is present at higher energies [163]. This can lead to unusual temperature-
dependent effects at high energies, which can not be attributed to interband transitions.
Such temperature-dependent spectral weight transfer around 5000 cm−1 was already re-
ported in 2008 for the ab-plane of Ba- and SrFe2As2 [266], and later also confirmed along
the c-axis of Ba(Fe0.926Co0.074)2As2 [131]. The direction of spectral weight transfer, its
independence of Co doping and its energy scale are not compatible with a Mott-like cor-
relation mechanism, but can be explained with Hund’s rule coupling effects [163, 164].
Due to Hund’s coupling, electron spins tend to align parallel. This can lead on the one
hand to the localization of electrons, if their kinetic energy is smaller than the coupling
energy; on the other hand, the thus induced local and itinerant electrons are not isolated
from each other, but still coupled via Hund’s coupling [164]. As at low temperatures,
thermal excitations become weak, more and more itinerant electrons get localized by this
interaction, explaining an increasing spectral weight transfer to high energies.
Pseudogap
In cuprates, the pseudogap in the density of states is directly visible in the out-of-plane
conductivity: while σc(ω) is rather flat at T > T ∗ (indicating incoherent transport),
the low-frequency conductivity gets suppressed below T ∗. Surprisingly, the gap value
is basically temperature-independent. An extended Drude analysis indicates that this
process is intimately related to a gap in the excitation spectrum, visible as the onset of
in-plane coherence and a gap in the frequency-dependent in-plane scattering rate (due to
the coupling to a bosonic resonance mode).
4.4 Iron-based superconductors 55
In iron pnictides, the appearance of a pseudogap is yet not well established. Up to
now, two different “types” of pseudogaps were proposed from optical measurements. In
underdoped Ba1−xKxFe2As2, spin density wave and superconducting order coexist. Addi-
tionally, a gap-like hump structure appears well above Tc for frequencies around 150 cm−1,
corresponding to the energy range of the superconducting gap [136, 137]. Dai et al. argued
via a spectral weight analysis that while the spin density wave is a competitive order to
superconductivity, this pseudogap acts as a precursor (Tc < TPG < TSDW) [137].
One should note, however, that a similar feature was already observed in BaFe2As2 [132],
as well as optimally electron and hole doped compounds [133–135]. In those cases, alter-
native interpretations were given, involving a low-lying interband transition [133, 134] or
an impurity band [134].
Moon et al. investigated single crystals of the Ba 122 family [138]. For optimally sub-
stituted Co and P compounds, they observed a shallow dip in the conductivity around
650 cm−1 that is accompanied by a threshold in 1/τ(ω), typically for the pseudogap in
cuprates. This feature does not appear in the parent compound and the overdoped re-
gion, coinciding with the development of antiferromagnetic correlations. Therefore, they
suggested that in iron pnictides, antiferromagnetic fluctuations related to the spin density
wave instability of the parent compound cause a pseudogap.
Nematic phase and in-plane anisotropy
Optical studies on mechanically detwinned Ba(Fe1−xCox)2As2 as-grown and annealed sam-
ples were performed by Dusza [167, 170, 172] and Nakajima et al. [169, 171], respectively.
In both cases, a pronounced anisotropy at finite frequencies appears that can be attributed
to an anisotropic spin density wave gap formation (see Fig. 4.11). This anisotropy extends
up to very high frequencies, well exceeding the energy scale of kBTs,SDW. Moreover, the
FeAs phonon around 260 cm−1 gets highly anisotropic; in BaFe2As2, it basically disap-
pears along the a-axis. Detailed measurements on twinned BaFe2As2 evidenced a phonon
splitting below Ts,SDW, with the minority contribution (along the a-axis) having a higher
center frequency [174].
Using local density approximation combined with dynamical mean field theory, Yin et
al. [168] calculated the anisotropic optical conductivity for BaFe2As2 resulting from orbital
polarization. They found three extra excitations appearing in the spin density wave phase
around 1000 cm−1. While two lower energy excitations are much more pronounced along
the a-direction, the third peak is more pronounced along the b-direction. All this is in
good agreement with the results shown in Fig. 4.11. However, one should note that the
56 4 Electrodynamic properties
Figure 4.11: In-plane conductivity of mechanically detwinned BaFe2As2 (adapted from
Ref. [169]) for (a) E ‖ a and (b) E ‖ b-axis and temperatures below (blue line) and above
(red line) Ts,SDW. At low energies and temperatures, σa > σb is observed, consistent with
resistivity measurements. A pronounced anisotropy appears in particular at finite frequencies
that can be attributed to an anisotropic spin density wave gap formation. Furthermore, the
FeAs phonon around 260 cm−1 disappears in σa(ω). A cusp-like shape for the lowest energy
spin density wave feature in σb is only observed by Nakajima et al.. Along the b-direction,
spectral weight is transferred up to very high energies.
experiments reveal spectral weight transfer to even higher energies than predicted, in
particular along the b-direction (∼ 17000 cm−1).
From a multi-component analysis one should be able to distinguish whether the un-
conventional behaviour ρb > ρa results from the anisotropy in the scattering rate or the
Fermi surface parameters n/m∗ (determined by the Drude spectral weight), as 1/ρ =
σdc = nq2τ/m∗. Unfortunately, there is no consensus concerning this topic: Dusza et
al. claim that the anisotropy results from the Fermi surface parameters, outweighing the
conventionally expected 1/τa > 1/τb [167, 170]. In contrast, Nakajima et al. conclude
1/τb > 1/τa, while the Drude weight stays rather isotropic [171]. In chapter 9, we will
discuss our results for magnetically detwinned EuFe2As2.
While those measurements were obtained under constant external stress due to a me-
chanical clamp, Mirri et al. investigated the optical anisotropy that is induced in BaFe2As2
4.4 Iron-based superconductors 57
by a tunable Helium gas pressure cell [173]. While optical anisotropy can be induced by
pressure below and above Ts,SDW (consistent with resistivity measurements), a hysteretic
behaviour and a persistent detwinning (after the pressure is reduced to zero) can be only
detected below Ts,SDW. Furthermore, they observe at Ts,SDW a divergence of the reflectiv-
ity anisotropy normalized to the applied pressure. This behaviour is strikingly similar to
resistivity measurements under tunable strain, indicating a nematic transition [25].
Quantum criticality
In the proximity of an antiferromagnetic quantum critical point, spin fluctuations should
be strong enough to modify the scattering process of quasiparticles and induce non-Fermi
liquid behaviour. Optical measurements are in principle an ideal tool to get further insight
into this topic: different conduction channels can be disentangled, uncovering the dc
conductivity and scattering rate of coherent carriers.
In Ba(Fe0.92Co0.08)2As2 and Ba(Fe0.95Ni0.05)2As2, the normal state resistivity can be
well fitted up to high temperatures with R(T ) ∝ Tn, using the exponents n = 1.25
and n = 1.5, respectively [128, 130]. However, a multi-component analysis by Wu et al.
uncovered in both cases a “hidden” Fermi liquid behaviour 1/σdc(T ) ∝ 1/τ(T ) ∝ T 2 of
the narrow Drude, being masked by a temperature-independent incoherent background.
In contrast to those compounds, the resistivity in Ba0.6K0.4Fe2As2 is rather linear at
low temperatures, but shows a tendency towards saturation above 175K [161]. Here, Dai
et al. concluded from a multi-component analysis that the incoherent background masks
non-Fermi liquid behaviour of the narrow Drude (1/σdc(T ) ∝ 1/τ(T ) ∝ T ), extending
up to room temperature. This holds also for BaFe2(As0.7P0.3)2. Most importantly, the
authors demonstrated that the spectral weight at a certain cut-off frequency follows the
same temperature-dependence as the inverse scattering rate, giving a model-independent
proof of their findings.
As already mentioned in chapter 3.2.2, a diverging effective mass around the optimum
substitution level was up to now only uncovered for BaFe2(As1−xPx)2, but not for Co
doped compounds [83, 84]. Therefore, those on the first view contradictory results of Wu
and Dai et al. could be another indication how sensitively the electronic properties of iron
pnictides dependent on the substitution position. A model-independent spectral weight
analysis on electron doped compounds could shed further light on this topic.

5
MATERIALS AND METHODS
In this chapter, the basic concepts of Fourier-ransform Intfrared (FTIR) spectroscopy and
Superconducting Quantum Interference Device (SQUID) magnetometry are introduced.
As the corresponding setups used for the measurements in this thesis are either commercial
machines or cryostats constructed in the framework of another thesis, the description
concentrates on the main principles. The chapter concludes with an overview about the
investigated samples.
5.1 FTIR spectroscopy
Fourier-transform spectroscopy is a powerful tool to study the electrodynamic proper-
ties of solids [113]. Instead of time-consuming frequency sweeps needed for example in
conventional grating spectrometers, the energy resolution is gained via a Fourier transfor-
mation of interfered light. Today, this method is widely used in the infrared, as here light
sources, beamsplitters, mirrors, filters, windows and detectors are available that cover a
broad frequency range; the commercially available setups contain usually modifications of
a Michelson interferometer (see Fig. 5.1).
In a conventional Michelson interferometer, monochromatic light is split into two ap-
proximately equal parts, which follow different beam paths, before they interfere again at
the beamsplitter and pass (or get reflected by) a sample. The interference pattern depends
on the optical path difference. By modulating the length of one of the light paths with
60 5 Materials and methods
Figure 5.1: Schematic drawing of the beampath in a Michelson interferometer. Light from
a source passes a semi-transparent beamsplitter; half of the light gets reflected by a fixed
mirror, the other half by a movable one. After the reflection on these mirrors, the two beams
meet again at the beamsplitter and interfere. The interfered light passes the sample (or gets
reflected on it) and finally is collected by the detector that records the intensity dependent on
the position of the movable mirror (i.e. on the optical path difference).
a movable mirror, one obtains the intensity as a function of mirror position; this spatial
dependence can be translated to a frequency-dependence via Fourier transformation, no
matter whether the light is mono- or polychromatic. This allows rapid recording of spectra
over a broad energy range.
As an obtained spectrum contains both, information about the sample and the light
source, one has to normalize it properly. For a transmission spectrum, this normalization
is done by a comparison measurement without the sample; for a reflection spectrum, the
response of a metallic mirror (usually gold, silver or aluminium) that possesses a reflection
close to unity is taken.
In order to obtain reliable absolute values, one has to make sure that sample and ref-
erence have the same size and surface consistence. There are basically three widely used
technical implementations in order to satisfy those requirements:
• The same size of sample and reference can be guaranteed by taking the same aperture
in both measurements. This is commonly done for transmission measurements, as
well as for reflection measurements on films or other homogeneous, rather flat and
big samples.
• A microscope can be used to focus infrared light on very small, flat and homoge-
neous areas of both, sample and mirrors. The spot size is much smaller than the
dimensions of sample and reference, guaranteeing the same amount of light hitting
both specimens.
5.1 FTIR spectroscopy 61
• Alternatively, after measuring the reflection of a sample, one can coat its surface
in-situ with a thin gold layer, creating the corresponding “perfect” mirror with the
same size and surface consistence; all measurements are then repeated on the gold
coated samples (under the same experimental conditions). In order to account for
any time-dependent influences (for example caused by source or detector), one can
take additionally the spectrum of a standard reference mirror.
Table 5.1 summarizes which approaches were taken for the infrared reflection measure-
ments performed in the framework of this thesis, as well as important technical param-
eters. Microscope measurements were carried out on a Bruker Vertex spectrometer with
attached Hyperion microscope at the 1st Physical Institute, Stuttgart; gold evaporation
measurements on a Bruker IFS 66v/s in the group of D. N. Basov at the UC San Diego.
In gold evaporation measurements, the sample gets mounted point-like on a copper cone.
This does not only avoid back-reflections from the sample holder, but also minimizes the
glued area and thus induced strain on the sample, being important for the magnetic de-
twinnnig experiments described in chapter 9. The interesting temperature range between
15K and 290K was accessible by Helium flow cryostats; all cryostats were designed to con-
tain a mechanically movable holder that allows precise positioning of sample and reference
in the focus of the light (see Ref. [175] and [176] for the detailed designs).
Range Magnet Technique Detector Beamsplitter Source Window
FFIR no gold 1.6K Bolometer Mylar 23µm Xenon PP
FIR no gold 4.2K Bolometer Mylar 6µm Globar PP
MIR no microscope 77K Photovoltaic KBr Globar KBr
NIR no microscope 77K InSb CaF2 Tungsten KBr
FFIR yes gold 1.6K Bolometer Mylar 23µm Xenon PP
FIR yes gold 4.2K Bolometer Mylar 6µm Globar PP
MIR yes gold 4.2K Photovoltaic KBr Globar PP
Table 5.1: Technical parameters of the FTIR-measurements performed in the framework of
this thesis for the different frequency ranges. One can distinguish between measurements with
and without magnetic field, as well as measurements, where absolute values were obtained
via in-situ gold evaporation or the availability of small spot sizes in a microscope setup.
Furthermore, the used detectors, beamsplitters, sources and windows (PP: polypropylene) are
given. One should note that the mid-infrared spectral range was not recorded by a conventional
MCT-detector, as it displays strong non-linearity effects non-negligible in the case of high
reflecting iron pnictides.
Fig. 5.2 displays the advanced design of the magneto-optical setup [177]. A helium
flow cryostat is directly connected to a 9T Oxford Spectromag, meaning that only one
polypropylene window has to be transmitted in reflection measurements. This reduces
62 5 Materials and methods
intensity losses caused by the window; however, this window can not be changed, meaning
that most of the light in the mid-infrared frequency range gets absorbed. A linear transla-
tor allows the positioning of sample and reference mirror in the focus of the light, as well
as the movement of the sample to the gold evaporation unit.
Figure 5.2: Magneto-optical setup as designed and constructed in the group of D. N. Basov,
UC San Diego (adapted from Ref. [177]). A helium flow cryostat is directly connected to
the vacuum chamber of a 9T Oxford Spectromag magnet. A linear translator allows the
positioning of sample and reference in the focus of the light, as well as the movement of the
sample to the gold evaporation unit.
5.2 SQUID magnetometry
A Superconducting Quantum Interference Device is able to convert magnetic flux to a
voltage with an extremely high sensitivity that reaches the quantum limit [2, 178]. It
consists of a superconducting loop that is interrupted by one (rf or ac SQUID) or two (dc
SQUID) Josephson junctions. In an external magnetic field, the combination of Josephson
effect and flux quantization causes a voltage drop across the loop that varies periodically
with the external field (if the bias current through the loop is fixed); the periodicity is one
elemental flux quantum Φ0.
In order to enhance the sensitivity, the SQUID sensor is usually not directly exposed
to the magnetic field that should be measured, but shielded from the environment. The
magnetic field of interest is then inductively coupled to the SQUID via a flux transformer
5.2 SQUID magnetometry 63
that consists in the easiest case of a pickup coil (exposed to the environment) and an
input coil (close to the SQUID). In order to avoid background signals, one can also use a
gradiometer; it consists of coils wound in opposite directions. As a magnetic field rapidly
decreases spatially, one can thus distinguish between local and distant magnetic field
sources: while the latter induces equally, but opposite currents within the two coils, local
fields of interest will cause a net signal.
Magnetic Property Measurement System
Magnetization measurements performed in the framework of this thesis were obtained on a
7T MPMS XL (Magnetic Property Measurement System) built by Quantum Design [91].
It consists of an rf SQUID sensor, protected by a superconducting shield that guarantees
a stable environment. The detection coil is a second-order gradiometer, consisting of three
sets of coils, where the outer coils are wound opposite to the inner ones. In the dc mode,
the sample is moved through those detection coils, changing the flux. This flux change is
then detected by the SQUID sensor; the overall output signal is the absolute magnetization
in “emu” (electromagnetic unit), which is usually normalized to the mass of the sample.
Furthermore, one can also perform ac measurements, where a small ac drive magnetic
field is applied. This causes a time-dependent moment in the sample that allows the mea-
surement of the “dynamic susceptibility” without motion [179]. At very low frequencies,
this quantity corresponds to the static susceptibility χ that can be extracted from the
slope of field-dependent dc magnetization measurements. At higher frequencies, however,
the signal might gain a phase shift ϕ. In this case, the susceptibility is conventionally
described by the real and imaginary parts:
χ′ = χ cosϕ (5.1)
χ′′ = χ sinϕ (5.2)
where the imaginary component χ′′ indicates dissipative processes in the sample; those
appear for example in ferromagnets, spin glasses or type II superconductors.
The MPMS includes computer controlled temperature and magnetic field stabilization;
temperatures between 1.6K and 400K, as well as magnetic fields between -7T and 7T are
accessible. In order to reveal hysteretic behaviour, special care has to be taken concerning
the temperature and field setting mode [10]. When measuring at stabilized temperatures
T , the stabilization process usually also includes oscillating around the target temperature
and its duration depends on the setpoint temperature. For a material with time-dependent
magnetization M , both lead to non-reproducibile M(T ) curves. Therefore, we typically
64 5 Materials and methods
chose to sweep the temperature in M(T ) measurements1. For the field setting, the “oscil-
lating mode” is the most accurate, as the magnetic field over- and undershoots the target
value in cycles with decreasing relative amplitude in order to acquire an optimal result.
However, for hysteretic samples one should take the “no overshoot” mode, meaning that
the magnetic field is changed monotonously to the desired value.
Furthermore, one has to consider the effect of the remanent magnetization captured
in the superconducting coils. Usually, we therefore determine the zero field by searching
at temperatures above any hysteretic phase the magnetic field (in the range of a few G),
which leads to zero signal at the SQUID. However, as the cooling process in a homogeneous
zero field can be crucial (especially for superconductors), some measurements were also
done using the Quantum Design “ultra low field” option which guarantees field nulling
better than 0.05G remanent field2. We did not find any qualitative difference of the
magnetization compared to measurements with our standard procedure to determine the
zero field.
Samples are typically mounted with the help of a plastic straw. In the case of low-signal
measurements, the mounting should be as symmetric as possible around the sample in
order to avoid that the background signal has a different center than the sample position;
in this case, an asymmetric signal would be generated that can not be analysed by the
MPMS software. For measurements with the magnetic field applied along the cleaved
surface of a plate-like sample, the sample can be fixed between two stripes of plastic foil
by wrapping Teflon tape around them. For the perpendicular direction, both halfs of a
gelatine capsule are padded by Teflon tape or cotton to form a plateau where in between
the sample can be placed. Both, plastic foil and gelatine capsule, can be sewed in the
straw.
5.3 Investigated samples
In the framework of this thesis, several EuFe2(As1−xPx)2 high quality single crystals syn-
thesized in the group of P. Gegenwart (University of Göttingen / Augsburg) by the Bridge-
1 Typical measurements take less than 10 s with the settings: 4 cm scan length, 2 scans per measurements
and 24 points, i.e. for a temperature sweep with 0.2K/min, the temperature error is less than 0.05K
and thus negligible (visible also in the absent thermal hysteresis in the paramagnetic regime). For ac
measurements covering a big temperature range, we typically chose the sweep velocity 0.1K/min, as
here measurements usually are slower. With the parameters: 1G drive amplitude, 7Hz wave frequency,
amplifier gain 1, 1 block to average, 1 scan per measurement and 1 s settling time, measurements are
faster than 1min, i.e. in this case the temperature error is less than 0.1K.
2 Those measurements were performed in the group of R. Kremer, MPI FKF, Stuttgart
5.3 Investigated samples 65
man method [230] were investigated by magnetization measurements (see chapter 7); Table
5.2 summarizes their compositions x and masses m.
x 0 0.055 0.09 0.12 0.16 0.165
m(mg) 6.1 9.7 0.45 1.1 2.3 7.0
x 0.17 0.26 0.35 0.39 1
m(mg) 1.2 0.44 0.59 4.0 0.16
Table 5.2: Compositions x and masses m of EuFe2(As1−xPx)2 single crystals investigated in
magnetization measurements (see chapter 7).
For optical measurements in the infrared frequency range (see chapter 8), further freshly
cleaved EuFe2As2 and BaFe2As2 single crystals with shiny surfaces> 1mm2 were available;
for terahertz measurements (see attachment A), thin Ba(Fe1−xCox)2As2 films grown by
pulsed laser deposition [180] were supplied by S. Haindl and K. Iida (IFW Dresden).

6
EU BASED IRON PNICTIDES
EuFe2As2 is exceptional among the parent compounds of the iron pnictides, as it exhibits
- additional to the Fe spin density wave - long-range magnetic order of the Eu2+ local
moments at low temperatures. Nevertheless, bulk superconductivity can be induced by
mechanical pressure, isovalent substitution and by electron or hole doping. Thus, Eu based
iron pnictides offer the extraordinary possibility to study the interplay of unconventional
superconductivity, itinerant and local magnetism.
In this chapter, first the magnetic properties of EuFe2As2 are introduced. Their de-
velopment under pressure, doping and Eu substitution are in the focus of the following
discussion, providing a basis for a unified phase diagram which will be presented in chap-
ter 7. Afterwards, the electronic properties of Eu based iron pnictides are reviewed,
focusing on the influence of the Eu2+ magnetic moments. Additionally, measurements
on Eu 122 compounds that revealed important general properties for iron pnictides are
shortly presented.
6.1 EuFe2As2
Measurements using a commercial SQUID magnetometer are ideal to get first insight into
the magnetic properties of a material. The standard procedures commonly employed to Eu
122 iron pnictides are summarized in Table 6.1. One should note that further investigations
68 6 Eu based iron pnictides
such as (resonant) x-ray scattering, Mössbauer studies and neutron diffraction1 are usually
needed to completely understand the magnetic ordering of such layered materials, in which
often inter- and intralayer interactions compete, causing “exotic” types of magnetism.
Measurement Information
M(T ) at T = Ts,SDW Feature at spin density wave transition.
M(T ) at T > TEu Curie-Weiss fit provides information about the predom-
inant magnetic interactions between Eu2+ spins and the
valency of Eu.
M(T ) and M(H)
at T ≤ TEu
Shape of curves provides information about the ordering.
M(T ) at T = TEu TEu shifts with increasing field to lower temperatures for
antiferromagnetic order, to higher temperatures for ferro-
magnetism.
M(T ) at T < TEu Hysteresis often results from ferromagnetism, spin glass
behaviour or superconductivity.
M(H) at T < TEu Saturated moment gives evidence about the Eu valency.
Table 6.1: Summary of standard procedures to get information about the magnetism in
Eu 122 iron pnictides from temperature- (T ) and field- (H) dependent magnetization (M)
measurements.
Combined magnetization and Mössbauer studies revealed already in 1993 that EuFe2As2
exhibits two magnetic transitions: an itinerant ordering in the Fe subsystem at ∼ 190K
is followed at lower temperatures (∼ 19K) by the local ordering of magnetic Eu2+ mo-
ments [216]. The itinerant order can be identified as a spin density wave that is accom-
panied by a tetragonal-to-orthorhombic structural phase transition [26]. Resistivity and
specific heat show only one sharp feature at Ts,SDW, indicating a first-order transition sim-
ilar to SrFe2As2 (see Fig. 6.1a-b, [27, 28, 181]). The spin density wave is also visible as a
jump in the magnetization (see Fig. 6.1c, [182]). However, as divalent Eu2+ magnetic mo-
ments (S = 7/2, L = 0) dominate the magnetization, usually a paramagnetic background
has to be subtracted before identifying the tiny feature.
Below TEu ∼ 19K, the temperature-dependent magnetization is basically constant along
the c-axis, while a clear cusp appears for magnetic fields applied in the ab-plane (see
Fig. 6.1d-e). Both evidences antiferromagnetic behaviour. However, the Curie-Weiss fit
indicates predominant ferromagnetic interactions among the Eu2+ spins [28, 182, 216].
Therefore, in analogy to other layered systems, A-type antiferromagnetism was proposed,
meaning that spins order ferromagnetically within the ab-plane plane, but neighbouring
layers are coupled antiferromagnetically. This suggestion was confirmed by neutron and
1 Unfortunately, Eu is a strong neutron absorber, complicating those investigations [8].
6.1 EuFe2As2 69
1 0 2 0 3 00
2
1 6 0 2 0 0 0
4
8
0 1 0 0 2 0 0
0 . 2
0 . 4
0
2
0 1 2 0
3
6
0
3
6
1 5 0
2 0 0
( e )  H  | |  c ,  0 . 1  T
  χ d
c (e
mu
 / m
ol)
T  ( K )
 
   
 (10 -4 emu / mol)
T  ( K )
 
( c )
( b )

 a
b (m
Ω
 cm
)
T s , S D W
T E u
T  ( K )
 
( a )
( g )  H  | |  c
( f )  H  | |  a b
  χ d
c (e
mu
 / m
ol)
 
( d )  H  | |  a b     0 . 1  T
M (µB  / f.u.)
µB H  ( T )
 
2 K
1 5 K
2 5 K
M (µB  / f.u.)
 
2 K
1 5 K
2 5 K
C (J / mol K)
 
Figure 6.1: Standard characterization measurements on EuFe2As2. (a) The resistivity ρab(T )
shows kinks at Ts,SDW and TEu [224]. (b) While the specific heat C(T ) exhibits a pronounced
peak at Ts,SDW, (c) for magnetization measurements the paramagnetic background first has to
be extracted to identify a tiny feature caused by the spin density wave transition [28]. (d) The
temperature-dependent dc susceptibility χdc(T ) = M(T )/µ0H shows for an in-plane magnetic
field (H ‖ ab) a cusp at TEu and (e) flattens at T < TEu for H ‖ c. Both is typical for an
antiferromagnet with the easy axis in the ab-plane. (f) At 2K (blue line), M(H) saturates for
H ‖ ab at ∼ 1.0T, (g) for H ‖ c at ∼ 1.6T. The saturation fields increase for 15K (purple
line) and 25K (magenta line). A step-like increase for H ‖ ab indicates a spin-flip or flop (also
called “metamagnetic transition”), which is typical for an antiferromagnet [182].
resonant x-ray diffraction measurements [8, 183, 189]; the detailed magnetic structure of
EuFe2As2 is shown in Fig. 6.2. Both, itinerant Fe and local Eu2+ order are commensurate,
with the spins pointing parallel or antiparallel along the a-axis, consistent with theoretical
predictions [181]. One should note that Mössbauer and magnetic torque measurements
indicate a slight canting (∼ 10◦) of the Eu2+ moments out of the ab-plane [234, 253], which
was not observed by neutron and resonant x-ray measurements [8, 183, 189, 195]. While
the Eu2+ magnetic order is already suppressed at fields of only ∼ 1T [7], the spin density
wave is still robust in pulsed magnetic fields of 55T [190].
70 6 Eu based iron pnictides
Figure 6.2: Magnetic struc-
ture of EuFe2As2 at 2.5K [8].
Fe2+ moments (brown ar-
rows) align antiferromagnet-
ically along the a- and the
c-axis, but ferromagnetically
along the b-axis. Eu2+ mo-
ments (blue arrows) align
within one Eu layer ferro-
magnetically along the a-
axis, and neighbouring ab-
planes are coupled antiferro-
magnetically.
Table 6.2 summarizes the magnetic properties of related compounds that are located
at the “end” of Eu 122 phase diagrams. Only EuFe2As2 exhibits a spin density wave
transition. Furthermore, the Eu2+ magnetic order varies tremendously among the different
compounds, although Eu is in all cases divalent1. The origin of the huge diversity of
different phases is quite simple: as different layers are too far separated for a direct overlap
of the Eu 4f -orbitals, the magnetic interactions are probably mediated via conduction
electrons by the indirect RKKY-exchange [36]. However, this indirect coupling oscillates
between ferro- and antiferromagnetic regimes depending on the details of the Fermi surface.
Theoretical calculations by Akbari et al. revealed even an influence of the spin density
wave on the RKKY-exchange (see also chapter 7.1, [11, 219]). Thus, when passing through
the Eu 122 phase diagrams, strong changes in the Eu2+ magnetic order can be expected.
Compound TEu Weiss Proposed
order
Direction Ref.
EuFe2As2 19K FM A-type AFM a-axis [8, 216]
EuFe2P2 29K FM FM c-axis [210, 211]
EuRu2As2 17K FM FM c-axis [215]
EuCo2As2 39K FM A-type AFM
vs. helical
ab-plane vs.
almost along
c-axis
[214, 251]
EuNi2As2 14K AFM [216]
Table 6.2: Characteristic information about the Eu2+ magnetism in Eu 122 parent com-
pounds: magnetic ordering temperature TEu, predominant spin exchange given by the sign of
the Curie or Néel temperature, proposed order and spin direction.
1 In the case of EuCo2P2 and EuRh2As2, mixed Eu valencies between 2 and 3 appear [217, 218]. For both,
incommensurate helimagnetism was observed. Bandstructure calculations indicate a strong sensitivity
of the magnetic configuration on the Eu valency [218].
6.2 Phase diagrams 71
6.2 Phase diagrams
In order to compare several compounds, the transition temperatures are consistently de-
termined as followed: superconductivity is defined by its onset and the zero resistivity
temperature, Tc,on and Tc,0, respectively. The Eu2+ magnetic ordering temperature TEu
corresponds to a kink in resistivity and a peak in magnetization measurements. Standard
measurements on Eu 122 pnictides often do not show clearly distinguishable features that
would allow a distinct separation of structural and spin density wave transition tempera-
tures. Thus, for the sake of simplicity, those transitions will be treated as one and referred
to as Ts,SDW.
6.2.1 Pressurized systems
In the case of isovalent substitution, a certain element is replaced by a smaller (larger)
one to shrink (expand) the unit cell similar to applied mechanical pressure. However, one
should keep in mind that even isovalent substitution induces additional chemical disorder.
It is still under debate, whether such disorder could be the actual tuning parameter through
the iron pnictide phase diagrams [68].
Mechanical pressure
In 2009, Miclea et al. reported that pressures around 2GPa induce in EuFe2As2 supercon-
ductivity up to ∼ 30K [29]. However, zero resistivity was prohibited by a re-entrance of
resistivity at the Eu2+ magnetic ordering temperature (see Fig. 6.3a). Detailed investiga-
tions by Matsubayashi and Kurita et al. revealed that bulk superconductivity is achieved
only if hydrostatic pressure is transmitted ([222, 224], see Fig. 6.3b), reconciling several
pressure studies [188, 220, 221, 223, 225–229, 232].
Fig. 6.4 displays the phase diagram of EuFe2As2 under hydrostatic pressure [222, 224].
At low pressures, the spin density wave gets continuously suppressed and the Eu2+ mag-
netic ordering temperature increases slightly (see also Fig. 6.3c). Around ∼2GPa, TEu
starts to rise strongly. Surprisingly, this change in Eu2+ magnetism coincides with the
pressure, where the onset of superconductivity - without reaching zero resistance - can be
observed. Thus, in a narrow pressure range, Eu2+ magnetism, spin density wave order
and traces of superconductivity coexist. Zero resistance and bulk superconductivity oc-
curs only between ∼ 2.5 − 3GPa. It disappears as soon as the Eu2+ magnetic ordering
temperature is as high as Tc,on.
Magnetization measurements indicate that A-type antiferromagnetic Eu2+ order coex-
ists with superconductivity. Above ∼ 6GPa, a ferromagnetic signal is observed, visible in
a clear out-of-phase signal of the ac susceptibility (see Fig. 6.3d, [222]). TEu increases fur-
72 6 Eu based iron pnictides
0 2 0 4 00 . 0
0 . 2
0 . 4
0 5 0 1 0 0 1 5 0 2 0 0 0 . 0
0 . 2
0 . 4
T c , o n
T E u
 ( b )  
2 . 3 0  G P a
 ( a )  
T  ( K )

 (m
Ω
 cm
)
 
 
2 . 0 3  G P a
T c , o n
T s , S D W
T E u
 0  G P a 1 . 1  G P a 1 . 9  G P a 2 . 2  G P a 2 . 6  G P a
T  ( K )

 (m
Ω cm)
 
1 5 2 0 2 51
2
3
4
2 0 4 0 6 0
1 . 1  G P a
0  G P a  χ d
c (e
mu
 / m
ol)
T E u , A F M
0 . 8  G P a
T  ( K )
 ( c )  
T E u , F M8 G P a
 ( d )  
   χ'ac  (a.u.)6 G P a
4 G P a
T E u , A F M
   χ''ac  (a.u.)
T  ( K )
 
Figure 6.3: Characteristic temperature-dependent in-plane resistivity and magnetization of
EuFe2As2 under pressure. Grey arrows highlight the development of the transition tempera-
tures with pressure. (a) Using silicone oil as pressure transmitter, superconductivity sets in at
Tc,on ∼ 30K, but due to a resistivity re-entrance at TEu, zero resistivity is not achieved [29].
(b) Using Daphne 7474 as transmitting medium, Ts,SDW is continuously suppressed with pres-
sure. Around 2.6GPa, zero resistance without re-entrance and non-Fermi liquid behavior
(R(T ) ∼ T for T > Tc) is observed [224]. (c) DC susceptibility: at low pressures, TEu in-
creases slightly. The cusp is typical for antiferromagnetic order [222]. (d) AC susceptibility:
antiferromagnetism does not induce an out-of-phase signal (χ′′ ≈ 0 at 4GPa). However, at
∼ 6GPa a second feature appears with χ′′ > 0 that strongly shifts to higher temperature
and gets dominant with increasing pressure. The strong out-of-phase signal is typical for
ferromagnetism [222].
6.2 Phase diagrams 73
0 2 4 6 8 1 0 1 20
2 0
4 0
1 0 0
1 5 0  E u F e 2 A s 2   T s , S D W T c , o n T c , 0 T E u
                 
 
P r e s s u r e  ( G P a )
 T (
K)
 
Figure 6.4: Phase diagram of EuFe2As2 under pressure (open symbols: Ref. [222], closed
symbols: Ref. [224]). TEu (blue diamonds) slightly increases at low pressures and starts to rise
stronger just before Ts,SDW (black squares) gets suppressed and the superconducting dome is
positioned (Tc,on: light red circles, Tc,0: red circles).
ther up to pressures around 10GPa, where a collapsed tetragonal phase transition takes
place [221, 223]. As the ionic radius of Eu2+ is larger than that of Eu3+, this struc-
tural phase transition coincides with an increase of the Eu valency. As trivalent Eu is
nonmagnetic, TEu decreases for higher pressures [222].
Isovalent substitution: EuFe2(As1-xPx)2
In 2009, Ren et al. discovered in EuFe2(As0.7P0.3)2 superconductivity that sets in at
∼ 26K and coexists with Eu2+ ferromagnetism below ∼ 20K [30]. Both transitions
are visible in the specific heat, proving their bulk character. This observation attracted
tremendous interest in the condensed matter community, as superconductivity and ferro-
magnetism are usually antagonistic phenomena (see chapter 3.3) and “chemical” pressure
was discovered as a tuning parameter through the iron pnictide phase diagram.
It turned out that the electronic properties of EuFe2(As1-xPx)2 are extremely sensitive
to the synthesis, possibly due to procedure-dependent internal strain: for single crystals
grown by the Bridgeman method, the superconducting dome appears around x ∼ 0.2 [9,
10, 230, 233, 235, 238, 240, 241, 272, 280], while for polycrystals as well as single crystals
grown by solid state reaction the dome is shifted to x ∼ 0.3 [30, 231, 232, 234, 236, 237,
243]. However, the Eu2+ magnetic order is not affected by the growth process. Fig. 6.5
compares the resulting phase diagrams, which resemble a lot EuFe2As2 under pressure.
Most remarkably, TEu starts to increase above x ∼ 0.12, which again coincides with the
onset of superconductivity. This reveals a significant interplay between electronic and
magnetic properties in those compounds.
74 6 Eu based iron pnictides
However, in contrast to EuFe2As2 under pressure, TEu decreases at lower substitution
levels. It is intriguing to assign the minimum around x ∼ 0.12 to the change from anti- to
ferromagnetic Eu2+ ordering, as signatures of ferromagnetism are observed at high sub-
stitution levels, consistent also with theoretical calculations [207, 239]. However, several
measurements indicated antiferromagnetic Eu2+ order up to significantly higher P concen-
trations [230, 243]. Furthermore, even results for the pure P compound are contradictory:
while Mössbauer and magnetization measurements indicate a successive helical ordering
around 26K with the spins tilted 15 ◦ from the c-axis, neutron measurements state pure
ferromagnetism. It should be noted that indications for successive magnetic orderings
were also reported for mixed compounds [232, 234, 236, 237, 243]; in Ref. [242], the lower
transition was attributed to a minority phase. One contribution of this thesis was to rec-
oncile those - on the first view contradictory - reports (see Table 6.3), which is presented
in more detail in chapter 7, as well as in Ref. [9] and [10].
0 . 0 0 . 4 0 . 80
1 0
2 0
1 0 0
2 0 0
0 . 0 0 . 4 0 . 8
( a )  B r i d g e m a n ( b )  S o l i d  s t a t e  r e a c t i o n  
 
 
T (K
)
T s , S D W   T c , o n   T c , 0    T E u  
P  c o n t e n t  i n  E u F e 2 ( A s 1 - x P x ) 2
 
Figure 6.5: Phase Diagram of EuFe2(As1-xPx)2 for samples grown by (a) the Bridgeman
method [9, 10, 230, 233, 235, 238, 240, 241, 272, 280] and (b) solid state reaction [30, 231,
234, 236, 237]. In both cases, TEu (blue diamonds) shows a minimum around x ∼ 0.12.
This minimum is close to the composition, where Ts,SDW gets suppressed (black squares) and
superconductivity sets in (Tc,on: light red circles, Tc,0: red circles).
Isovalent substitution: Eu(Fe1-xRux)2As2
An alternative way of isovalent substitution is the replacement of Fe by Ru. It should
be noted that Ru influences the volume of the unit cell much less than P substitu-
tion [246]. Nevertheless, Eu(Fe1-xRux)2As2 also shows bulk superconductivity in a narrow
range around x ∼ 0.2 (see Fig. 6.6, [31, 245]). However, the onset of superconductivity
can be observed at least up to x = 0.55, which is in stark contrast to the mechanically
pressurized or P substituted case. One obvious difference to those systems is that the
6.2 Phase diagrams 75
Technique Sample Observation Eu2+ Ref.
Specific heat Poly Increasing magnetic field broad-
ens and shifts anomaly to
higher temperatures.
FM [30]
Magnetic
compton
scattering
Poly Enhanced spin polarization of
the Fe-3d orbital.
FM [231]
Mössbauer Poly Increased Eu hyperfine field,
Eu2+ spins almost aligned along
c-axis (20◦ tilted).
FM [234]
Neutron Single No antiferromagnetic reflec-
tions, Eu2+ spins aligned along
c-axis.
FM [241]
Neutron Single Eu2+ spins aligned along c-axis,
minority phase with lower or-
dering temperature.
FM [242]
Magneti-
zation
Single Shape and field-dependence of
magnetization.
AFM [230,
243]
Muon, Möss-
bauer
Single Eu2+ spins almost aligned along
c-axis (12◦ tilted).
AFM [243]
Table 6.3: Arguments for Eu2+ ferromagnetism (FM) vs. antiferromagnetism (AFM) in
superconducting EuFe2(As1-xPx)2 polycrystalline samples (poly) or single crystals (single).
Eu2+ magnetic ordering temperatures of EuFe2As2 and EuRu2As2 are quite similar and
therefore, TEu basically stays constant in the whole phase diagram. Thus, it is intriguing
to conclude that superconductivity gets suppressed, if the Eu2+ magnetic ordering ex-
ceeds Tc. However, this conclusion does not explain why Eu(Fe1-xRux)2As2 exhibits bulk
superconductivity only in a very narrow range.
Despite the lower ordering temperatures than in the case of EuFe2P2, EuRu2As2 is also
suggested to order ferromagnetically along the c-axis (see Table 6.2). Therefore, it is not
surprising that for Eu(Fe1-xRux)2As2, successive anti- and ferromagnetic transitions were
observed [31, 245], too, and Mössbauer studies on a superconducting sample indicate a
reorientation of the Eu2+ spins towards the c-axis [31].
Mechanical vs. chemical pressure
In order to compare the influence of mechanical and chemical pressure, Sun and Tokiwa
et al. investigated EuFe2As2 and EuFe2(As1-xPx)2 under pressure, concluding that the
76 6 Eu based iron pnictides
0 . 0 0 . 5 1 . 00
1 0
2 0
1 0 0
2 0 0
1 0 2 0 3 0 0 . 0
0 . 2
0 . 4( b ) T s , S D W T c , o n T c , 0 T E u
 R u  c o n t e n t  i n  E u ( F e 1 - x R u x ) 2 A s 2
 
T (K
)
( a )
T c , o n
x  =  0 . 2 5
 T  ( K )

 / 
300K
x  =  0 . 5 5
x  =  0 . 4 8
Figure 6.6: (a) Phase diagram of Eu(Fe1-xRux)2As2 [245]. TEu (blue diamonds) stays almost
constant. Superconductivity sets in (light red circles), as soon as Ts,SDW (black squares) is
suppressed. While zero resistivity (red circles) is achieved only around x ∼ 0.2, traces of
superconductivity exist up to x = 0.55, (b) visible in resistivity measurements for x = 0.25
(magenta line), 0.48 (purple line) and 0.55 (pink line), which also exhibit a resistivity re-
entrance at TEu.
overall behaviour is very similar [232, 238]1. However, when incorporating also the Eu2+
magnetic order in the phase diagram, as it is done in Fig. 6.7, it gets obvious that the
actual processes are more complex: choosing the equivalent pressure for complete P substi-
tution x =ˆ 15.4GPa, one can map reasonable well the electronic properties on top of each
other, however, not the Eu2+ magnetic ordering temperature. Moreover, when compar-
ing the influence on the crystallographic c- and a-axes (see Fig. 6.8), mechanical pressure
compresses the c-axis significantly stronger than P substitution if one uses the above cho-
sen equivalent. Thus, assuming that isovalent substitution just acts as chemical pressure
is clearly oversimplified: actually superconductivity is induced much faster compared to
mechanical pressure. The most plausible scenario is that the disorder induced by isovalent
substitution causes the differences in the phase diagram. Disorder could also weaken the
RKKY-exchange, explaining why TEu first decreases in EuFe2(As1-xPx)2.
1 Sun et al. proposed that a pressure-induced valence change of Eu sets in already at the left side of the
superconducting dome for both, EuFe2As2 under mechanical pressure and EuFe2(As1-xPx)2 [232]. This
could lead to additional electron doping, possibly even favouring superconductivity. However, previous
Mössbauer studies on superconducting EuFe2(As0.7P0.3)2 did not reveal any Eu3+ foreign phase [243]
and Matsubayashi et al. [222] revealed valency changes in EuFe2As2 only at much higher pressures.
Intriguingly, changes in the valency are reported in both cases close to the solidification of the pressure
transmitting medium. It is not clear how this should induce a measurement error, nevertheless further
investigations are necessary to clarify this issue.
6.2 Phase diagrams 77
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00
2 0
4 0
1 0 0
2 0 0 0 5 1 0 1 5
 T s , S D W T c , 0 T E u
      
 C h e m i c a l   p r e s s u r e
 
T (K
)
E u F e 2 A s 2
 M e c h a n i c a l  p r e s s u r e  ( G P a )
Figure 6.7: Phase diagrams of EuFe2As2 single crystals under chemical (P substitution, open
dark symbols, [9, 10, 230, 233, 235, 238, 240, 241, 272, 280]) and mechanical pressure (closed
bright symbols, [222, 224]) mapped on top of each other, using the relation: P substitution
x =ˆ 15.4GPa. While the electronic properties are quite similar, TEu (blue diamonds) develops
differently. However, in both cases TEu starts to increase stronger close to the pressure, where
Ts,SDW (black squares) gets suppressed and superconductivity appears (Tc,0: red circles).
0 . 0 0 . 4 0 . 8
1 0
1 1
1 2
0 . 0 0 . 4 0 . 8
3
4
5
0 5 1 0 1 5 0 5 1 0 1 5
c - 
axis
 (Å)
C h e m i c a l  p r e s s u r e  ( P  s u b s t i t u t i o n )
 
c o l l a p s e d  t e t r a g o n a l
 M e c h a n i c a l   C h e m i c a l
 
a - axis (Å)
  M e c h a n i c a l  p r e s s u r e  ( G P a )  
Figure 6.8: Crystallographic c-axis (left) and a-axis (right) of EuFe2As2 under chemical
(P substitution, blue open points, [230, 236]) and mechanical pressure (green squares, [221]).
Using the equivalent: P substitution x =ˆ 15.4GPa that maps the electronic properties on top
of each other, reveals that mechanical pressure contracts the c-axis much stronger than P
substitution.
78 6 Eu based iron pnictides
Summary
In summary, when comparing the phase diagram of mechanically pressurized EuFe2As2
with those of EuFe2(As1-xPx)2 and Eu(Fe1-xRux)2As2, we can conclude for the interplay
of superconductivity and magnetism:
• Microscopic coexistence of spin density wave ordering and superconductivity was yet
not evidenced.
• TEu does not behave universal. However, for mechanically pressurized EuFe2As2 and
EuFe2(As1-xPx)2, it increases strongly as soon as the spin density wave is suppressed
and superconductivity sets in.
• Considering only bulk superconductivity, the superconducting dome is rather nar-
row in all cases. For mechanical pressure and P substitution, superconductivity is
suppressed as soon as TEu ≈ Tc,on.
• In all phase diagrams, the Eu2+ magnetic order changes with substitution. However,
contradictory reports exist which kind of magnetism coexists with superconductivity.
6.2.2 Electron doping
In the case of 122 iron pnictides, electron doping can be realized by the substitution of Fe
by an atom that prefers a lower valence state. Indeed, superconductivity up to ∼ 25K was
found in Co doped BaFe2As2 [247]. However, similar approaches were much less successful
for Eu based 122 iron pnictides.
Eu(Fe1-xCox)2As2
In 2009, Jiang et al. presented results on Eu(Fe0.89Co0.11)2As2 single crystals grown by
using (Fe,Co)As as self-flux, which showed the onset of superconductivity at ∼ 21K [32].
However, with this synthesis technique only polycrystals where produced that exhibit zero
resistivity at low temperatures [249], but no single crystals [248–251, 258, 260].1 The
synthesis of single crystals with zero resistance could be achieved only by using Sn-flux,
however, with very low transition temperatures (significantly below 10K) [252–257, 259].
Fig. 6.9 compares the resulting phase diagrams2. One should note that here, the growth
1 Chen et al. argued that in their polycrystals, the coupling between conduction electrons and local
Eu2+ moments is reduced, visible in resistivity measurements with less obvious features at TEu and the
absence of re-entrant superconductivity [249].
2 Only the study by Ying et al. [248] does not fit to the others. The reason is probably that only nominal
sample compositions are given. Due to this uncertainty, it is excluded from the further discussions.
6.2 Phase diagrams 79
technique influences all properties, also the Eu2+ magnetic transition. In both cases, the
Eu2+ magnetic ordering temperature shows a minimum, where structural as well as spin
density wave gets suppressed and the rather narrow superconducting dome is positioned
around this composition. Mössbauer experiments on superconducting compounds indi-
cate that the spin density wave does not take place in the whole sample volume [254].
Thus, again rather phase separation than microscopic coexistence of superconductivity
and itinerant Fe magnetism is observed.
0 . 0 0 . 2 0 . 40
1 0
2 0
1 0 0
2 0 0
0 . 0 0 . 2 0 . 4
( b )  S n - f l u x
i n  E u ( F e 1 - x C o x ) 2 A s 2
 
 
T (K
)
( a )  S e l f - f l u x
 E l e c t r o n  d o p i n g
T s , S D W   T c , o n   T c , 0    T E u   
Figure 6.9: Phase diagram of Eu(Fe1-xCox)2As2 samples grown using (a) self-flux [249–
251, 258, 260] and (b) Sn-flux [252–257, 259]. In both cases, the Eu2+ magnetic ordering
temperature (blue diamonds) shows a minimum around the composition, where Ts,SDW (black
squares) gets suppressed and the superconducting dome is positioned (Tc,on: light red circles,
Tc,0: light red circles). Zero resistivity for self-flux grown samples was only observed in
polycrystalline samples [249].
More similarities to mechanically pressurized and isovalently substituted EuFe2As2 can
be found when comparing the evolution of Eu2+ magnetic order throughout the phase
diagram: as soon as the spin density wave gets suppressed, the Eu2+ spins cant more and
more out of the ab-plane. Although magnetization measurements show up to high Co
contents indications for antiferromagnetic interlayer coupling (often interpreted in terms
of canted antiferromagnetism [253, 254, 257] or helimagnetism [32, 251]) and multiple
magnetic transitions [250, 251, 256, 257], neutron diffraction measurements on a super-
conducting sample concluded ferromagnetic ordering along the c-direction with a moment
size of 6.2µB, slightly lower than the theoretical expected value of ∼ 7µB. Those contra-
dictory reports get even more mysterious, when considering that EuCo2As2 shows very
similar magnetic behaviour to EuFe2As2: even signatures of a metamagnetic transition
were observed in M(H)-curves around ∼ 3T [214].
80 6 Eu based iron pnictides
Eu(Fe1-xNix)2As2
Surprisingly, Ni substitution on the Fe site does not induce superconductivity at all [251,
261, 262]. Mössbauer measurements on doped compounds reveal a canting of the Eu2+
spins out of the ab-plane and multiple magnetic transitions appear that were interpreted
in terms of a crossover from anti- to ferromagnetism. Ren et al. concluded that this
ferromagnetism suppresses superconductivity [261]. However, this argumentation has two
weak points: first of all, the end member EuNi2As2 is antiferromagnetic, and not ferro-
magnetic [216]. Secondly, when comparing the development of TEu and Ts,SDW for Co and
Ni, both can be mapped perfectly on top of each other at low doping level1 (see Fig. 6.10).
0 . 0 0 . 1 0 . 21 0
2 0
1 0 0
2 0 0
 E l e c t r o n  d o p i n g
T s , S D W   T E u  
c l o s e d  s y m b o l s :  C oo p e n  s y m b o l s :  N i
 
T (K
)
Figure 6.10: Phase di-
agram of Eu(Fe1-xYx)2As2
with Y = Co [249, 258]
(closed symbols) or Ni [261]
(open symbols). The x-
axis of the Ni phase diagram
was expanded by a factor
of two, as Ni can provide
twice as much electrons as
Co. TEu (blue diamonds)
and Ts,SDW (black squares)
perfectly match.
Eu(Fe1-xIrx)2As2
Up to now, the most “successful” approach to induce superconductivity by electron doping
has turned out to be Ir substitution [33, 263, 264]. In 2013, Paramanik et al. reported
for Eu(Fe0.86Ir0.14)2As2 polycrystals an onset of superconductivity at 22.6K and zero-
resistivity as well as diamagnetic shielding at 19K, which is disturbed by a resistivity re-
entrance due to Eu2+ magnetic ordering around 14K [33]. Only two months later, Jiao et
al. published results on Eu(Fe0.88Ir0.12)2As2 single crystals with a sharp superconducting
transition between 22K and 21K (without any resistivity re-entrance) [263]. Both groups
proposed a canting of the Eu2+ spins out of the ab-plane. However, whereas the first
group suggested canted A-type antiferromagnetic ordering of Eu2+, the latter favoured a
ferromagnetic ordering.
1 In order to compare them correctly, one has to consider that Ni substitution provides two electrons
per substituent, whereas Co provides only one. Thus, the x-scale of the Ni phase diagram should be
expanded by a factor of two. Indeed, it is quite surprising that the mapping works out so well, as the
end members of the phase diagrams, EuNi2As2 and EuCo2As2, have quite different Eu2+ magnetic
ordering temperatures (see Table 6.2).
6.2 Phase diagrams 81
Summary
Summing up, electron doping induces superconductivity in EuFe2As2 when substituting
Fe by Co or Ir. While in the latter case, zero resistivity and a clear diamagnetic shielding
was observed around 20K, the results for Co doping are less convincing: the diamagnetic
shielding is significantly lower and the phase diagram strongly depends on the growth
technique. Ni substitution does not induce superconductivity at all, although Ts,SDW and
TEu show exactly the same behaviour as for Co doping.
When comparing electron doping to isovalent substitution and mechanical pressure, the
overall behaviour is very similar: superconductivity probably does not coexist with the
spin density wave order on a microscopic scale and TEu shows an almost identical behaviour
as in the case of P substitution. The reports about the type of Eu2+ magnetic order are
as contradictory as for isovalent substitution. Despite those similarities, one new aspect
concerning the interplay of superconductivity and magnetism should be emphasized: the
results for Co doping clearly show that superconductivity with zero resistivity can appear,
even when the onset temperature is much lower than TEu. Thus, one could speculate
that superconductivity is only suppressed by the Eu2+ magnetic order, if the two antag-
onistic phenomena would like to set in at similar temperatures. This might happen for
Ni substitution, as Ni doping usually leads to slightly lower critical temperatures than
Co [247, 265].
6.2.3 Eu dilution
Chemical substitution at the Eu site does not only act as doping or isovalent pressure, it
also weakens the Eu2+ magnetism. Up to now, poly- and single crystals were successfully
grown for Ca, Sr, Ba, K, Na and La substitution: Ca, Sr and Ba are isovalent substitu-
tions; K and Na substitution leads to hole doping, La to electron doping. In some cases,
those approaches were further combined with physical pressure or additional substitutions
at another element site (“codoping”). Unfortunately, although the magnetic and super-
conducting properties are directly linked to each other, detailed studies on the evolution
of the Eu2+ magnetism dependent on dilution level are still rare.
Isovalent substitution
Isovalent substitution on the Eu site is not expected to induce superconductivity, as cor-
responding 122 parent compounds exhibit “only” structural as well as spin density wave
transitions. Those appear for Ca, Eu, Sr and Ba approximately at 170K, 190K, 205K
and 140K, respectively [5]. One should note that the transition temperatures do not just
82 6 Eu based iron pnictides
follow the ionic radii, which are increasing from Ca to Ba [66].1 Thus, only Ca substitution
will induce positive chemical pressure and shrink the unit cell volume, while Ba and Sr
will have the opposite effect.
The dilution effect on the local Eu2+ magnetic order can be summarized as followed:
• As expected, Ba substitution continuously suppresses Ts,SDW [269]. While the lowest
detectable TEu = 0.5K was found for x = 0.45, all samples with higher Ba content
(except BaFe2As2) still show at low temperatures an enhanced response of the spe-
cific heat. This indicates that Eu2+ magnetic moments significantly influence the
material’s properties even at very high dilution levels.
• In the case of Ca substitution, the Eu2+ magnetic transition is completely suppressed
at x = 0.75, but for 50% dilution still as high as 9K [267, 268]. Additional physi-
cal pressure on Eu0.5Ca0.5Fe2As2 induces superconductivity with a maximum Tc of
24K and possibly a coexistence region of spin density wave ordering, local Eu2+
magnetism and superconductivity (around ∼ 1.4GPa).
• Several studies investigated the superconductivity in Sr diluted samples with addi-
tional 11-14% Co-doping [270–274]. While Eu(Fe1-xCox)2As2 often only shows traces
of superconductivity, in Eu diluted specimen bulk superconductivity was observed
up to 15K. It was suggested that superconductivity disappears as soon as Tc < TEu
(see Fig. 6.11, [271]). Specific heat measurements under external magnetic fields
showed that an antiferromagnetic Eu2+ order at 2K persists up to a Eu dilution of
as high as 80% [273].
Thus, the Eu2+ magnetism in EuFe2As2 iron pnictides is surprisingly robust against iso-
valent dilution.
Hole doping
In 2008, Jeevan et al. reported for hole doped Eu0.5K0.5Fe2As2 polycrystals a super-
conducting transition at 32K [34]. The high quality of the samples was indicated by a
rather sharp resistivity transition with a width of less than 2K. Bulk superconductiv-
ity was evidenced by a well-defined anomaly in the specific heat and a full diamagnetic
shielding. However, those measurements revealed only very weak features below 10K
1 The reason why BaFe2As2 shows significantly lower structural and spin density wave transition tem-
peratures as the others is yet not clear. Previous quantum oscillation measurements indicated effective
masses systematically smaller than in the case of EuFe2As2, meaning that the latter is much more
correlated [209].
6.2 Phase diagrams 83
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00
1 0
2 0
3 0  T c , o n T c , 0 T E u
E u 1 - x S r x ( F e 0 . 8 4 C o 0 . 1 4 ) 2 A s 2
 
T (K
)
S r  c o n t e n t
Figure 6.11: Phase diagram of Eu1-xSrx(Fe0.86Co0.14)2As2 [271]. The Eu2+ magnetic or-
der (blue diamonds) is continuously suppressed with Sr substitution. Superconductivity and
magnetism coexist, as long as the onset of superconductivity (Tc,on: light red circle) and zero
resistance temperature (Tc,0: light red circle) are well above TEu.
that could be ascribed to Eu2+ magnetism. As dilution typically leads to the suppres-
sion of magnetic order, it is very tentative to assign weak signatures of Eu2+ ordering
to short-range interactions. However, one has to keep in mind that even in non-diluted
compounds, the superconducting signal can be strong enough to mask Eu2+ magnetism.
Indeed, systematic magnetization studies on x = 0.38 polycrystals revealed that a small
peak buried by the diamagnetic signal shifts with increasing magnetic field towards lower
temperatures, indicating a long-range antiferromagnetic ordering [279]. Measurements on
codoped Eu0.5K0.5(Fe1-yNiy)2As2 give further evidence for such a long range magnetic or-
der at 50% dilution level: as soon as Ni doping has suppressed superconductivity, a strong
antiferromagnetic Eu2+ signal can be detected around 8K [286].
Fig. 6.12 shows the phase diagram of Eu1-xKxFe2As2. Further experimental studies [275–
282] showed that x = 0.5 actually represents the optimal doping level for poly- and single
crystals. It should be noted that the synthesis of single crystals was successfully performed
only in 2012, as K is highly reactive and hard to be controlled. Therefore, the single
crystal phase diagram is still incomplete, especially concerning higher substitution levels.
However, those doping levels are of special interest, as KFe2As2 is a particular end member
of the iron pnictides: it is superconducting with a Tc of 3.8K [283]. In Fig. 6.12, also
studies on the effect of Na doping are included [284, 285]. First measurements indicate
a rather broad superconducting dome similar to K doping (see Fig. 6.12). Additional P
substitution on a 30% diluted sample was able to increase Tc by 5K [287].
In summary, hole doping combined with Eu dilution leads to a rather broad super-
conducting dome with high Tc, which is consistent with other 122 iron pnictides [80].
84 6 Eu based iron pnictides
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00
2 0
4 0
1 2 0
1 6 0
2 0 0 E u 1 - x N a x F e 2 A s 2    T s , S D W      T c , 0
E u 1 - x K x F e 2 A s 2    T s , S D W      T c , o n      T c , 0      T E u   
 
                        T (K
)
H o l e  d o p i n g
Figure 6.12: Phase diagram of hole doped Eu1-xYxFe2As2 (Y = Na [286], K [279, 280]). The
superconducting dome and the corresponding transition temperatures are marked in red (Na:
dark red stars for Tc,0; K: light red circles for Tc,on and red circles for Tc,0; closed symbols:
single crystals [280], open symbols: polycrystalline samples [279]). The underdoped part of
the dome is depicted more transparent, as here evidence for bulk superconductivity is not
yet provided. Ts,SDW is faster suppressed for Na (grey hexagons) than for K substitution
(black squares). TEu (blue diamonds) is continuously suppressed and disappears around 60%
substitution level.
Although Na substitution leads to the faster suppression of the structual and spin density
wave transition, the superconducting domes are very similar. Experimental studies on the
Eu2+ magnetism are complicated, as the diamagnetic shielding typical for a bulk supercon-
ductor masks the Eu2+ signal. However, there is growing experimental evidence indicating
a coexistence of Eu2+ long-range magnetic order and superconductivity, consistent with
the results from isovalent Eu dilution.
Electron doping
Substituting Eu by the rare earth ion La leads to the suppression of the structural and
spin density wave transition, probably due to electron doping [288–291]. However, only
traces of superconductivity were found for the maximum possible solid-solution of x =
0.27.
Zhang et al. applied additional pressure on x = 0.22 and 0.27 samples, successfully
inducing superconductivity with sharp transitions and zero resistivity (see Fig. 6.13,
[291]). Interestingly, neither La doping nor additional pressure up to 2.2GPa do notably
influence the Eu2+ magnetic transition temperature. Indeed, TEu slightly increases under
pressure. Surprisingly, one can observe the coexistence of spin density wave magnetism,
superconductivity and local Eu2+ magnetism, while Tc is always smaller than TEu.
6.2 Phase diagrams 85
0 . 0 0 . 1 0 . 20
5 0
1 0 0
1 5 0
2 0 0
0 1 2
 
T (K
)
L a  c o n t e n t
E u 1 - x L a x F e 2 A s 2   T s , S D W T E u T c , o n T c , 0
E u 0 . 7 3 L a 0 . 2 7 F e 2 A s 2  u n d e r  p r e s s u r e
 
P r e s s u r e  ( G P a )
Figure 6.13: Phase diagram of Eu1-xLaxFe2As2 (left) and Eu0.73La0.27Fe2As2 under pressure
(right). Black squares correspond to Ts,SDW and blue diamonds to TEu. While zero resistivity
Tc,0 (red circles) appears only in a narrow dome for Eu0.73La0.27Fe2As2 under pressure, the
onset of superconductivity Tc,on (light red circles) appears in a much broader range. A coex-
istence region of spin density wave magnetism, superconductivity and local Eu2+ magnetism
shows up.
Summary: Eu dilution
When summarizing all those studies on Eu diluted compounds, the most important find-
ings concerning the interplay of magnetism and superconductivity are:
• There is growing experimental evidence that the Eu2+ antiferromagnetic interlayer
coupling is quite robust against dilution [273, 279, 286], as can be seen in Fig. 6.14.
Overall, a rather smooth decrease of TEu with dilution level takes place. This is
typical for an intermetallic compound with local antiferromagnetism that is diluted
with nonmagnetic ions [271]. Ba substitution seems to suppress the Eu2+ magnetic
ordering the fastest. Interestingly, ionic radii as well as Ts,SDW changes the most
in the case of Eu substitution by Ba. This indicates a complex interplay between
structural, electronic and magnetic properties.
• It is quite surprising that when comparing EuFe2As2 and Eu0.73La0.27Fe2As2 un-
der pressure, the latter diluted compound exhibits significantly lower critical tem-
peratures [291]. This implies that in some cases, disorder might be even more
harmful to superconductivity than Eu2+ magnetism. In contrast, Tc increases in
Eu0.7Na0.3Fe2As2 by additional P substitution on the As site [287] and in Eu1-xSrx-
(Fe0.86Co0.14)2As2 by increasing Eu dilution [271].
• Indications for phase coexistence of (zero-resistance) superconductivity with spin
density wave as well as diluted Eu2+ magnetism was reported in several compounds
86 6 Eu based iron pnictides
0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 00
1 0
2 0
 E u 1 - x B a x F e 2 A s 2   E u 1 - x C a x F e 2 A s 2   E u 1 - x S r x ( F e 0 . 8 4 C o 0 . 1 4 ) 2 A s 2   E u 1 - x K x F e 2 A s 2  
 
T (K
)
E u  d i l u t i o n  l e v e l
T E u :
Figure 6.14: Suppression of the Eu2+ magnetic ordering temperature TEu with increasing
Eu dilution for Eu1-xYxFe2As2. Y = Ba (pink open squares, [269]), Ca (beige stars, [268]),
Sr (codoped with 14% Co) (blue open diamonds, [271]) and K (dark cyan closed hexagons,
[279].
[267, 268, 285, 291], which is in stark contrast to non-diluted systems. Further
systematic studies on these compounds is highly desirable in order to shed new light
on the complex interplay between superconductivity and magnetism.
6.3 Electronic properties
6.3.1 Normal state properties
Band structure
Early angle resolved photoemission studies (ARPES) on EuFe2As2 [191, 192] revealed a
band structure typical for 122 iron pnictides: in the paramagnetic phase, electron pock-
ets around the X-point ((pi,pi)-point) and hole pockets around the Γ -point ((0,0)-point)
could be resolved. Below the spin density wave transition, the electron-like bands (at the
X-point) are folded back to the Γ -point, where they hybridize with the hole-like bands,
leading to the opening of a spin density wave gap and a droplet-like Fermi surface. Such
rather three-dimensional Fermi surface sections are also consistent with quantum oscilla-
tion measurements [209].
Those ARPES studies did not resolve any change when crossing the Eu2+ magnetic
ordering temperature, indicating a weak coupling between the Eu and FeAs subsystems.
Therefore, Eu based compounds were examined in further studies in order to get character-
istic information about 122 iron pnictides, and the Eu2+ magnetic ordering was completely
neglected [199, 205, 235, 290, 293]. For example, EuFe2(As1-xPx)2 was the first chemically
pressurized superconductor investigated by ARPES [235]. It was found that P substitution
6.3 Electronic properties 87
mainly influences the hole pockets in the center of the Brillouin zone, leading to a strongly
three-dimensional Fermi surface with reduced nesting and (at least at low P substitution)
to a charge-neutral development, which can not be described by a simple rigid-band shift1.
In contrast to the early investigations on EuFe2As2, recent results show that the coupling
between Eu and FeAs layers can not be neglected [204]. While former studies were carried
out with energies, where the photoemission cross section of the d-orbitals is dominant,
Adhikary et al. also used photon energies, which are sensitive to p-orbitals. This revealed
that the electronic states near the Fermi energy level possess large p-orbital contributions
due to Eu-As and Fe-As hybridizations, and are sensitive to the Eu2+ ordering.
Electronic transport
The electronic transport properties of EuFe2As2 are similar to other iron pnictides (see
chapter 3.2.2, [188]): although a spin density wave takes place at elevated temperatures
Ts,SDW ∼ 190K, the resistivity (of twinned samples) stays metallic down to lowest temper-
atures (see also Fig. 6.1). At TEu, the resistivity exhibits only a slight kink; the influence
on the scattering rate and thus also on the optical properties is negligible [184]. While
Hall and thermopower measurements indicate that the carriers dominating the electronic
transport above Ts,SDW are holes [28, 280], also the influence of Dirac fermions was sug-
gested [255].
In order to study the spin density wave, besides ARPES also optical spectroscopy [146,
184, 186] and scanning tunneling microscope (STM) measurements [203] were performed
on EuFe2As2. While ARPES studies reported a spin density wave gap 2∆ ≈ 50 −
70meV [191], STM results indicate a gap value of 2∆ ≈ 90meV, with a small suppression
of the density of states at the Fermi energy that persists even up to higher temperatures
than Ts,SDW. Further contradictory results were obtained from optical measurements in
the infrared frequency range: while Wu et al. found only one spin density wave gap below
161meV [184], Moon et al. resolved two energy gaps below 56 and 178meV, consistent
with BaFe2As2 and SrFe2As2 [146, 266].
1 It was found that an electron pocket with yz-orbital character and a hole pocket with xy-character do
not change with P substitution. Both stay basically two-dimensional. However, a strongly dispersive
hole pocket with z2-orbital character increases with increasing P content, and the almost degenerate hole
pockets with xz- and yz-orbital character are strongly suppressed at the Γ -point (and even disappear
close to optimal doping), while they remain almost unchanged at the Z-point. A reduction from three
to only one hole pocket at the Γ -point is consistent with DFT calculations [207].
88 6 Eu based iron pnictides
Coupling between magnetic and electronic subsystems
Probably the most interesting question about Eu 122 pnictides is, how strong the local
Eu2+ magnetic moments are coupled to the itinerant electrons in the FeAs layers. In the
case of superconducting compounds, the influence of the Eu2+ magnetism on the elec-
tronic properties is clearly visible in transferred hyperfine fields from the Eu2+ moments
on Fe of about 1T [234, 251], causing phenomena such as the re-entrance of resistivity
in the superconducting phase and field-enhanced superconductivity (see chapter 6.3.2).
For EuFe2As2, however, the situation is more complicated: it was concluded that electron
scattering on the local Eu2+ moments plays only a minor role for the transport proper-
ties [188] and the reflectivity basically does not change at the Eu2+ magnetic ordering
temperature [184]. Only recently, ARPES [204], Mössbauer [200] and resonant x-ray mea-
surements [195] could resolve signatures of coupled FeAs and Eu subsystems. In order
to get more information about the coupling strength, electron and nuclear magnetic spin
resonance studies are discussed in the following.
Electron spin resonance (ESR) is in principle a powerful tool to investigate the spin
dynamics in Eu based iron pnictides, as one probes the relaxation of the local Eu2+
spins which is dominated by the interaction with conduction electrons [187, 202, 248, 258,
269, 272, 277, 289]. Therefore, the resonance field and linewidth of the ESR signal both
depend on the exchange coupling between Eu2+ spins and itinerant electrons, as well as
on the electronic density of states at the Fermi energy. In a common metal, the ESR
linewidth increases linearly with temperature (“Korringa relaxation”); the g-factor, which
is determined from the resonance field, is temperature-independent and shifted compared
to its vacuum value (“Pauli susceptibility”). However, if the conduction electrons couple
stronger to the Eu2+ spins than to the lattice, the microwave energy absorbed by the
Eu2+ moments is not emitted fast enough to the lattice (“bottleneck scenario”) [258, 272].
Instead, it is kept in the magnetic system of Eu2+ spins and conduction electrons. As a
consequence, the ESR response depends on experimental parameters such as microwave
frequency and Eu concentration. Unfortunately, there is up to now no consensus whether
such a bottleneck scenario is observed in Eu based iron pnictides or not [258, 269, 272].1
1 Garcia et al. argued that an almost unchanged g-factor through the phase diagram (which does thus
not reflect the evolution of the Fermi surface), the measured magnetic field-dependence of the linewidth
and opposing evolutions of the calculated density of states at the Fermi energy and the actual linewidth
slope, all suggest a bottleneck scenario for Eu(Fe1-xCox)2As2 [258]. However, Krug von Nidda et al.
did neither observe any field dependence of the linewidth, nor that Eu dilution changes its slope [272].
Furthermore, Rosa et al. reported that when replacing Eu by Ba, the spin density wave is suppressed
and the Korringa slope decreases simultaneously; opposite to what one would expect in the bottleneck
scenario [269].
6.3 Electronic properties 89
A much clearer picture can be drawn by nuclear magnetic resonance (NMR) spec-
troscopy, which probes the spin polarization of 75As nuclei that takes place via the Fermi
contact interaction with delocalized carriers. If the Eu2+ local moments are interacting
with the conduction electrons, this should be visible in the signal. Thus, NMR spec-
troscopy is ideal to investigate the coupling between Eu2+ magnetic moments and the
FeAs layers. Up to now, 75As NMR investigations were performed on Eu(Fe0.995Co0.005)2-
As2 [252] and Eu diluted compounds [273, 281]. It was found that the typical measurement
parameters - spin-lattice relaxation rate, spin-spin relaxation rate and the shift of the cen-
tral line - all follow a Curie-Weiss law. Furthermore, even in diluted compounds, the
spin-lattice relaxation is more than two times larger than those of Ba 122 pnictides, and
it increases with the Eu content; the latter is also true for the Curie-Weiss constant. All
this proves that the 75As nuclei interact with the localized Eu2+ moments. In order to
get an estimate about the coupling between the FeAs layers and Eu subsystems, one can
calculate the hyperfine coupling by relating the central line shift to the dc magnetic sus-
ceptibility. For Eu(Fe0.995Co0.005)2As2, the hyperfine coupling is 60 times larger than for
NdFeAsO0.85F0.15, providing direct experimental evidence for a strong coupling between
the Eu2+ localized moments and the conduction electrons in the FeAs layers [252].
Electronic in-plane anisotropy
Up to now, most of the investigations on the in-plane anisotropy of iron pnictides con-
centrated on Ba(Fe1-xCox)2As2. Recently, magnetic torque measurements on very small
samples [295], as well as resistivity and thermopower measurements on mechanically de-
twinned crystals were also performed on Eu compounds [197, 240]. In those studies, the
focus was on investigating the general in-plane anisotropy and possible nematic behaviour
of iron pnictides, and the Eu2+ magnetic order was neglected.
In order to examine whether the Eu2+ magnetism leads to an additional anisotropic
response, Fig. 6.15 depicts resistivity data for Eu(Fe1-xCox)2As2 [197]. The overall be-
haviour is similar to Ba 122-compounds (see chapter 3.2.2); the Eu2+ magnetic order does
not notably induce additional anisotropy.
Magnetic detwinning
Although magnetic fields are usually very ineffective to detwin iron pnictides [24], EuFe2-
As2 can be completely detwinned below TEu by small magnetic fields (∼ 1T) applied along
one of the orthorhombic axes [7]. In the corresponding experiment, Xiao et al. observed
already at 0T a strong imbalance of twin domains, possibly due to strain induced by
90 6 Eu based iron pnictides
0 . 6
0 . 8
1 . 0
0 1 0 0 2 0 0
1 . 0
1 . 5
0 1 0 0 2 0 0
T E uT E u T S D W
 
 a 
 b
 
 

 (T
) / 

 (30
0K)
T S D W
 T  ( K )
 
 

 b
 / 

a
( b )  x  =  0 . 0 3 4( a )  x  =  0
T s
 
 
 T  ( K )
 
 
Figure 6.15: Temperature-dependent resistivity ρ(T ) [197] and its anisotropy for mechan-
ically detwinned Eu(Fe1-xCox)2As2 with (a) x = 0 and (b) x = 0.034. Vertical lines mark
the transition temperatures TEu (orange; kink in resistivity), TSDW (red; maximum in specific
heat, minimum in dρ/dT ) and Ts (brown; onset of hump in specific heat). The anisotropy
with ρb > ρa arises already slightly above Ts and increases with doping. The Eu2+ magnetic
order does not notably induce additional anisotropy.
the mounting of the crystal1, and a magnetic field was applied along the orthorhombic
a-axis of the minority domain type (defined as (100)o-direction). Fig. 6.16 summarizes the
main results. At low fields, the intensity of the (400)o-reflection (representing the minority
twins) first decreases, before it abruptly increases around 0.7T and the (040)o-reflection
completely disappears. Only a slight hysteresis was revealed. The authors attributed their
observations to a giant spin-lattice coupling that leads at high fields to a detwinning of the
crystal with its longer orthorhombic a-axis aligned parallel to the external magnetic field;
the changes at low fields were interpreted in terms of a tilting of the minority domains out
of their balance position due to internal strain induced by the detwinning process.
Xiao et al. also performed magneto-resistance measurements on EuFe2As2, concluding
that the main observations can be well explained by Eu2+ spin scattering [198]. For
currents and magnetic fields applied parallel to one of the orthorhombic in-plane axes,
a giant, unconventional magneto-resistance effect takes place: at temperatures T < TEu,
the resistance first increases with increasing magnetic field, until it abruptly decreases at
the Eu2+ spin-flip field (∼ 0.7T). The low field behaviour resembles the positive magneto-
resistance that appears when an external magnetic field is applied parallel to the sublattice
magnetization of an antiferromagnet; the abrupt decrease can be understood in terms of
1 Proposed in private communications by the main author Y. Xiao.
6.3 Electronic properties 91
3.9 4.0 4.1
0
200
400
600
Hs||s(100)O
0.5T
H ||s(100)O
1T 0T
(040)O
In
te
ns
ity
s(a
.su
.)
H(r.sl.su.)
(400)O 3.9
4.1
4.0
3.9
4.0
4.1
4.2
0 1 2 3
Magneticsfields(T)
(r.
sl.
su
.)
H
(a) (b)
(400)O
(040)O
(400)O
(040)O
Figure 6.16: Selected Bragg reflections of EuFe2As2 at 2K with the magnetic field applied
along one of the orthorhombic axes [7]. Momentum transfer Q-scans around the (400)o and
(040)o reflections (a) under three typical magnetic fields 0T (black), 0.5T (green) and 1T
(red line) as well as (b) for decreasing and increasing magnetic fields displayed in a contour
plot. HD1Crit marks the field, where twins tilt out of their balance position, caused by internal
strain due to the detwinning at HD2Crit.
superzone boundary theory, which predicts an energy gap in the antiferromagnetic state;
as soon as the Eu2+ spins flip along the external magnetic field, the antiferromagnetic
state and thus the energy gap gets destroyed and the resistivity decreases. In contrast, at
temperatures slightly above the Eu2+ magnetic ordering, the resistance directly decreases
with increasing field. This can be explained in terms of suppressed spin fluctuations in a
magnetic field.
Chapter 9 will show measurements done in the framework of this thesis, demonstrating
that the magnetic detwinning is actually more complex than presented by Xiao et al..
Furthermore, those studies prove that the magneto-resistance is mainly governed by twin
domain dynamics (and not Eu2+ spin scattering), causing distinct hysteretic behaviour
which can be observed when well-defined cooling procedures are obeyed.
6.3.2 Superconducting properties
Quantum criticality
Non-Fermi liquid behaviour, indicated for example by a linear temperature-dependence of
the resistivity, was discovered in several unconventional superconductors around optimal
doping [292]. Its appearance is widely discussed as due to an underlying quantum critical
point or strong spin fluctuations in the vicinity of a suppressed magnetic order. While
non-Fermi liquid behaviour above the superconducting dome is also commonly observed
in iron pnictides, a divergent quasiparticle mass evidencing a quantum critical point was
92 6 Eu based iron pnictides
(up to now) only confirmed for BaFe2(As1-xPx)2, possibly because this is a very clean
system [83, 84].
In order to elucidate the origin of non-Fermi liquid behaviour in iron pnictides in more
detail, Kurita et al. investigated pressurized EuFe2As2, which shows above the super-
conducting dome a linear temperature-dependence of the resistivity [229]. For optimum
pressure, while resistivity and Hall measurements at 0T ruled out any divergent quasipar-
ticle mass, Fermi liquid behaviour could be restored in magnetic fields around 10T. From
those studies, the following conclusions were proposed: on the one hand, as EuFe2As2
under pressure can be considered as an even cleaner system as BaFe2(As1-xPx)2, the non-
divergent quasiparticles mass demonstrates that quantum criticality is not the key ingre-
dient for high temperature superconductivity in iron pnictides. On the other hand, the
latter results under high magnetic fields indicate that spin fluctuations drive the uncon-
ventional scattering above the superconducting dome: probably, the external fields which
are further enhanced by the Eu2+ moments lead to a high enough internal field to suppress
the spin fluctuations. This is an impressive example of how important information about
unconventional superconductivity can be revealed by Eu based iron pnictides.
Influence of Eu magnetism
Understanding the interplay between superconductivity and magnetism is one of the great
challenges of today’s solid state physics. Indeed, the coexistence of Eu2+ magnetic order
and superconductivity is surprising from a very fundamental point of view: how can the
Fe electrons contribute on the one hand to superconductivity and mediate on the other
hand the Eu2+ magnetic RKKY-exchange? In order to understand this interplay in more
detail, here the main observations are summarized.
• The competition of the two orders gets very obvious in the case of the resistivity
re-entrance which appears in several superconducting samples at TEu. Magnetic
Compton scattering experiments on P and Co substituted Eu compounds indicated
that the Fe 3d-contribution is strongly enhanced around TEu [231, 260]. This en-
hancement can be quickly suppressed with relatively small magnetic fields in the
ab-plane, consistent with the suppression of the re-entrance or even an enhance-
ment of Tc found in magneto-resistance measurements [32, 220, 256, 270]. Early
work suggested that those observations are due to the suppression of magnon ex-
citations [32, 270]. However, as previous experiments demonstrated below TEu a
spin canting of the Eu2+ moments and thus a ferromagnetic component along the
c-direction, it was proposed that the suppression of the canting by in-plane magnetic
fields likely causes the field enhanced superconductivity [9, 256]. Interestingly, the
re-entrance only appears when TEu and Tc are very close to each other [238]. This
6.3 Electronic properties 93
is consistent with observations made in chapter 6.2: superconductivity can appear
much below TEu (for example in the case of Co doping), however, if TEu and Tc
directly compete with each other, superconductivity disappears (for example for P
substitution).
• Strikingly, the Eu2+ magnetic order was also found to influence the superconducting
gap: while in BaFe2(As1-xPx)2 nodal superconductivity was observed, for P substi-
tuted Eu compounds infrared and ESR measurements indicated an isotropic s-wave
gap [233, 272]. One possible explanation for the different behaviour is that the nodes
in iron-based superconductors are not given by symmetry and thus can be lifted by
Eu2+ spin scattering [72, 233]. However, a differing band structure due to the short-
ened c-axis (compared to Ba 122 compounds) might be also the reason [294].
• Microscopic coexistence of superconductivity and Eu2+ magnetism was demonstrated
recently by muon spin relaxation and Mössbauer spectroscopy on EuFe2(As1-xPx)2
[243].
Upper critical fields
Compared to other iron pnictides, the Eu 122 family shows significantly reduced critical
fields Bc1 and Bc2. In Eu diluted compounds, lower critical fields of only 10 -100mT
are reported [272, 276, 277, 279]; for non-diluted compounds, the Meissner state can be
even completely absent [263]. While on the one hand, determining those very small lower
critical fields is experimentally challenging, on the other hand, the reduction of Bc2 to
an experimentally accessible scale opens new perspectives: in the case of EuFe2As2 under
pressure, it was found that the upper critical fields (∼ 20T at 0K) are slightly anisotropic,
and their temperature-dependence revealed a concave curvature around 1T, similar to the
Jaccarino-Peter compensation effect (see chapter 3.3.3, [220, 225]). The results could
be nicely described by an internal exchange field of ∼ 75T due to the magnetic Eu2+
moments, explaining the reduced upper critical fields compared to other iron pnictides. For
diluted Eu0.5K0.5Fe2As2 [282] and EuxSr1-x(Fe0.89Co0.11)2As2 (x = 0.20 and 0.46) [274],
the upper critical fields (∼ 60T for K and 20-30T for Sr substitution) are consistent with
a dominant Pauli paramagnetic effect that is proportional to the critical temperature Tc.
Interestingly, a concave curvature similar to EuFe2As2 under pressure was also observed
for Sr substitution. Although the authors ascribed the unconventional slope to multiband
effects, the analysis in terms of internal compensation fields would be interesting; especially
as the effect was observed to weaken with Eu dilution.

7
MAGNETIZATION STUDIES ON
EuFe2(As1−xPx)2
Although high quality single- and polycrystalline EuFe2(As1−xPx)2 samples were soon
available after the discovery of superconductivity in EuFe2(As0.7P0.3)2 [30], investigations
on a series of samples are still rare (see chapter 6). In our opinion, however, it needs
exactly such systematic studies in order to understand the complex dynamics in Eu based
iron pnictides. Therefore, we have performed in- and out-of-plane magnetization mea-
surements on a complete set of high quality EuFe2(As1−xPx)2 (x = 0, 0.055, 0.09, 0.12,
0.16, 0.165, 0.17, 0.26, 0.35, 0.39, 1) single crystals (see chapter 5.3), which elucidated
the complex magnetic ordering in those compounds and contributed important insights
into the interplay of superconductivity and magnetism. The main results can be found in
Ref. [9] and Ref. [10], as well as are described in the following in more detail.
7.1 Canted A-type antiferromagnetism
In 2011, the first phase diagrams were published for EuFe2(As1−xPx)2 [230, 234]. Despite
the availability of single- and polycrystalline samples over the whole phase diagram, they
could not deliver a clear picture of how the Eu2+ order changes with chemical pressure and
a serious debate was launched which kind of magnetism coexists with superconductivity.
We approached this question by low-field in- and out-of-plane magnetization measurements
96 7 Magnetization studies on EuFe2(As1−xPx)2
on a series of EuFe2(As1−xPx)2 single crystals (x = 0, 0.055, 0.12 and 0.35) that should
be non-superconducting according to the phase diagram of Ref. [230]; the results which
are published partially in Ref. [9] are presented in this section.
EuFe2(As0.88P0.12)2
Fig. 7.1 shows the temperature-dependent dc susceptibility χdc(T ) = M(T )/µ0H for x
= 0.12, measured parallel and perpendicular to the ab-plane. The shape of the field-
cooled curves (see Fig. 7.1a,b) is characteristic for the A-type antiferromagnetism identified
in the parent compound: while at TN ∼ 16K, a cusp appears for H ‖ ab, the out-
of-plane magnetization flattens. With increasing field, the transition temperature TN is
suppressed and a broad shoulder appears that is typical for field-induced ferromagnetism;
the suppression is faster for H ‖ ab, consistent with the anisotropy of EuFe2As2.
Figure 7.1: Temperature-dependent dc susceptibility χdc(T ) = M(T )/µ0H of
EuFe2(As0.88P0.12)2: (a) FC curves with H ‖ ab, (b) FC curves with H ‖ c and (c) ZFC
(black open squares) as well as FC (orange closed circles) curves with H ‖ c for various
applied fields. The shape of the FC curves is characteristic for antiferromagnetic interlayer
coupling. However, a distinct hysteresis appears for H ‖ c at small magnetic fields.
7.1 Canted A-type antiferromagnetism 97
Nevertheless, we find at low magnetic fields a distinct difference between the field-cooled
and zero-field cooled curves for H ‖ c that is quickly suppressed with increasing field (see
Fig. 7.1c). In order to study this hysteresis, we have also measured the field-dependence of
the magnetization, concentrating on low fields (see Fig. 7.2a). We observe a clear hysteresis
for H ‖ c; for H ‖ ab, only a much smaller hysteresis appears, which is likely caused by our
limited precision in crystal alignment. To follow the opening of the hysteresis for H ‖ c,
we plot in Fig. 7.2b the difference ∆Mc between the magnetization curves acquired by
sweeping the field down and up (i.e. the hysteresis height). ∆Mc decreases on raising the
temperature, until the hysteresis vanishes at TN and it is instructive to compare this trend
with the difference between the ZFC and FC curves at the same field. The two trends
coincide, demonstrating for T < TN the development of a ferromagnetic component along
the crystallographic c-direction.
Figure 7.2: (a) Field-dependent isothermal magnetization M(H) of EuFe2(As0.88P0.12)2 for
H ‖ ab (brown) and H ‖ c (orange) at T = 2K. (b) Height of the H ‖ c hysteresis ∆Mc
(difference between the magnetization curves acquired by sweeping the field down and up, left
panel), compared to the temperature-dependence of the difference between the ZFC and FC
curves at 20G (right panel); the dotted lines are a guide to the eye to stress the correlation
between the two trends.
Other compositions
Further temperature-dependent out-of-plane measurements on a x = 0.35 single crystal
reveal a similar behaviour as for EuFe2(As0.88P0.12)2, while signatures of hysteretic be-
haviour in the M(T ) curves of EuFe2As2 and EuFe2(As0.945P0.055)2 are much less clear;
corresponding low-field hysteresis measurements at 2K with H ‖ c can not resolve a
hysteresis for x = 0, while for x = 0.055 the hysteresis height is slightly and for x =
0.35 significantly positive (see Fig. 7.3). Therefore, we conclude that the ferromagnetic
98 7 Magnetization studies on EuFe2(As1−xPx)2
component develops already at P concentrations much smaller than those where super-
conductivity sets in, and persists further in the overdoped range.
Figure 7.3: Magnetization curves of EuFe2As2, EuFe2(As0.945P0.055)2, and
EuFe2(As0.65P0.35)2: temperature-dependent dc susceptibility χdc(T ) = M(T )/µ0H
(upper panels) measured with H = 20G (H ‖ c, ZFC: black open squares, FC: orange closed
circles) and hysteresis height ∆Mc (lower panels, 2K: blue closed circles, 10K: red open
circles); for x = 0.35, also ∆Mab is given. The hysteresis height for H ‖ c reveals already a
small hysteresis for x = 0.055, which is much more evident for x = 0.35. In the latter case,
a distinct hysteresis opening is also visible for in-plane measurements, which has a different
temperature-dependence.
Fig. 7.3d also displays a comparison between isothermal in- and out-of-plane magneti-
zation loops of EuFe2(As0.65P0.35)2. One observes a distinct hysteresis opening for H ‖ ab
as well as a small opening for H ‖ c. The different temperature-dependence of ∆Mab and
∆Mc indicates two unequal hysteretic mechanisms.
Interpretation
By analysing measurements of the magnetic properties of various non-superconducting
Eu 122 compounds, we identify a ferromagnetic contribution along the c-direction that
7.1 Canted A-type antiferromagnetism 99
becomes stronger with increasing P substitution. Strikingly, we are able to verify a small
out-of-plane ferromagnetic contribution already for x = 0.055, a concentration that is
much smaller than those where superconductivity sets in. We have also investigated a
single crystal of the overdoped substitution range (x = 0.35), where we find hysteretic
behaviour for H ‖ c and H ‖ ab. As in- and out-of-plane hysteresis show a different
temperature-dependence, we conclude unequal hysteretic mechanisms for the two crystal-
lographic directions. In the following discussion, we want to concentrate on the out-of-
plane ferromagnetic component.
As already discussed in chapter 6, Mössbauer measurements indicate even for EuFe2As2
a small canting of the Eu2+ moments out of the ab-plane; it increases strongly with
increasing P substitution until the Eu2+ spins are aligned almost along the c-direction
when superconductivity sets in [234]. We show that this canting leads in magnetic sus-
ceptibility measurements to a ferromagnetic signal along the c-axis, i.e. hysteretic be-
haviour. The fact that one cannot resolve any hysteresis in the parent compound is
consistent with an extremely small spin canting, which becomes already more pronounced
for EuFe2(As0.945P0.055)2.
We believe that the hysteresis loops observed in our single crystal measurements for
H ‖ c constitute the key to reconcile the various phase diagrams of Eu 122 pnictides
proposed in literature [230, 234]. Since contributions from the c-direction are unavoidable
in measurements on polycrystalline samples, a hysteresis is always seen as soon as the
spin canting is sufficiently pronounced. In the following we compare the phase diagram
of Ref. [230] (based on single crystal measurements with H ‖ ab) with that of Ref. [234]
(where polycrystalline samples were investigated). While the former group observes sig-
natures of antiferromagnetic Eu2+ order in the superconducting phase, the latter claims
the coexistence of ferromagnetism and superconductivity. Indeed, those statements do
not contradict each other, if one considers that Ref. [230] is only sensitive to the order-
ing of the Eu2+ moments in the ab-plane, while Ref. [234] detects a superposition of in-
and out-of-plane coupling: both measurements are consistent with superconductivity that
coexists with canted antiferromagnetism, meaning that the interlayer coupling is antifer-
romagnetically, but the spins are canted with a ferromagnetic net component along the
c-direction.
It is intriguing that the canting develops with the suppression of the spin density wave,
implying that the Eu2+ spin orientation is defined by the spin density wave anisotropy.
Calculations by Akbari et al. on multiband iron pnictides confirm an influence of the itin-
erant spin density wave phase on the RKKY-interaction between localized moments [11].
They show that the spin rotational symmetry is broken by the two-dimensional spin den-
100 7 Magnetization studies on EuFe2(As1−xPx)2
sity wave which results in an anisotropic RKKY-interaction described by an anisotropic
XXZ-type Heisenberg exchange. This anisotropy is only present in the spin density wave
state and vanishes in the normal state. As this exchange is a general feature of rare
earth based systems, such a ferromagnetic out-of-plane component that develops with the
suppression of the spin density wave can be also expected for other Eu 122 pnictides.
7.2 Re-entrant spin glass
Although the in-plane magnetization measurements on EuFe2(As0.65P0.35)2 presented in
Fig. 7.3 imply for high P concentrations - in accordance with many other publications (see
chapter 6) - ferromagnetic interlayer coupling, our detailed investigations reveal a more
complex, time-dependent behaviour. Therefore, we have performed a systematic study of
the superconducting and magnetic properties of a complete set of EuFe2(As1−xPx)2 (x =
0, 0.055, 0.09, 0.12, 0.16, 0.165, 0.17, 0.26, 0.35, 0.39, 1) single crystals (see chapter 5.3)
using dc and ac magnetization (see chapter 5.2), dc resistivity and heat capacity mea-
surements1. In order to account for the time-dependencies, the temperature is usually
swept continuously in M(T ) cycles (see chapter 5.2); furthermore we distinguish between
field-cooled curves that were obtained while decreasing (“field-cooled cooled”: FCC) and
increasing (“field-cooled heat”: FCH) the temperature. Results are published in Ref. [10]2.
EuFe2P2
Fig. 7.4 and Fig. 7.5 show the in-plane (H ‖ ab) magnetic behaviour of a EuFe2P2 single
crystal. In a very small probing field of 2G two consecutive magnetic transitions can
be clearly resolved in the zero-field cooled and field-cooled dc magnetic susceptibility. A
sharp peak at T1 ∼ 29.0K is followed by an upturn starting at T2 ≈ 27.7K, leading to a
second peak at ∼ 27K in the ZFC magnetization. Whereas the transition at T1 exhibits no
thermal hysteresis, the second transition at T2 is characterized by a pronounced ZFC-FCC
hysteresis which vanishes if a larger dc magnetic field (H ‖ ab) is applied (see Fig. 7.5). It
can be finally suppressed for fields around 500G. Increasing the field even higher shifts the
peak at T1 down (see Fig. 7.4c) and at around 1T, the peak has completely disappeared.
Note that a broad shoulder develops at ∼ 0.3T, which was interpreted for EuFe2As2 as due
to a metamagnetic transition [182]. Furthermore, specific heat measurements on the single
1 Magnetization data are complemented with four point dc resistivity measurements with a current of the
typical value 1mA. In the case of small resistances (especially for the c-direction measurements), lock-
in technique with low frequencies (77Hz) was used. Transition temperatures derived from resistivity
measurements are indicated with “∗”. Heat capacities were measured with a relaxation-type calorimeter.
2 Preliminary studies can be also found in Ref. [296].
7.2 Re-entrant spin glass 101
crystal show a sharp peak at T1 with a broad shoulder at lower temperatures, consistent
with the width of the anomaly for polycrystalline samples reported in Ref. [211] and prove
that both transitions are bulk properties (see Fig. 7.4b).
Figure 7.4: Magnetization curves of EuFe2P2 (H ‖ ab), together with specific heat data.
(a) Temperature-dependent FCC curves χdc(T ) = M(T )/µ0H at small fields between 2G
(orange) and 100G (purple) show two consecutive magnetic transitions at T1 = 29.0K and
T2 = 27.7K; the transition at lower temperature T2 is quickly suppressed in the external
field. (b) Temperature-dependent ZFC (black open squares) and FCC (orange filled circles) dc
susceptibility χdc(T ) (upper panels) measured with H = 2G, revealing that a strong hysteresis
sets in at T < T2. The lower panel adds the temperature-dependent heat capacity Cp for our
single crystal (purple filled diamonds) and for polycrystalline EuFe2P2 (open dark blue stars,
[234]). The single crystal heat capacity shows a sharp feature at T1 that is followed by a broad
shoulder (visible also in the data of polycrystalline EuFe2P2). (c) ZFC magnetization for
500G (dark blue), 0.1T (blue), 0.3T (cyan), 0.5T (dark cyan) and 1T (green). T1 decreases
with increasing external field, also depicted in the inset.
102 7 Magnetization studies on EuFe2(As1−xPx)2
Figure 7.5: (a) ZFC (black open squares) and FCC (orange filled circles) in-plane magneti-
zation curves of EuFe2P2 at H = 2G, 5G, 20G, 100G, 500G and 0.1T (H ‖ ab), as well as
(b) ZFC (black open squares) and FCC (brown filled circles) out-of-plane magnetization at
H = 2G. The in-plane low-temperature transition and any irreversibility has disappeared at
500G; out-of-plane, a small hysteresis due to spin canting can be identified at low fields.
In order to get more insight into the character of the second transition at T2 we studied in
detail its thermal hysteresis and frequency-dependence by ac magnetization measurements.
Fig. 7.6a displays the differences between the ZFC, FCC and FCH susceptibilities for an
in-plane field of 2G. The thermal hysteresis is visible in the ZFC-FCC splitting at T < T2.
Repeated FCC and FCH cycles (heating / cooling rates 0.2 K/min) revealed a very slow
time-dependence of the magnetization below T2, leading to a growth of the magnetization
and consequently a negative difference of FCH - FCC.
A time-dependence of the magnetization below T2 is also visible in a time-dependence
of the ZFC magnetization which after some rapid initial increase grows almost linearly in
time with a rate of ∼1%/h (see Fig. 7.6b). The time-dependence of the magnetization
becomes also apparent in a frequency-dependence of the real and imaginary component of
the ac susceptibility, χ′ac(T ) and χ′′ac(T ), as depicted in Fig. 7.6c. Below T2 a peak appears
in both components (χ′ac ≈ 50×χ′′ac) which shifts to higher temperature with increasing
frequency following a Vogel-Fulcher behaviour (see Fig. 7.6d). We can rule out any relation
of the time and frequency-dependence to flux line lattice dynamics, since EuFe2P2 is far
off from any proposed superconducting phase [230, 236].
7.2 Re-entrant spin glass 103
Figure 7.6: Magnetization curves of EuFe2P2 (H ‖ ab). (a) Magnetic hysteresis sets in at
T < T2, visible in χdc,FCC −χdc,ZFC > 0 (green stars) (µ0H = 2G); ZFC and FCC curves are
depicted in the upper panel for a direct comparison of the characteristic temperatures T1 and
T2. Time-dependence for T < T2 is revealed by FC cycling, visible in χdc,FCH − χdc,FCC < 0
(pink open diamonds) and (b) time-dependent magnetization after ZFC cooling (µ0H = 2G,
25K: blue closed squares, 28.5K: pink open circles). (c) A frequency-dependence in the ac
susceptibility χ′ac(T ) and χ′′ac(T ) (no dc field, ac drive amplitude 1G, 0.1Hz: dark grey open
triangles, 100Hz: brown closed circles) sets in also below T2. (d) Vogel-Fulcher-Fit of the
peak below T2 in χ′′ac(T ).
Until now, magnetic ordering at higher P concentrations in polycrystalline and single
crystalline samples of EuFe2(As1−xPx)2 was assigned to ferromagnetism [230, 234, 236].
Measurements on polycrystalline samples [234, 236], however, are not able to allow conclu-
sions about a possible antiferromagnetic interlayer coupling, and measurements on single
crystals of EuFe2(As1−xPx)2 [230] failed to reveal two separate magnetic transitions and
their different thermal hysteretic behaviour because of too coarse temperature steps.
In view of the shape of the M(T ) anomaly at T1 (see Fig. 7.4c) we suggest that the
Eu2+ moments in EuFe2P2 order in a canted A-type antiferromagnetic structure with
104 7 Magnetization studies on EuFe2(As1−xPx)2
the spin components being ferromagnetically aligned along the c-axis1. Additionally, we
detect below T2 a second phase transition with glassy character which we associate to
the ordering of the in-plane components of the Eu2+ moments. The development of a
glassy phase below a magnetic phase transition, commonly referred to as re-entrant spin
glass [38, 297–299], indicates a competition between antiferromagnetic and ferromagnetic
spin exchange interactions in the system.
In the case of EuFe2P2, the antiferromagnetic RKKY interlayer coupling competes with
the ferromagnetic intralayer interactions of the spins. In fact, DFT based calculations re-
vealed a very small energy difference of antiferromagnetic and ferromagnetic ground states
for EuFe2(As1−xPx)2 [230]. We therefore suggest that in EuFe2P2, competition between
ferro- and antiferromagnetism causes glassy freezing of spin components in the ab-plane
at T2 and a decoupling of the magnetic Eu layers. Such a freezing of transverse magnetic
components following long range magnetic order (which has already set in) is consistent
with mean field theoretical calculations for a re-entrant spin glass [39]. Our conclusions
are not only supported by the time-dependent magnetization behavior at T < T2, but also
by the development of M(T ) with external fields: by application of a magnetic field of
∼ 500G along the ab-plane, the energy barrier between different equilibrium states can
be overcome, the glass transition is suppressed and the temperature-dependent magneti-
zation resembles that of EuFe2As2. This interpretation is consistent with neutron studies
by Ryan et al. [212], as those are not sensitive to the freezing of the small in-plane spin
component, as long as the ferromagnetic spin component along the c-axis still exists.
EuFe2(As0.835P0.165)2
In order to study the complex interplay of magnetism and superconductivity in mixed As
- P samples we have investigated in detail the magnetic and superconducting properties of
a single crystal of EuFe2(As0.835P0.165)2. The in-plane electrical resistivity (see Fig. 7.7)
proves the onset of superconductivity at T ∗c,on ∼ 22K indicated by a steep initial decrease
of the resistivity. Zooming into the transition reveals re-entrant behaviour at about 19K
followed by a smooth decrease towards zero resistivity which is achieved only below T ∗c,0 ≈
9K.
Fig. 7.9 displays the corresponding zero-field and field-cooled cooled temperature-de-
pendent magnetization. Both, in- and out-of-plane magnetization are very similar to
EuFe2P2: for H ‖ ab, two peaks are visible that are shifted to slightly lower temperatures
(T1 ∼ 19.0K, T2 ∼ 16.8K); for H ‖ c, a slight hysteresis below T1 indicates the spin
1 Due to sample shape effects we can not distinguish between A-type antiferromagnetism and helimag-
netism.
7.2 Re-entrant spin glass 105
Figure 7.7: In-plane resistivity curves of superconducting EuFe2(As0.835P0.165)2 with T ∗c,on ∼
22K. At T > T ∗c,on, R(T ) is linear; below ∼ 19K, a re-entrance of resistivity appears. Zero
resistivity is reached only below T ∗c,0 ∼ 9K
canting along the c-axis. Additionally, a pronounced downturn occurs below 15K for both
field directions, which ends up in a diamagnetic signal for H ‖ c. While the in-plane
low-temperature transition at T2 has already disappeared at 500G, irreversibilities due to
superconductivity remain at least up to 0.5T.
Further evidence for a spin glass transition can be found in Fig. 7.8, which compares
the low-temperature resistivity behaviour to selected ac and dc magnetization data. A
difference between ZFC and FCH curves sets in at T < Tc,on. However, FC cycling
reveals two time-dependent glassy transitions, as χdc,FCH − χdc,FCC > 0 at T < Tc,on
and χdc,FCH − χdc,FCC < 0 at T < T2 (pink open diamonds). We therefore conclude that
superconducting EuFe2(As0.835P0.165)2 shows an analogous re-entrant spin glass behaviour
as EuFe2P2. The additional positive peak in the FCH-FCC curve between 17K and 21K
could be ascribed to vortex dynamics, as it coincides with the steep initial decrease of the
resistivity marking the onset of superconductivity.
Having this interpretation in mind, we can also interpret all the other features in the ac
susceptibility: the resistivity re-entrance and T ∗c,0 are both accompanied by a sharp peak
in χ′′ac(T ). Such a feature, which comes along with a dip in χ′ac (slightly visible for the
100G curve) was reported for several high-Tc SC and is known as “peak effect” [300, 301]
arising due to a maximum in the critical current density. The broad peak in χ′′ac(T ) at
T < T2 could be a sign of granular SC or of flux reaching the center of the sample according
to Bean’s critical state model [302, 303]. However, as χdc,FCH − χdc,FCC < 0 exactly at
T < T2, it probably arises due to the spin glass transition. Furthermore, one should note
that in-plane ac susceptibility measurements with applied high dc fields H ‖ ab are able
to reveal a diamagnetic in-plane shielding signal if the dc field is large enough (∼ 1T) to
saturate the Eu2+ magnetism.
106 7 Magnetization studies on EuFe2(As1−xPx)2
Figure 7.8: (a) Details of the resistivity curves as well as (b) in-plane magnetization curves
(H ‖ ab) of EuFe2(As0.835P0.165)2, in order to determine the transition temperatures. Dashed
lines are guides to the eye, highlighting T ∗c,50 = Tc,on ∼ 20.8K (purple), T1 ∼ 19.5K (red),
T2 ∼ 16.8K (blue) and T ∗c,0 ∼ 9.0K (purple). (b) In-plane ZFC (black open squares) and
FCC (orange filled circles) magnetization shows atH = 2G two magnetic transitions similar to
x = 1.0 with a steep drop in the ZFC curve below ∼ 15K (measured with the Quantum Design
ultra low field option, see chapter 5.2). A difference between ZFC and FCH curves sets in at
T < Tc,on; FC cycling reveals two time-dependent glassy transitions, as χdc,FCH−χdc,FCC > 0
at T < Tc,on and χdc,FCH − χdc,FCC < 0 at T < T2 (pink open diamonds). Combining
ac susceptibility measurements (drive 1G, frequency 7Hz) with dc fields (0G: grey open
triangles, 100G: violet closed circles, 0.3T: pink open diamonds, 1T: purple closed circles),
negative susceptibility χ′ac < 0 is revealed for H = 1T below 15K. χ′′ac(T ) shows a non-zero-
signal below Tc,on, a sharp peak at the maximum re-entrant resistivity (that is accompanied
by a small dip in χ′ac(T )), a broad hump below T2 and again a sharp peak at Tc,0. Increasing
the dc field from 0 to 100G only suppresses the broad hump below T2.
7.2 Re-entrant spin glass 107
Figure 7.9: (a) ZFC (black open squares) and FCC (orange filled circles) in-plane mag-
netization curves of EuFe2(As0.835P0.165)2 at H = 2G, 100G, 500G, 0.3T, 0.5T and 1.0T
(H ‖ ab), as well as (b) ZFC (black open squares) and FCC (brown filled circles) out-of-plane
magnetization at H = 2G (measured with the Quantum Design ultra low field option, see
chapter 5.2). The in-plane low-temperature transition at T2 (marked by a shoulder) has dis-
appeared at 500G, however, irreversibilities due to superconductivity remain at least up to
0.5T; out-of-plane, a small hysteresis due to spin canting can be identified, as well as a steep
drop in the ZFC curve below ∼ 15K, reaching negative magnetization.
Figure 7.10: Field-dependent magnetization curves of EuFe2(As0.835P0.165)2 for H ‖ ab
(left) and H ‖ c (right), at several temperatures between 2K (blue) and 25K (red). At 2K,
a distinct hysteresis that remains up to highest applied fields (7T) is clearly visible (see also
inset), indicating superconductivity.
108 7 Magnetization studies on EuFe2(As1−xPx)2
Finally, we have also measured the in- and out-of-plane field-dependent magnetization
curves at various temperatures (see Fig. 7.10). Most remarkably, we find at 2K a distinct
hysteresis that remains up to highest applied fields (7T), typical for a hard superconductor
according to Bean’s critical state model (see chapter 3.3.2).
EuFe2(As0.65P0.35)2
We have also investigated a single crystal of EuFe2(As0.65P0.35)2 in more detail, in order
to address the open question about the width of the superconducting dome. Fig. 7.11a
displays the corresponding in-plane resistivity, showing a sharp drop around T1 ∼ 20.7K,
which fades in a broad shoulder at T2 ∼ 18.8K. Such a resistivity behaviour was interpreted
by Cao et al. [236] as re-entrant superconductivity.
However, in-plane ZFC magnetization measurements reveal two magnetic transitions
similar to x = 1.0, indicating the onset of canted antiferromagnetism and re-entrant spin
glass behaviour at T1 and T2, respectively (see Fig. 7.11 and Fig. 7.12). Indeed, any out-
of-phase susceptibility signal is already suppressed at 100G, the same field, where the T2
transition gets barely visible in ZFC and FC measurements. Furthermore, no diamagnetic
signal is visible in any dc or ac susceptibility measurement. One should note that the
double-feature in M(T ) curves for superconducting samples was in some cases assigned
to result from the Paramagnetic Meissner Effect [234]. However, this effect would only
appear in the FC curve [304], whereas we observe features also in ZFC data.
Furthermore, we have also measured the in- and out-of-plane field-dependent magne-
tization curves at various temperatures (see Fig. 7.13). In contrast to superconducting
EuFe2(As0.835P0.165)2 (see Fig. 7.10), we find at 2K no high-field hysteresis. Therefore, we
conclude that EuFe2(As0.65P0.35)2 is not superconducting; it displays similar to EuFe2P2
canted antiferromagnetism and re-entrant spin glass behaviour.
7.2 Re-entrant spin glass 109
Figure 7.11: (a) Details of the resistivity curves as well as (b) in-plane magnetization curves
(H ‖ ab) of EuFe2(As0.65P0.35)2, in order to determine the transition temperatures. Dashed
lines are guides to the eye, highlighting T1 ∼ 20.7K (red) and T2 ∼ 18.8K (blue). (a) The
resistivity approaches 22K rather linear. A sharp drop is visible around T1, which fades in a
broad shoulder at ∼ T2. (b) The in-plane ZFC (black open squares) and FCC (orange filled
circles) magnetization shows atH = 2G two magnetic transitions similar to x = 1.0 (measured
with the Quantum Design ultra low field option, see chapter 5.2). At T < T2, a difference
between ZFC and FCH curves sets in (green filled stars), and FC cycling reveals a glassy
transition with χdc,FCH − χdc,FCC < 0 (pink open diamonds). Combining ac susceptibility
measurements (drive 1G, frequency 7Hz) with dc fields (0G: grey open triangles, 100G: violet
closed circles, 1T: purple open circles), suppresses in χ′ac(T ) already at 100G the T2 transition
and at 1T also the T1 transition; however, there is no signature of negative susceptibility.
χ′′ac(T ) shows a non-zero-signal below T2, which is completely suppressed at 100G.
110 7 Magnetization studies on EuFe2(As1−xPx)2
Figure 7.12: (a) ZFC (black open squares) and FCC (orange filled circles) in-plane magne-
tization curves of EuFe2(As0.65P0.35)2 at H = 2G, 5G, 20G, 100G, 500G, 0.3T, 0.5T and
1.0T (H ‖ ab, 2G curves were measured with the Quantum Design ultra low field option, see
chapter 5.2). The distinct in-plane low-temperature transition at T2 (marked by a shoulder)
has almost vanished at 100G.
Figure 7.13: Field-dependent magnetization curves of EuFe2(As0.65P0.35)2 for H ‖ ab (left)
and H ‖ c (right), at several temperatures between 2K (blue) and 25K (red). No high-field
hysteresis can be observed (see also inset).
7.3 Phase diagram 111
7.3 Phase diagram
In order to follow the compositional dependence of the two magnetic transitions con-
sistently found in EuFe2P2, EuFe2(As0.835P0.165)2, and EuFe2(As0.65P0.35)2, we have ex-
tended our studies to EuFe2(As1−xPx)2 single crystals with x = 0, 0.055, 0.09, 0.12, 0.16,
0.17, 0.26, 0.35 and 0.39; corresponding in-plane dc magnetization curves measured at 2G
are depicted in Fig. 7.14. In all P substituted specimen we observe two consecutive mag-
netic transitions, which we ascribe, in analogy to the previous sections, to a canted A-type
antiferromagnetic transition at T1 = TN and to a glassy freezing of the spin components
in the ab-plane at T2 = Tglass, with TN > Tglass.
Figure 7.14: ZFC (black open squares), FCC (brown filled circles) and FCH (orange filled
circles) in-plane magnetization curves of EuFe2(As1−xPx)2 with x = 0.09, 0.16, 0.17, 0.26 and
0.39 at H = 2G (H ‖ ab). Arrows are guides to the eye, highlighting Tc,on (purple), T1 (red)
and T2 (blue).
In Fig. 7.15 we have compiled the resulting magnetic phase diagram together with the
superconducting dome. According to our investigations on single crystals the re-entrant
spin glass transition appears for all P substituted specimen. The effect of chemical disorder
of the As and P anions on the RKKY-exchange must be ruled out as the origin of the
glass transition since it occurs also in well-ordered EuFe2P2 crystals. We rather ascribe
the glass transition to a competition of ferromagnetic interactions within a layer with
antiferromagnetic RKKY-interactions between neighbouring layers.
112 7 Magnetization studies on EuFe2(As1−xPx)2
Figure 7.15: Phase Diagram of EuFe2(As1−xPx)2. TN = T1 (red dots) indicates a canted
A-type antiferromagnetic transition, with a ferromagnetic net component of the Eu2+ spins
along the c-direction, Tglass = T2 (blue triangles) a spin glass transition due to the freezing of
the spins in the ab-plane and Tc,on the onset of superconductivity (grey squares). Closed sym-
bols indicate transition temperatures deduced from magnetization, open ones from resistivity
measurements [305]. Shadowed lines are guides to the eye. The light grey area indicates the
onset of superconductivity, while bulk superconductivity is fully developed in the dark grey
regime [230, 238].
The transition temperatures exhibit a nonmonotonic behaviour with P substitution. At
low P concentration, 0 < x . 0.12, the antiferromagnetic Eu2+ transition temperature
follows the transition temperature of the spin density wave. Coupling of the itinerant Fe
magnetism and the Eu2+ local spin moments was theoretically predicted and experimen-
tally confirmed by the increasing canting of spins out of the ab-plane concomitant with
the suppression of the spin density wave (see section 7.1). With increasing canting, the
ferromagnetic component of the Eu2+ spins along the c-direction increases, and the compe-
tition with the antiferromagnetic RKKY-interaction between the layers is enhanced which
finally leads to the development of the spin glass phase. In the superconducting regime,
the transition temperatures vary only slightly with P concentration. When superconduc-
7.4 Outlook 113
tivity is finally suppressed, both transition temperatures, T1 and T2, increase markedly,
probably due to a Lifshitz transition [235, 238, 280] which affects the RKKY-exchange.
Antiferromagnetic interlayer coupling developing up to high P concentrations, as well
as a rather narrow superconducting dome, are consistent with experiments on EuFe2As2
under pressure [222]. Between the concentrations x ≈ 0.12 and x ≈ 0.26 the onset of a
superconducting transition is found, while fully developed bulk superconductivity occurs
in an even narrower regime [230, 238]. As concluded previously, a Lifshitz transition near
x ≈ 0.23 coincides with the upper limit of superconductivity [235, 238, 280]. Investigations
of polycrystalline samples, however, resulted in a somewhat broader dome extending to
an upper limit of x ≈ 0.4 [234, 236]. The assignment of the upper limit was based on the
assumption that two subsequent resistivity anomalies seen in samples with x ≈ 0.4 indicate
the onset of superconductivity succeeded by a resistivity re-entrance due to Eu2+ magnetic
ordering. Our experiments on single crystals rather indicate that these two anomalies are
purely of magnetic origin as we do not see any signature of superconductivity in our x=0.35
crystal.
7.4 Outlook
The main results of this chapter were already published in 2011 [9] and 2013 [10]. As the
research on Eu based iron pnictides was pretty active since then, this section summarizes
the response of the community on our results, as well as general conclusions we can draw
for Eu based iron pnictides.
Eu magnetism
The idea of a ferromagnetic component along the c-axis due to the Eu2+ spin canting was
directly accepted by the community for EuFe2(As1−xPx)2 [236], as well as evidenced for
Co and Ir doped compounds [33, 253, 254, 257, 263]. We want to note, however, that
we would be very careful to interpret the different absolute values of ab-plane and c-axis
magnetization as being connected to this canting [253]: demagnetization effects (see chap-
ter 2.1) play a very important role for the rare earth systems - even in the paramagnetic
phase close to the magnetic transition(s) - as can be seen in Fig. 7.16 for the parent com-
pound1. When recalculating the susceptibility by considering a demagnetization factor
close to that of an infinite flat plate (Nc → 1; the sample thickness is two orders of mag-
1 The volume of the sample was calculated by its mass, molar mass, and the lattice constants published
in Ref. [230].
114 7 Magnetization studies on EuFe2(As1−xPx)2
nitude smaller than the in-plane dimensions), one can basically suppress and even reverse
the anisotropy.
Figure 7.16: (a) Temperature-dependent volume (V ) susceptibility χdc(T ) = M(T )/µ0H/V
of EuFe2As2 for H ‖ ab (orange) and H ‖ c (brown) at H = 20G: (a) as measured; (b) cor-
rected with the demagnetization factor Nc = 1, Nab = 0; (c) corrected with Nc = 0.65,
Nab = 0.175. Demagnetization effects are strong enough to reduce or even reverse the
anisotropy of χdc(T ).
Furthermore, we want to stress that antiferromagnetic interlayer coupling developing
up to high P concentrations is consistent with experiments on EuFe2As2 under pressure
[222]. Recent neutron measurements suggest for superconducting Co as well as P substi-
tuted compounds that the Eu2+ moments are basically aligned along the c-axis; a second
transition was either not detected [241, 259] or attributed to a minority phase [241]. Im-
portantly, this is not contradictory to our results of the re-entrant spin glass phase: first
of all, the neutron measurements can not exclude a small spin component staying in the
ab-plane; secondly, we do not expect any typical antiferromagnetic signal in the re-entrant
spin glass phase. For the future, we suggest neutron studies under an in-plane magnetic
field that suppresses the spin glass phase; in this case, possibly antiferromagnetic reflec-
tions could be detected.
Finally, we want to note that successive magnetic orderings can be identified also in
the case of Ru substitution [31], Co doping [250, 251, 256, 257] and Ir doping [263]. This
implies the appearance of a re-entrant spin glass phase in all those compounds.
Therefore, we conclude that our magnetic phase diagram derived for EuFe2(As1−xPx)2
(see Fig. 7.15) is characteristic for (non-diluted) Eu based iron pnictides. In order to
confirm this, we suggest time-dependent measurements also on other compounds.
7.4 Outlook 115
Interplay of superconductivity and magnetism
The question how bulk superconductivity can coexist with Eu2+ magnetic ordering is quite
fundamental and requires the exact knowledge of the magnetic structure. Consistent with
Mössbauer and neutron powder diffraction [212, 234, 241], the results of our experiments
imply that in superconducting samples, a large net component of the Eu2+ spins is fer-
romagnetically aligned perpendicular to the layers. In addition, we find that glass-like
dynamics and freezing of the in-plane component develops below T2 which destroys coher-
ence between the Eu layers. Superconductivity in the iron pnictides is commonly believed
to take place mainly in the FeAs layers. In this scenario, the inner field resulting from
the Eu2+ ferromagnetic component along the c-axis could be screened by the formation of
spontaneous vortices perpendicular to the layers [31]. Together with the destroyed coher-
ence between the Eu layers due to the glass dynamics, this scenario might be the key to
understand how superconductivity can coexist with the usually strong Eu2+ magnetism.

8
OPTICAL PROPERTIES OF EuFe2As2
In this chapter, the in-plane optical response of EuFe2As2 is analysed. Particular focus
is set on the applicability of different modelling approaches, and the determination of
model-independent trends.
8.1 Overview
The temperature-dependent in-plane optical reflectivity of EuFe2As2 was measured in a
wide frequency range from 40 to 10000 cm−1 (see chapter 5.1), using an infrared Fourier
transform spectrometer; the corresponding optical conductivity was calculated via the
Kramer’s Kronig analysis. For the low-frequency extrapolation, in a first iteration the
Hagen Rubens relation was used, which got subsequently replaced in the fitting process;
the thus determined temperature-dependence of σdc follows nicely the resistivity curve
(as will be shown below). At high frequencies, the optical response was extended up to
30000 cm−1 by room temperature measurements with a Woollam spectroscopic ellipsome-
ter1; higher frequencies were extrapolated following measurements up to 32 eV carried out
for BaFe2As2 [169].
1 Ellipsometry measurements were performed by J. Braun at the 1. Physical Institute, Stuttgart.
118 8 Optical properties of EuFe2As2
Fig. 8.1a,b displays the thus obtained spectra at 200K and 290K, focusing on the high
frequency range. There is considerable spectral weight transfer up to very high energies,
which probably can be ascribed to Hund’s coupling (see chapter 4.4.5); the total spectral
weight is not recovered in the infrared frequency range.
Figure 8.1: (a-b) Frequency-dependent in-plane reflectivity and conductivity of EuFe2As2
at T =200K (purple) and 290K (red), as well as (c-d) spectral weight (SW) analysis. While
(c) displays the frequency-dependent spectral weight for 15K (blue), 30K (light blue), 180K
(dark blue), 200K (purple) and 220K (violet) normalized to 290K, (d) shows the total spectral
weight at 10000 cm−1; the linear fit (green dashed line) acts as a guide to the eye. With
decreasing temperature, spectral weight is shifted to high energies (above ∼ 6000 cm−1); the
total spectral weight is not recovered at 10000 cm−1.
At T < Ts,SDW = 190K, a gap develops in the optical spectrum, and additional spec-
tral weight transfer appears at low energies (see Fig. 8.1f and Fig. 8.2). We find only
one clearly visible gap, leading at 15K to a peak in the optical conductivity around
1400 cm−1 ≈ 10.8 kBTs,SDW. Its asymmetric shape is typical for a spin density wave gap
(see chapter 4.3), but could indicate also the existence of two neighbouring features (as
theoretically proposed by Yin et al. [168]). One should further note the FeAs phonon at
around 260 cm−1, which gains at T < Ts,SDW considerably oscillator strength and shifts
to higher frequencies.
Our finding of a single spin density wave gap is consistent with Ref. [184], however, we
are also aware that an additional smaller gap around the BCS weak coupling limit was
8.1 Overview 119
reported by Moon et al. [146]. As we investigated a sample of the same batch as Ref. [184],
one can speculate that the occurrence of the low-energy feature might strongly depend
on the sample quality1, but we are not aware of any similar reports for other compounds.
Therefore, it is intriguing to relate this untypical behaviour to the influence of the Eu2+
magnetism. Unfortunately, while there are predictions for the influence of the spin density
wave on the Eu2+ magnetism [11], the reverse case is - to our best knowledge - not yet
considered theoretically. Furthermore, one should note that the spectra at 15K and 30K
are basically the same within the experimental error, meaning that Eu2+ spin scattering
seems to have a negligible influence on the optical properties in the infrared frequency
range.
Figure 8.2: Frequency-dependent in-plane reflectivity and conductivity of EuFe2As2 at
T =15K (blue), 30K (light cyan), 180K (dark blue) and 290K (red). At T < Ts,SDW, a gap de-
velops in the optical spectrum and spectral weight is shifted to ∼ 1150 cm−1 and ∼ 1400 cm−1
at 180K and 15K, respectively; furthermore, the FeAs phonon at around 260 cm−1 gains con-
siderably oscillator strength. One should note that the spectra at 15K and 30K are the same
within the resolution. The noise visible in the conductivity spectrum at low frequencies is
typical for a reflectivity close to unity; data are not smoothed.
1 While our sample has a residual resistivity ratio R(300K)/R(5K) of ∼ 4.1, the one of Moon et al. has
only a ratio of ∼ 2.4.
120 8 Optical properties of EuFe2As2
8.2 Multi-component analysis
As already discussed in chapter 4.4.2, the multiband character of iron pnictides complicates
any analysis of optical spectra. Different multi-component models exist, however, it is
still not clear which one should be favoured and how much the modelling influences the
outcome of the analysis. Therefore, we have analyzed the optical response of twinned
EuFe2As2, using three different modeling approaches and discuss the commonly found
features. Importantly, we always show (semi-)logarithmic and linear plots, emphasizing
the low- and high-energy range, respectively.
Broad Drude approach
In 2010, Wu et al. proposed that the spectra of iron pnictides contain a temperature-
independent background in the mid-infrared energy range that can be fitted by a very
broad Drude term [128, 130]. However, a closer inspection reveals that such a temperature-
independent approximation is too rough due to the considerable spectral weight transfer
up to very high energies (see Fig. 8.1).
In order to investigate, whether such a broad Drude approach with temperature-depen-
dent parameters can be used to nicely describe the infrared response of EuFe2As2, Fig. 8.3
and Fig. 8.4 display the thus fitted spectra at 290K and 15K, respectively. At 290K, the
overall fit quality is good; however, one can note a slight discrepancy in the far-infrared,
where the fit first over- and then underestimates the response.
Indeed, this is exactly the energy range, where the model fails at low temperatures:
at 15K, an upturn of the conductivity above ∼ 350 cm−1 implies an additional, broad
Lorentzian at frequencies above 1000 cm−1. Fig. 8.4 excludes that a broad Lorentzian
around 3.4kBTs,SDW (the smaller gap found by Moon et al. [146]) can describe this feature.
Therefore, we conclude that the broad Drude approach is too oversimplified in order to
model nicely the far-infrared response of iron pnictides.
8.2 Multi-component analysis 121
Figure 8.3: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =290K in different logarithmic and linear plot styles. Grey squares rep-
resent data points, red lines the result of a broad Drude fit; the composition of the single
components is displayed in (c). The overall fit quality of the broad Drude approach is good;
slight discrepancies can be found in the far-infrared.
122 8 Optical properties of EuFe2As2
Figure 8.4: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =15K in different logarithmic and linear plot styles. Grey squares represent
data points, red lines the result of a broad Drude fit; the composition of the single components
is displayed in (c). A spin density wave gap leads to the piling up of an asymmetric peak
at ∼ 1400 cm−1 ≈ 10.8kBTs,SDW. The broad Drude approach fails to fit the spectra between
∼ 350 cm−1 and 1000 cm−1, even if we assume that the broader Drude is gapped with a gap
value of 3.4kBTs,SDW.
8.2 Multi-component analysis 123
MIR band approach
As already noted by Tu et al. [142], a multi-component analysis with only one Drude and a
series of Lorentzians that model incoherent transport in the mid-infrared is able to describe
the carrier dynamics of iron pnictides. Fig. 8.5 and Fig. 8.6 prove that such a fitting
approach is able to nicely describe spectra at high and low temperatures, respectively.
Figure 8.5: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =290K in different logarithmic and linear plot styles. Grey squares represent
data points, red lines the result of a MIR band fit; the composition of the single components
is displayed in (c). The MIR band approach nicely describes the spectra above Ts,SDW.
The corresponding temperature-dependent fit parameters are displayed in Fig. 8.7. Typ-
ically for a metal, the Drude component narrows smoothly with decreasing temperature,
until the scattering rate rapidly decreases for T < Ts,SDW (see Fig. 8.7a). One should note
that the obtained σdc values perfectly follow the temperature-dependence of the resistivity.
124 8 Optical properties of EuFe2As2
Figure 8.6: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =15K in different logarithmic and linear plot styles. Grey squares represent
data points, red lines the result of a MIR band fit; the composition of the single components
is displayed in (c). The MIR band approach nicely describes the spectra below Ts,SDW.
However, the increase of σdc with lowering temperature does not outweigh the decrease
of the scattering rate: Drude spectral weight is already lost above the spin density wave
transition. As can be seen in Fig. 8.7c, at T > Ts,SDW, the spectral weight is transferred
to the hump-like structure around 6000 cm−1 (and even higher energies), which shows a
significant blueshift with decreasing temperature; any spectral weight transfer is stopped
below the spin density wave transition. Interestingly, the width of this feature is constant
above Ts,SDW, but decreases rapidly at T < Ts,SDW - directly reflecting the behaviour of
the Drude component. Those observations indicate a strong relationship to the dynamics
8.2 Multi-component analysis 125
of the itinerant carriers, consistent with the suggestion that the bump originates from
Hund’s coupling.
Figure 8.7: Temperature-dependent fit parameters for the MIR band approach: (a) Scatter-
ing rate Γ , σdc compared to results from resistivity measurements (normalized to σdc(300K),
cyan curve), and spectral weight (SW) of the Drude component; (b) Center frequency ν,
damping Γ and spectral weight (SW) of the feature that is attributed to Hund’s coupling;
(c) spectral weight of the temperature-dependent components. The grey, vertical dashed line
denotes Ts,SDW; other dashed lines are a guide to the eye.
Fig. 8.7d also displays the spectral weight of the other temperature-dependent fit compo-
nents. Their total spectral weight decreases with decreasing temperature, as was already
discussed in the general spectral weight analysis (see Fig. 8.1). As the MIR band fol-
lows the behaviour of the Drude component, it probably contains a strong contribution
from itinerant carriers; indeed, the spectral weight gapped in the spin density wave phase
mostly corresponds to changes in the mid-infrared frequency range.
126 8 Optical properties of EuFe2As2
Subtraction approach
As in general, a model that includes two Drude components as well as a mid-infrared band
is overdetermined, one needs additional information for a reasonable fitting approach.
Here, we focus on the result of recent infrared studies: by subtracting low temperature
conductivity spectra from that at room temperature, Marsik et al. found for Ba, Sr and Ca
compounds a well-defined feature around 1000 cm−1 that could be attributed to interband
transitions involving Fe hole pockets [12].
Figure 8.8: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =290K in different logarithmic and linear plot styles, as well as (e) the
conductivity difference ∆σ1 = σ1(200K) − σ1(290K). Grey squares represent data points,
red lines the result of a fit with two Drude components and a Lorentzian at 1000 cm−1 that
can be attributed to interband transitions involving Fe hole pockets; the composition of the
single components is displayed in (c). The fitting approach nicely describes the spectra above
Ts,SDW.
8.2 Multi-component analysis 127
We believe that such a subtraction feature can be nicely described by a Lorentzian at
1000 cm−1 that broadens with increasing temperature. Indeed, EuFe2As2 shows the same
feature (see Fig. 8.8e). Therefore, we have fitted the spectra with two Drude components
and one Lorentzian at 1000 cm−1 that broadens with increasing temperature; the other fit
parameters of the Lorentzian are held constant in first approximation. As can be seen in
Fig. 8.8 and Fig. 8.9, the spectra can be nicely described by this approach.
Figure 8.9: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =15K in different logarithmic and linear plot styles. Grey squares repre-
sent data points, red lines the result of a fit with two Drude components and a Lorentzian
at 1000 cm−1 that can be attributed to interband transitions involving Fe hole pockets; the
composition of the single components is displayed in (c). The fitting approach nicely describes
the spectra below Ts,SDW.
However, one should note that other fitting variants are possible, too; for instance,
we have also fitted the high-temperature spectra under the condition that the broader
128 8 Optical properties of EuFe2As2
Drude should not get too broad (not to violate the Mott-Ioffe-Regel limit), allowing a
changing spectral weight of the Lorentzian at 1000 cm−1. The corresponding temperature-
dependent fit parameters of both fitting approaches are displayed in Fig. 8.10. The results
for the narrow Drude and the bump around 6000 cm−1 are independent from the fitting
approach. However, we can not disentangle the parameters for the broad Drude and the
Lorentzian at 1000 cm−1; a realistic description probably lies in between or even contains
more temperature-dependent Lorentzians (for example another one at 2300 cm−1 [12]).
However, we want to point out that with this model, we only see gap-like features in the
spectral weight of the Drude components, proving that this description is more realistic
than a general MIR band approach with only one Drude.
Figure 8.10: Temperature-dependent fit parameters for the model with two Drude compo-
nents and a Lorentzian at 1000 cm−1 under two different constraints: in the one case (filled
squares), only the damping of the Lorentzian was changed; in the other case (open points),
the scattering rate of the broad Drude was forced significantly below 1000 cm−1. (a) Scatter-
ing rate Γ of the narrow Drude; (b) scattering rate Γ of the broad Drude; (c) σdc (sum of
both Drude components) compared to results from resistivity measurements (normalized to
σdc(300K), cyan curve); (d) Center frequency ν and damping Γ of the feature that is attributed
to Hund’s coupling; (e) damping Γ of the Lorentzian at 1000 cm−1; (f) spectral weight of the
temperature-dependent components. The grey, vertical dashed line denotes Ts,SDW; other
dashed lines are a guide to the eye.
8.2 Multi-component analysis 129
Summary
We have shown exemplarily on EuFe2As2 that a broad Drude model without any additional
interband transitions in the mid-infrared is too oversimplified to describe the temperature-
dependent spectra of iron pnictides. In contrast, a more general MIR band approach yields
better results. The most realistic results are obtained with a model that contains two
Drude components (probably representing electron and hole bands) and a Lorentzian at
1000 cm−1, which can be attributed to interband transitions involving Fe hole pockets [12].
In particular, we find that some fitting results are independent from the model:
• The spin density wave gap affects the spectral weight and the scattering rate of both
Drude components.
• For temperatures above Ts,SDW, spectral weight is transferred from the narrow
Drude, but also from higher frequencies in the mid-infrared (and thus either from the
broad Drude or the interband transition at 1000 cm−1), to the bump-like structure
around 6000 cm−1 and even higher energies. At T < Ts,SDW, this spectral weight
transfer stops and the bump considerably narrows - directly reflecting the behaviour
of the Drude component(s). Those observations indicate a strong relationship to
the dynamics of the itinerant carriers, consistent with the suggestion that the bump
originates from Hund’s coupling.

9
MAGNETIC DETWINNING OF
EuFe2As2
As it was known that EuFe2As2 can be completely detwinned by applying relatively small
magnetic fields (∼ 1T) at temperatures T < TEu (see chapter 6.3.1), we performed a series
of magneto-optical measurements in order to study the electronic in-plane anisotropy of
iron pnictides without the need of complex mechanical detwinning devices. In this chapter,
we concentrate on the results from magneto-optical FIR measurements, which revealed a
much more complicated magnetic detwinning mechanism than expected from previous
neutron studies [7]. Combined with magnetization measurements, the observations can
be explained by an indirect magnetoelastic coupling of the Eu2+ spins to the lattice.
Those findings are further confirmed by resistivity, magneto-resistance, thermal expansion
and magnetostriction measurements and are published in Ref. [13]. Finally, preliminary
results on infrared measurements over a broad frequency range on persistently detwinned
EuFe2As2 are presented.
For all measurements, a well-defined cooling procedure was obeyed: first, the sample
was cooled from T > Ts,SDW to low temperatures in zero magnetic field and the zero-
field cooled (ZFC) response was measured. Afterwards, when an in-plane magnetic field
132 9 Magnetic detwinning of EuFe2As2
parallel to the [110]T-direction1 was first applied and then removed, we call this “field
treatment” (FT).
9.1 Magneto-optical measurements
The far-infrared spectral range is ideal to investigate the detwinning mechanism, as it is
governed by the anisotropic spin density wave gap as well as the FeAs phonon, and the
zero-field reflectivity is not notably influenced by the Eu2+ spin scattering (see chapter 8).
Detwinning at T < TEu
Fig. 9.1 displays the FIR reflectivity of EuFe2As2 at T = 15K for H ‖ [110]T with
H = 0T (ZFC), 1.0T, and 0T after field treatment (with 1T). The main observations
can be summarized as:
• The zero-field cooled 0T curves perfectly merge, indicating an initially balanced twin
domain ratio2.
• At a magnetic field of 1T, a notable difference is induced between the two polar-
izations: while the reflectivity is enhanced for E ‖ H, it is suppressed for the per-
pendicular polarization. At the same time, the FeAs phonon gets strongly reduced
for E ‖ H and enhanced for the perpendicular direction. In accordance with optical
studies on BaFe2As2 using mechanical clamps (see chapter 4.4.5), those observations
indicate that the crystal is detwinned with the orthorhombic a-axis being aligned
along the external field: a ‖ H. This is consistent with the results from neutron
studies [7].
• Surprisingly, we also observe a notable difference between the two polarizations after
the magnetic field is switched off, opposite to that at 1T. This indicates a second
detwinning process with b ‖ H at even lower magnetic fields, which stays persistent
after the field is removed.
In order to investigate this two-step detwinning process in more detail, we have per-
formed a series of magneto-optical FIR measurements with small field steps of ≤ 0.1T.
The results for E ⊥ H are shown in Fig. 9.2 and 9.3; for clarity, the relative reflectivity
1 We adapt the notation of the tetragonal system [hkl]T which is rotated by 45 ◦ along the c-axis with
respect to the orthorhombic system [hkl]O, e.g. [110]T = [100]O
2 The sample was mounted point-like on a copper cone. This avoids not only back-reflections from the
sample holder, but also minimizes the glued area and therefore external stress on the sample.
9.1 Magneto-optical measurements 133
Figure 9.1: Frequency-dependent reflectivity of EuFe2As2 at T =15K, for H = 0T (ZFC),
1T and 0T after FT (H ‖ [110]T); while the upper panel displays the whole FIR range, the
lower panel focuses on the FeAs phonon mode at ∼ 260 cm−1. The magnetic field induces
anisotropy between R(E ‖ H) (red) and R(E ⊥ H) (black) as well as changes the FeAs
phonon mode, both corresponding to the magnetic detwinning. A distinct anisotropy remains
after the magnetic field is switched off; it is opposite to that at 1T.
is displayed, i.e. the reflectivity normalized to its initial zero-field value. While Fig. 9.2 is
a false-colour plot of the field and frequency-dependent relative reflectivity, revealing on
the first view the main dynamics, Fig. 9.3 resolves the details in a conventional plot. It
can be concluded:
• For increasing magnetic fields, the reflectivity rises rapidly at around 0.1T for fre-
quencies1 above ∼ 300 cm−1, afterwards staying almost constant. Thus, H1 ∼ 0.1T
can be identified as the critical field where twin domains preferentially align with
b ‖ H. A sharp drop in the reflectivity at H2 ∼ 0.65T marks the second, opposite
detwinning process with a ‖ H. For higher fields, the reflectivity stays again almost
constant.
• For decreasing fields, the latter process is reversible with a slightly lower critical field
∼ 0.60T. However, the detwinning at low fields is persistent.
1 The behaviour at lower frequencies is more complex, probably as Eu2+ spin scattering plays here a
more important role.
134 9 Magnetic detwinning of EuFe2As2
• One should note the distinct changes of the FeAs phonon, which is strongly reduced
at low and enhanced at high fields (see Fig. 9.3b). Those strong phonon changes
(which follow the intensity changes of the reflectivity) support that a structural
detwinning causes the electronic anisotropy.
Figure 9.2: False colour plot of the frequency- and field-dependent FIR relative reflectivity
R(H)/R(0T) of EuFe2As2 at T =15K (H ‖ [110]T, E ⊥ H). The detwinning fields (where
the reflectivity abruptly de- and increases) can be identified as H1 ∼ 0.1T and H2 ∼ 0.65T
for increasing, and H2 ∼ 0.6T for decreasing fields.
9.1 Magneto-optical measurements 135
Figure 9.3: Frequency-dependent relative reflectivity (normalized to the ZFC reflectivity) of
EuFe2As2 at T =15K, for H = 0T (ZFC), 1T and 0T after FT (H ‖ [110]T, E ⊥ H); while
the upper panel displays the whole FIR range, the lower panel focuses on the FeAs phonon
mode at ∼ 260 cm−1. For increasing fields (left panels), the reflectivity first decreases and then
increases abruptly at ∼ 0.1T and ∼ 0.65T, respectively. For decreasing fields only the upper
process takes place at ∼ 0.60T; the lower process is irreversible. The low-field detwinning
is accompanied by a reduction of the FeAs phonon oscillator strength; the high-field process
by an enhancement. Grey dashed arrows mark the direction of the spectral changes with
sweeping the magnetic field.
136 9 Magnetic detwinning of EuFe2As2
Detwinning at T > TEu
While the neutron studies concentrated on temperatures T < TEu, we have also investi-
gated whether any magnetic detwinning can be observed above TEu.
Fig. 9.4 displays the FIR reflectivity of EuFe2As2 at T = 30K for H ‖ [110]T with
H = 0T (ZFC), 1.0T, and 0T after field treatment (with 1T):
• Similar to the measurements at 15K, the zero-field cooled 0T curves perfectly merge,
proving an initially balanced twin domain ratio as well as the high quality of the
measurements.
• At a magnetic field of 1T, a notable difference is induced between the two polar-
izations, similar to that at 15K. This indicates that the crystal gets sufficiently
detwinned also at temperatures T > TEu by small magnetic fields with a ‖ H.
• Again, we also observe a notable difference between the two polarizations after the
magnetic field is switched off. However, now the direction of the anisotropy is the
same as at 1T, indicating only one (persistent) detwinning process.
Figure 9.4: Frequency-dependent FIR reflectivity of EuFe2As2 at T =30K, for H = 0T
(ZFC), 1T and 0T after FT (H ‖ [110]T). The magnetic field induces anisotropy between
R(E ‖ H) (red) and R(E ⊥ H) (black) as well as changes the FeAs phonon mode, both
corresponding to the magnetic detwinning. A distinct anisotropy remains after the magnetic
field is switched off.
A detailed series of measurements reveals that the detwinning process at 30K is rather
continuous, with the main changes arising between 0.3T and 0.7T (see Fig. 9.5). The
induced detwinning shows an almost complete persistence.
9.1 Magneto-optical measurements 137
Figure 9.5: False colour (upper panel) and conventional plot (lower panel) of the frequency
and field-dependent FIR relative reflectivity R(H)/R(0T) of EuFe2As2 at T =30K (H ‖
[110]T, E ⊥ H). The detwinning is rather continuous, with the main changes arising between
0.3T and 0.7T. A distinct anisotropy remains after the magnetic field is switched off.
138 9 Magnetic detwinning of EuFe2As2
Control measurements
In order to verify that the induced anisotropy corresponds to the magnetic detwinning,
measurements were repeated on EuFe2As2 with H ‖ [100]T, i.e. with the magnetic field at
a 45◦ angle to the orthorhombic axes and the easy axes of the Eu2+ magnetic moments.
In this case, no twin is favoured and thus, no detwinning should appear (limited by
the accuracy of aligning the crystal perfectly along the [100]T-direction). Additionally,
comparison measurements were performed on BaFe2As2 single crystals with H ‖ [110]T.
As can be seen in Fig. 9.5, in both control experiments no anisotropy is induced within
the limit of our resolution. This proves that the observed effects discussed above must be
related (i) to a redistribution of twins and (ii) to the presence of Eu2+ moments.
Figure 9.6: Frequency-dependent relative reflectivities of BaFe2As2 (T =15K) and EuFe2As2
(T =15K, 30K) for different magnetic field directions. Relative reflectivities of (a) BaFe2As2
with H ‖ [110]T = 0.5T (grey) and 1T (black) (T =15K, E ⊥ H) as well as of (b,c) EuFe2As2
with H ‖ [100]T = 1T ((b) T =15K and (c) 30K, E ‖ H: red, E ⊥ H: black) do not show
magnetic field induced anisotropy.
Heating persistence
As our experiments reveal a persistent detwinning induced by small magnetic fields at
low temperatures (T < Ts,SDW = 190K), a central question that arises is what happens
when a persistently detwinned crystal is heated up. Fig. 9.7 displays a series of reflectivity
measurements, where EuFe2As2 was subject of the following cooling and field treatment
procedure:
• Reflectivity spectra were taken after initial zero-field cooling at 30K and 15K, re-
vealing an isotropic response (see Fig. 9.7a,b).
• Field treatment at 15K (with 1T) induces a distinct anisotropy with R(E ‖ H) <
R(E ⊥ H), corresponding to a persistent detwinning for temperatures T < TEu with
9.2 Magnetization measurements 139
b ‖ H and a more pronounced spin density wave gap along the b-direction (compare
Fig. 9.7c with Fig. 8.2).
• This anisotropy persists when heating up to 30K (see Fig. 9.7d).
• Subsequent field treatment at 30K (with 1T) reverses the anisotropy, consistent
with a persistent detwinning for temperatures T > TEu with a ‖ H.
This proves that the persistent detwinning induced at temperatures T < TEu is robust
against heating up above the Eu2+ magnetic ordering temperature. However, subsequent
field treatment at T > TEu is able to inverse the anisotropy.
Figure 9.7: Frequency-dependent reflectivity of EuFe2As2 after ZFC at (a) T = 30K and
(b) 15K; the reflectivity is isotropic. (c) Field treatment at 15K (with 1T) induces a distinct
anisotropy, (d) which persists when heating (in 0T) to 30K. (e) Subsequent field treatment
at 30K (with 1T) reverses the anisotropy.
Indeed, the thus induced anisotropy persists up to the structural and spin density wave
transition at Ts,SDW, as demonstrated in Fig. 9.8. However, if the crystal was once heated
above Ts,SDW and cooled down afterwards in zero field, this anisotropy has completely
vanished (see Fig. 9.8d).
9.2 Magnetization measurements
Since the magneto-optical measurements indicate that the Eu2+ spins drive the detwin-
ning, magnetization measurements1 should provide further information about the complex
detwinning mechanism.
1 For the magnetization measurements, the sample was fixed between two stripes of plastic foil by wrap-
ping Teflon tape around them. This minimize the external stress on the sample.
140 9 Magnetic detwinning of EuFe2As2
Figure 9.8: Frequency-dependent reflectivity of EuFe2As2 after field treatment at T = 30K
with 1T (H ‖ [110]T) for (a) 30K, (b) 100K and (c) 180K. Although the magnetic field
is switched off during the measurement, the reflectivity along the orthorhombic axes is
anisotropic. (d) After the crystal was heated to 220K (well above Ts,SDW) and cooled down
again to 180K, any anisotropy disappeared.
Detwinning at T < TEu
Fig. 9.9a displays the field-dependent magnetization at 2K for H ‖ [110]T. In the first
field cycling after zero-field cooling,M(H) exhibits two transitions for increasing, but only
the upper one for decreasing field. The transition at higher fields can be identified as a
spin-flip due to the abrupt increase of the magnetization, which saturates afterwards (see
chapter 2.3). In further field sweeps, only the spin-flip is visible. Moreover, the low-field
transition is completely invisible for field sweeps with H ‖ [100]T, suggesting a relationship
to the magnetic detwinning with b ‖ H observed in the magneto-optical measurements.
Figure 9.9: Field-dependent magnetization of EuFe2As2 at T = 2K for different magnetic
field directions: (a) H ‖ [110]T and (b) H ‖ [100]T. (a) At ∼ 0.7T, M(H) sharply increases,
afterwards reaching saturation. Irreversible behaviour at around 0.1T is only observed during
the first field cycling and when the field is parallel to the crystal’s orthorhombic axes (black
points: increasing H after ZFC, red points: decreasing H within the first cycling, blue stars:
increasing H in the second cycling).
9.2 Magnetization measurements 141
Temperature-dependent magnetization measurements with H ‖ [110]T further support
this interpretation (see Figure 9.10):
• Zero-field cooled M(T ) curves obtained at very low fields show a peak at TEu, how-
ever, the magnetization does not drop to zero for lower temperatures (see Fig. 9.10a).
Indeed, the curve can be described as a superposition of antiferromagnetic suscepti-
bilities parallel and perpendicular to the easy axes (see chapter 2.3), corresponding
to equally distributed twin domains.
• For intermediate fields, M(T < TEu) shows a flat curvature, indicating an antifer-
romagnetic spin alignment with the easy axes perpendicular to the external field
(see Fig. 9.10b). As the easy axes of EuFe2As2 corresponds to its crystallographic
a-direction, this is consistent with the low-field magnetic detwinning (that leads to
b ‖ H).
• A similar flat curvature below TEu can be observed for very low fields after field
treatment (see Fig. 9.10d), indicating that the detwinning with b ‖ H is persistent.
• As expected from the field-dependent magnetization measurements, the transition
at TEu smears out above the spin-flip field, as field enforced ferromagnetism sets in
(see Fig. 9.10c).
Figure 9.10: Temperature-dependent magnetization for EuFe2As2 at certain magnetic fields
H ‖ [110]T with and without field treatment. (a) 0.1T (ZFC), (b) 0.3T (ZFC), (c) 0.9T
(ZFC), and (d) 0.1T (FT with 1T). (a) While the ZFC 0.1T curve displays a cusp at TEu,
(d) the corresponding FT curve displays a rather flat magnetization below TEu. (b) The latter
curvature is also observed at 0.3T (after ZFC). (c) M(T ) at 0.9T increases smoothly with
decreasing temperature without any distinct anomaly at TEu.
The question remains how exactly the spin-flip is related to the second detwinning
process with a ‖ H. Therefore, field-dependent magnetization measurements at 15K are
142 9 Magnetic detwinning of EuFe2As2
displayed together with the results from magneto-optical measurements in Fig. 9.11a. The
overall magnetization behaviour is very similar to that at 2K, despite a smooth increase
of the magnetization above the spin-flip field due to thermal fluctuations. While the
irreversible behaviour in optical and magnetization measurements appears in both cases
around H1 ∼ 0.1T, the spin-flip field HSF ∼ 0.5T slightly precedes the detwinning process
observed in the reflectivity by about 0.1T.
Figure 9.11: Field-dependent magnetizationM(H) (grey open circles) and false colour plot of
the frequency and field-dependent FIR relative reflectivity R(H)/R(0T) (E ⊥ H) of EuFe2As2
at (a) T =15K and (b) 30K (H ‖ [110]T). The detwinning fields H1 and H2 as well as the
spin-flip field HSF of Eu2+ can be identified (H1 < HSF < H2).
Detwinning at T > TEu
As can be seen in Fig. 9.11b, no transition is visible in M(H) for T = 30K. It is in-
triguing to associate the smooth increase of the magnetization with the rather continuous
detwinning process at T > TEu.
9.3 Detwinning mechanism 143
9.3 Detwinning mechanism
In summary, we have to explain how the magnetic detwinning takes place below and
above the local Eu2+ magnetic ordering. While at T < TEu, the crystal gets detwinned
with b ‖ H at very low fields (∼ 0.1T at 15K) and with a ‖ H at slightly higher magnetic
fields (∼ 0.6T at 15K), at T > TEu, only the latter takes place. Most strikingly, a
significant imbalance of twin domains remains even when the field is switched off, and the
temperature is raised up to T > Ts,SDW.
Indirect magneto-elastic coupling
The first question one should address is how the magnetic detwinning fields can be reduced
in EuFe2As2 by more than two orders of magnitude compared to other iron pnictides.
Magneto-elastic coupling usually arises due to spin-orbit interactions. However, the
orbital momentum of Eu2+ is zero; thus the magnetic anisotropy induced by spin-orbit
interactions is negligible. Another possibility to induce magnetic anisotropy is by dipole-
dipole interactions. However, the resulting anisotropy is much weaker [306]. Therefore,
other unconventional interactions must cause our observations.
From the doped or (chemically) pressurized Eu compounds, it is well known that the
Eu2+ and Fe2+ magnetic orders are strongly intertwined (see chapter 6). Furthermore, the
orbital moment of Fe2+ is non-zero, leading in BaFe2As2 to a significant magneto-elastic
coupling [24]. Hence, we suggest that the Eu2+ spins couple indirectly to the lattice via the
Fe2+ spins. Such an indirect magneto-elastic coupling was, to the best of our knowledge,
not yet observed before.
Detwinning at T < TEu
In order to explain the two-step detwinning process at temperatures T < TEu, a simple
model based on the competition between magneto-crystalline anisotropy ∆, antiferromag-
netic exchange coupling J and Zeeman energy is sufficient. Two twin domains have to
be considered, one with the easy a-axis perpendicular (type B‖) and one with it parallel
(type A‖) to the external field (see Fig. 9.12a).
144 9 Magnetic detwinning of EuFe2As2
(a) H = 0T (b) H ≈ H1 (c) H = HSF (d) H ≥ H2
Detwinning:
     a || H
a a a
a a a a
b b b
bbbb
a
b
c
a
b
c
H
H
H
(e) 
HSF
H
E
E0
twin BII
twin AII
Detwinning:
     b || H
twin BII
twin AII
H1 H2
Δ
Figure 9.12: Sketch of the twin distribution and spin configuration of EuFe2As2 dependent
on an (from left to right increasing) external magnetic field H ‖ [110]T at T < TEu. Top and
bottom rows show a detail of the EuFe2As2 crystal and magnetic structure (Eu atoms and
spins (blue), Fe atoms (yellow) and spins (brown), As atoms (green)) that correspond to the
twin distribution sketched in the middle row. (a) For H = 0T, the ZFC crystal is twinned and
the domains are equally distributed. The Eu2+ spins are ordered A-type antiferromagnetically
with the spin direction along the a-axis. (b) With external field, twin variant B‖ (red, bottom)
with b ‖ H gets energetically favoured and therefore grows on the expense of variant A‖ (green,
top), as soon as the energy difference exceeds the twin boundary pinning energy. (c) With
further increasing field, Eu2+ spins in the remaining type A‖ twins flip along the field direction.
Energetically, twin B‖ is still more favourable. (d) At slightly higher fields, twin A‖ is favoured
and the crystal is detwinned with a ‖ H. (e) Corresponding energy curves (E0: ground state).
While at low fields twin B‖ is energetically favourable (red area), twin A‖ gets favourable
at higher fields (green area). Detwinning takes place at H1 and H2, when the energy gain
exceeds the pinning energy of the twin boundary.
9.4 Other techniques 145
After cooling in zero magnetic field, the crystal is twinned with equally distributed
variants. The simplest form for the energy is then given by (see chapter 2.3):
E = −2Mµ0H(cos θ + cosϕ) + JM2 cos(θ + ϕ)
−12∆

sin2 θ + sin2 ϕ (B‖)
cos2 θ + cos2 ϕ (A‖)
,
(9.1)
where θ and ϕ are the angles between spins and magnetic field and E0 = −JM2 −∆ is
the 0T ground state energy. Minimizing the energy for θ = ϕ yields (see Fig. 9.12e):
E
B‖
min = E0 −
M2(µ0H)2
2JM2 +∆ (9.2)
E
A‖
min = E0 +∆−
M2(µ0H)2
2JM2 −∆ (9.3)
Thus, at low fields, the Eu2+ spins of variant B‖ gradually rotate towards the direction
of the external magnetic field, lowering the system’s energy. When EB‖min−E
A‖
min exceeds the
twin boundary pinning energy, variant B‖ grows irreversibly on the expense of variant A‖,
and the crystal gets detwinned with b ‖ H (see Fig. 9.12b). Increasing the magnetic
field further induces a spin-flip in variant A‖ (see Fig. 9.12c), but this twin variant is
energetically favourable only at slightly higher fields, when the crystal gets detwinned
with a ‖ H (see Fig. 9.12d).
As characteristic for domain dynamics, these processes are strongly irreversible, leading
to a significant persistent detwinning.
Detwinning at T > TEu
At T > TEu, the unordered Eu2+ spins gradually align along the direction of the external
field, leading to a net magnetic moment along H. This favours for H ‖ [110]T the domain
type, where the Fe2+ spins are aligned along the field direction. Therefore, a detwinning
with a ‖ H can be observed, as soon as the energy gain exceeds the twin boundary pinning
energy.
9.4 Other techniques
Additional resistivity, magneto-resistance, thermal expansion and magnetostriction mea-
surements were performed in the group of P. Gegenwart (by J. Maiwald, C. Stingl, N.
Bach, and I. Pietsch, University of Göttingen / Augsburg). The main results are depicted
in Fig. 9.13 and 9.14 and described in detail in Ref. [13].
146 9 Magnetic detwinning of EuFe2As2
Resistivity and magneto-resistance
Resistivity measurements after field treatment impressively demonstrate the persistent de-
twinning, as a strong anisotropy along the orthorhombic axes remains after the magnetic
field was switched off (see Fig. 9.13a,b). Consistent with the magneto-optical measure-
ments, the induced anisotropy is opposite for field treatment below and above TEu. One
should note that its magnitude agrees well with values obtained for mechanically detwinned
Eu compounds [197, 240], and remains virtually constant up to Ts,SDW.
Figure 9.13: Resistivity and magneto-resistance of ZFC EuFe2As2 (H ‖ [110]T, data taken
by J. Maiwald, University of Göttingen / Augsburg). (a,b) Temperature-dependent resistivity
ρFT(T ) after field treatment with 4T for currents parallel (red) and perpendicular (black) to
H, normalized to the corresponding zero-field cooled value. A strong anisotropy along the
orthorhombic axes remains after the magnetic field was switched off. For field treatment at
(a) T = 4K and (b) at 30K the opposite behaviour is observed. (c,d) Magneto-resistance
ρ‖(H)/ρ‖(0T) − 1 at (c) 5K and (d) 30K. (c) Below TEu, ρ‖(H) first increases and then
decreases with increasing H; (d) above TEu, it decreases with increasing H. The initial ZFC
value is not recovered after field sweeping.
Magneto-resistance measurements further resemble the results obtained by the magneto-
optical measurements, however, the critical fields seem to be different (Fig. 9.13c,d). The
main reason for this discrepancy is that all electronic contributions add up at zero fre-
quency, meaning that other field-dependent processes such as Eu2+ spin scattering also
play an important role [198]; this masks the response due to the magnetic detwinning.
Moreover, one should note that the electric contacts needed in resistivity measurements
9.4 Other techniques 147
induce significant stress on the sample. Indeed, already this force is often strong enough
to partially detwin a sample1 and might influence transition temperatures and fields.
Thermal expansion and magnetostriction
Concurrent evidence for a persistent structural detwinning is also found in thermal expan-
sion and magnetostriction measurements (see Fig. 9.14), techniques which directly probe
the induced length changes. Relative length changes are of the order of 10−3, exceeding
the typical magnetostriction of Eu based materials by at least two orders of magnitude.
Figure 9.14: Thermal expansion and magnetostriction ∆L(T )/L0 of ZFC EuFe2As2 (H ‖
[110]T, ∆L ‖ H, data taken by C. Stingl, N. Bach, and I. Pietsch, University of Göttingen).
(a) Thermal expansion after zero-field cooling (black) and field treatment with 2T at 4K
(cyan). Apart from transitions at TEu and Ts,SDW, the sample is shorter after field treatment.
(b,c) Magnetostriction at (b) 30K and (c) 5K for increasing (black, brown) and decreasing
(green) H. (c) While at T > TEu, the sample expands along H, (b) at T < TEu, it first
contracts and then expands. The initial ZFC value is not recovered after field sweeping.
By comparing those results with experimentally determined lattice constants [26], one
can yield information about the detwinning fraction. Assuming a temperature-independent
fraction n of twins with b ‖ H, the mean length of a unit cell in field direction follows as
L¯ = n · b(T ) + (1− n) · a(T ). (9.4)
1 Therefore, Fig. 9.13 only displays relative values of the resistivity.
148 9 Magnetic detwinning of EuFe2As2
The relative length change compared to aT (the tetragonal lattice constant at 300K) then
reads as:
∆L
L0
= L¯− aT
aT
. (9.5)
By setting n = 66%, we can reproduce the ZFC curve in Fig. 9.14 reasonably well, indi-
cating that the sample is already partially detwinned due to the uniaxial pressure from
the dilatometer, which favours twins with the shorter axis b ‖ ∆L. Nevertheless, the twin
configuration can be changed to n = 70% by field treatment. Importantly, the induced
imbalance of twin domains stays constant up to Ts,SDW
9.5 Detwinning fraction
From neutron measurements, we know that the crystal gets completely detwinned at
1T [7]. However, the question remains whether we can quantize the detwinning fraction
after field treatment. Unfortunately, our methods do not provide a key for a quantitative
estimate:
• As in BaFe2As2 the FeAs phonon is only visible along the b-direction, it is intriguing
to use this phonon in order to determine the detwinning fraction. In our measure-
ments on EuFe2As2, however, even for 1T (where the crystal should be completely
detwinned according to the neutron studies), the phonon is still visible in σa (see
Fig. 9.15). Its presence could be attributed to the imperfect polarizer and the im-
proper alignment of polarizer and sample with respect to the external magnetic field,
however, its suppression along the a-direction might be also strongly composition-
dependent - similar to the appearance of the smaller spin density wave gap (see also
section 9.6). Therefore, we are not able to extract reliable information about the
detwinning fraction by our magneto-optical measurements.
• Resistivity measurements show that the anisotropy induced by field treatment agrees
well with values obtained for mechanically detwinned Eu compounds [197, 240].
Therefore, the magnetic detwinning provides a good alternative to mechanical de-
vices; however, the absolute value of the detwinning fraction stays unclear.
• Thermal expansion and magnetostriction measurements can not be used to deter-
mine the detwinning fraction, as the uniaxial pressure from the dilatometer already
detwins the sample partially.
However, we speculate that more information can be extracted from already published
neutron diffraction data: in the first manuscript of Xiao et al., where no magnetic fields
were used at all, equally distributed twin domains were reported [8]. However, in a later
9.6 Further infrared studies 149
Figure 9.15: Polarization-dependent optical conductivity of EuFe2As2 around the FeAs
phonon mode at ∼ 260 cm−1 for 15K with and without magnetic field; 0T data were used for
an appropriate extrapolation before performing the Kramers-Kronig transformation. (a) 0T
(ZFC), (b) 1T (H ‖ [110]T, resolution 1 cm−1). In the magnetic field, the oscillator strength
of the phonon is enhanced for σb (E ⊥ H, black) and reduced for σa (E ‖ H, red).
study about the influence of magnetic fields on the structure and Eu2+ magnetism, the
same authors claimed at 0T a domain ratio of 1:3 [7]; the low-field detwinning process
was not observed at all. We suspect that the authors did not obey a well-defined cooling
process, causing at 0T an imbalanced twin domain ratio due to the persistent detwinning.
This would imply that field treatment partially detwins EuFe2As2 with the domain ratio
of 1:3.
One possible explanation why the crystal does not get completely detwinned at H1
and after field treatment is that we have to consider the three-dimensional nature of the
A-type antiferromagnetism, as presented in Fig. 9.16. Within one layer, Eu2+ spins of
next-nearest structural domains can be aligned parallel (see Fig. 9.16a,b) or antiparallel
(see Fig. 9.16c,d). The reorientation of the intermediate domain will be less favourable
for the latter case and might be prohibited. This would lead to a detwinning fraction of
75% (consistent with our reinterpretation of the neutron data): 50% of the domains are
initially oriented with b ‖ H, additional 25% can be reoriented by the field treatment (see
Fig. 9.16a,b).
9.6 Further infrared studies
We have also performed first test measurements over a broad energy range on magnetically
detwinned samples. However, the detectors available in the FFIR and MIR energy range
could not guarantee (in conjunction with the complex magneto-optical setup, see chap-
ter 5.1) a high enough signal-to-noise ratio as well as a sufficient time-stability for a com-
150 9 Magnetic detwinning of EuFe2As2
a
b
a
b
b
a
a
b
a
bb
a
a
b
b
a a
b
a
b b
a
a
b
(a)
(b)
(c)
(d)
Figure 9.16: Considering the three-dimensionality of A-type antiferromagnetism could ex-
plain, why the crystal gets not completely detwinned at H1. Within one layer, Eu2+ spins
(blue) of next-nearest structural domains can be aligned (a,b) parallel or (c,d) antiparallel.
The reorientation of the intermediate domain will be less favourable for the latter case.
plete gold evaporation run. Therefore, we present here only preliminary results at 30K1.
While FIR data are measured completely in the magneto-optical setup, the reflectivity of
the other energy ranges were obtained as followed: absolute values achieved in the conven-
tional zero-field cryostat were normalized by the ratio of the reflectivities before and after
field treatment, both obtained in the magneto-optical setup. FFIR data are smoothed; due
to strong absorptions in the MIR range originating from the non-exchangeable polypropy-
lene windows of the cryostat, the mid-infrared spectrum was strongly smoothed, as well
as cutted above 3000 cm−1; higher frequencies were extrapolated with the 0T data, low
frequencies according to the σdc-values. We note that all spectral ranges perfectly merge
(see Fig. 9.17).
Similar to the reports on BaFe2As2 (see chapter 4.4.5), we observe a strong anisotropy
in the mid-infrared frequency range. By fitting with the “subtraction approach” intro-
duced in chapter 8.2, we find 1/τb > 1/τa and slightly higher Drude weights for the
a-direction, similar to Ref. [171]. Furthermore, we confirm that the spin density wave gap
around ≈ 10.8kBTs,SDW consists of two features, with the higher feature stronger visible
in the b-direction. This is consistent with measurements and theoretical calculations for
BaFe2As2 [168, 169]. However, we do not observe any evidence for a lower spin density
wave gap along one of the main crystallographic directions, consistent with our results on
the twinned crystal (see section 8.1).
Furthermore, our observations concerning the FeAs phonon differ from the behaviour
reported for BaFe2As2, as already discussed in chapter 9.5. Along the orthorhombic a-
1 Further measurements on a newly constructed magneto-optical setup at the 1st Physical Institute,
Stuttgart are scheduled.
9.6 Further infrared studies 151
Figure 9.17: Frequency-dependent in-plane (a-b) reflectivity and (c-d) conductivity of
EuFe2As2 at T =30K in different logarithmic and linear plot styles. Grey (light cyan) squares
represent data points for E ‖ a (E ‖ b), black (dark cyan) lines the corresponding fit with
two Drude components and a Lorentzian at 1000 cm−1. (d) The phonon is narrower along the
b-direction and slightly shifted to lower frequencies.
direction, it has a reduced oscillator strength, but does not disappear. Indeed, we are able
to identify for σa(ω) a slight blueshift of the phonon (see Fig. 9.17d). This blueshift is
consistent with a weak higher-energy a-axis phonon contribution revealed for BaFe2As2
by Schafgans et al. [174]. We suggest that this contribution is more pronounced in the
case of EuFe2As2. Therefore, high-resolution far-infrared measurements on mechanically
detwinned EuFe2As2 crystals could give important information on the anisotropic phonon
dynamics in 122 iron pnictides, which are yet not well understood [171].
152 9 Magnetic detwinning of EuFe2As2
9.7 Outlook
Our magneto-optical and magnetization measurements reveal a dramatic reduction of
magnetic detwinning fields compared to other AFe2As2 (A = Ba, Sr, Ca) iron pnictides
by indirect magneto-elastic coupling of the Eu2+ ions. Such an indirect magneto-elastic
coupling was, to our best knowledge, not demonstrated before.
We find that only ∼ 0.1T are sufficient for persistent detwinning below the local Eu2+
ordering, accessible by typical laboratory magnetic fields; a significant imbalance of twin
domains remains constant up to the structural and electronic phase transition (190K).
This is surprising from a very fundamental point of view, as the detwinning induced at
low temperatures with very small magnetic fields persists up to much higher temperatures
and thus energy scales. This may even lead to technical applications.
With respect to the research on high temperature superconductors, the whole effect un-
covers a remarkable interdependence between magnetic, electronic and structural effects.
It is surprising that the Eu2+ magnetic order strongly affects the lattice, although it does
not destroy superconductivity in substituted compounds. This opens up unprecedented
possibilities for fundamental research concerning the interplay of superconductivity and
magnetism. Finally, our findings provide a unique possibility to study macroscopically the
intrinsic in-plane anisotropy of iron pnictides without the application of any symmetry-
breaking external force.
10
SUMMARY AND OUTLOOK
The investigations carried out in the framework of this thesis reveal that Eu based iron
pnictides offer a unique playground to examine the interplay of unconventional electronic
properties, superconductivity, itinerant and local magnetism.
Through systematic magnetization studies on a complete set of EuFe2(As1−xPx)2 single
crystals, we have derived the complex magnetic phase diagram of Eu 122 pnictides (see
chapter 7). As a first step, we identified a ferromagnetic out-of-plane component that
develops in the underdoped, non superconducting region of the phase diagram, consis-
tent with canted A-type antiferromagnetism. In addition, the Eu2+ magnetic transition
temperature TN is suppressed similar to the structural and spin density wave transition
Ts,SDW and rises again as soon as superconductivity sets in. This implies that the Eu2+
spin orientation in the parent compound is defined by the spin density wave anisotropy,
consistent with theoretical calculations by Akbari et al. [11]. Therefore, we conclude sig-
nificant interactions between the local Eu2+ and the (quasi-) itinerant Fe magnetism.
Furthermore, we identified the development of a re-entrant spin glass phase at lower
temperatures, characterized by time-dependent processes that appear due to the freezing
of the in-plane spin components. The corresponding transition temperature Tglass rises
quickly in the underdoped region until it is almost as high as TN for superconducting
compounds. For higher P substitution levels, both transition temperatures continuously
increase, separated only by ∼ 2K. One should further note the rather narrow supercon-
154 10 Summary and outlook
ducting dome, which might be related to a Lifshitz transition [235] that also affects the
RKKY-exchange. However, our studies rule out any change to ferromagnetic interlayer
coupling at high P substitutions.
All these findings are probably common features of (non-diluted) Eu based iron pnic-
tides, as discussed on the basis of a review given in chapter 6. It can be speculated
that the Eu2+ ferromagnetic component along the c-axis is screened by the formation of
spontaneous vortices perpendicular to the layers [31]. Most importantly, the glass-like dy-
namics indicate a decoupling of the Eu layers, therefore implying that superconductivity
in the intermediate FeAs layers is mostly unaffected by any magnetic interlayer coupling.
Thus, our findings elucidate how bulk superconductivity can coexist with the strong Eu2+
magnetic ordering.
Despite the interactions of local and itinerant magnetism revealed by our magnetization
studies, the electrodynamic response of EuFe2As2 is surprisingly unaffected by the Eu2+
magnetic transition, evidenced by infrared spectra that basically do not change when
passing TN (see chapter 8). However, we are able to confirm earlier results of Wu et
al. [184], who reported the absence of any spin density wave gap feature around the BCS
weak-coupling limit. Although it is intriguing to relate this absence to the local Eu2+
magnetism, such a relationship has (yet) no theoretical background.
In order to obtain more information about the general electrodynamic properties of
iron pnictides, we have further compared typical fitting approaches. We find that real-
istic results are obtained with a model that contains two Drude components (probably
representing electron and hole bands) and a Lorentzian around 1000 cm−1, which can be
attributed to interband transitions involving Fe hole pockets [12]. Importantly, we find
that regardless of the fitting method, the spin density wave transition affects not only both
Drude components, but also the spectral weight transfer to a bump-like structure in the
near-infrared and even higher energies. This supports a strong relationship of the latter
feature to the dynamics of the itinerant carriers, consistent with correlation effects due to
Hund’s rule coupling.
Finally, it was demonstrated in chapter 9 that magneto-optical measurements in the
far-infrared frequency range are ideal to investigate the magnetic detwinning mechanism
in EuFe2As2. We find that only ∼ 0.1T are sufficient for a persistent detwinning below the
local Eu2+ ordering temperature, which is accessible by typical laboratory magnetic fields;
above TN, only slightly higher fields (around 1T) are needed. We ascribe these observations
to an indirect magneto-elastic coupling of the Eu2+ ions via the Fe2+ spins, which was -
to our knowledge - not observed before, and give a simple model based on the competition
between magneto-crystalline anisotropy, antiferromagnetic exchange coupling and Zeeman
155
energy. Our findings are further confirmed by magnetization, magneto-striction, thermal
expanison and (magneto-)resistance measurements.
Most importantly, the term persistent detwinning implies that a significant imbalance
of twin domains remains when the magnetic field is switched off and the temperature is
raised up to Ts,SDW. Such strongly hysteretic behaviour is surprising from a very funda-
mental point of view, as the detwinning that is induced at low temperatures with very
small magnetic fields persists up to much higher temperatures and thus energy scales.
In summary, the whole effect uncovers a remarkable interdependence between magnetic,
electronic and structural effects in Eu based iron pnictides.
While all studies performed in the framework of this thesis concentrated on EuFe2-
(As1−xPx)2, we suggest that many of our findings have further implications for other
materials, especially for rare earth containing high-temperature superconductors such as
related Eu 122 pnictides, Ce 1111 pnictides and rutheno-cuprates [82, 307]. In chapter 6
and 7 we have already presented evidence for the canted antiferromagnetic and re-entrant
spin glass phase in other Eu 122 pnictides. One should note further that glass-like be-
haviour was also reported for rutheno-cuprates [308, 309] and CeFePO [310]; this implies
that glassy dynamics may be the key to how high-temperature superconductivity can
coexist with rare earth magnetism.
Furthermore, we are confident that the low-field persistent detwinning discovered in
EuFe2As2 actually appears also in other rare earth containing materials. Therefore, we are
planning further investigations on diluted Eu compounds. Moreover, the persistent mag-
netic detwinning is also interesting for other experimental techniques such as ARPES [311],
where the implementation of additional mechanical devices is challenging, and for theo-
reticians [312], since it provides the unique possibility to study the macroscopic in-plane
anisotropy close to the phase transition without the application of any symmetry-breaking
force.
Finally, one should note that the work presented here also opens up very concrete ques-
tions concerning the research on Eu based 122 superconductors that we want to address
in the near future. In this regard, we suggest that studies on diluted compounds may
uncover the source of the anomalies related to the spin density wave (see chapter 8) and
the superconducting gap [233]. Likewise, further optical investigations on superconducting
EuFe2(As1−xPx)2 compounds might reveal more information about the relationship of the
Lifshitz transition to the rather narrow superconducting dome. Furthermore, it will be
interesting to examine whether the indirect magneto-elastic coupling also influences the
nematic fluctuations [313]. Therefore, this thesis can be concluded safe in the knowledge
156 10 Summary and outlook
that it has not only contributed important insights, but also inspired future work in a very
interesting field of nowadays solid state research.
A
THZ INVESTIGATIONS ON BA 122
THIN FILMS
As already presented in chapter 4.4, many contradictory reports exist about the optical
properties of Ba(Fe1−xCox)2As2. In particular, the number of superconducting gaps as
well as the origin of the unexpected strong intra-gap absorption is highly debated. In the
following, our approaches to contribute to this topic are shortly summarized.
In all cases, a coherent source Terahertz spectrometer (4 - 45 cm−1) with a Mach-Zehnder
interferometer was used in order to measure the transmission and the corresponding phase
shift of Ba(Fe0.9Co0.1)2As2 thin films on dielectric (La,Sr)(Al,Ta)O3 (LSAT) or CaF2 sub-
strates; additional transmission measurements were performed to gain the optical proper-
ties of the substrates. Due to multiple reflections at the surfaces, the measured properties
oscillate with a periodicity dependent on the optical thickness of the sample (see Fig. A.1).
In the normal state, the optical conductivity of the film can be modeled with a single
Drude term, accounting for its metallic nature. In the superconducting state, each maxi-
mum is evaluated individually with two Drude terms: one with a very low scattering rate
that models the superconducting δ-function, the other one with a high scattering rate
accounting for the quasi-particle absorption [148]. The advantage of such an approach is
that it is independent of any model, i.e. for example of the gap symmetry. A more detailed
158 A THz investigations on Ba 122 thin films
description of the measurement technique and the analysis can be found in Ref. [148] and
Ref. [314].
A.1 Fabry-Pérot resonant technique
One of the main problems of such measurements is that the optical intra-gap conduc-
tivity of metallic superconductors can be extracted experimentally only with rather large
uncertainty, caused by the huge negative value of the dielectric constant that mainly deter-
mines the transmission. Therefore, we have performed systematic studies of Fabry-Pérot
resonators, which consist of two identical superconducting iron pnictide thin films on LSAT
substrates that are positioned face-to-face to each other, separated by a spacer. The cor-
responding results that are already published in Ref [315] and Ref [316] are summarized
in this section.
Enhancement principle
Fig. A.1a shows exemplarily the calculated transmission of such a Fabry-Pérot arrange-
ment compared to the spectrum of a usual sample (single film on substrate) and the
spectrum that would be caused by light passing two identical free standing films. For the
Fabry-Pérot arrangement, a complex transmission pattern develops due to multiple reflec-
tions at numerous interfaces: the highest peaks arise at frequencies where the transmission
of both, the single film on a substrate and the free standing films resonator, is maximized.
In the minima of the substrate-film arrangement, the spectrum of the Fabry-Pérot res-
onator corresponds to the free standing films system. The resonances of the Fabry-Pérot
arrangement enhance in amplitude over several orders of magnitude and exceed at some
points the transmission of the single film on a substrate. As the maximum sensitivity to
σ1(ω) of the films is achieved when the whole peak structure is experimentally resolved,
one is restricted to rather thin films to achieve transmissivity at least of the order 10−5,
which is the resolution limit of the spectrometer.
The enhancement of sensitivity with respect to σ1(ω) can be demonstrated by nomo-
grams, showing lines of constant transmission coefficient and phase shift plotted in the
coordinates of real and imaginary parts of σ(ω) (or other optical constants) of the films.
Fig. A.2 compares the nomograms of a single film and a Fabry-Pérot resonator on the basis
of 30 nm Ba(Fe0.9Co0.1)2As2 film data that is representative for iron pnictides. The line of
constant transmission coefficient is noticeably less steep for the Fabry-Pérot arrangement,
meaning that the accuracy to σ1(ω) is higher, whereas the accuracy to the phase decreases.
When fitting the spectra, the accuracy to σ1(ω) also benefits from “double-structures” in
the THz spectra of Fabry-Pérot resonators, which emerge when the resonances between
A.1 Fabry-Pérot resonant technique 159
Figure A.1: (a) Calculated transmission at temperatures T > Tc (left panel) and T < Tc
(right panel) for a single film on substrate (black dashed line), two free standing films (red
dashed-dotted line) and the Fabry-Pérot (FP) arrangement (green line). The Fabry-Pérot
resonator is shown schematically in the inset of (a). Model parameters are chosen close to
measurements (dsub = 0.495mm, dgap = 1.934mm, dfilm = 30nm, σ1(T > Tc) = 6000Ωcm−1,
σ1(T < Tc) = 2000Ωcm−1, ωp = 3464cm−1). (b) Nomogram: calculated constant values of
transmission coefficient Θ (solid lines) and phase shift Φ (dashed lines) in optical constant co-
ordinates (vertical: σ1, horizontal: 1) with the values typical for a 30 nm Ba(Fe0.9Co0.1)2As2
film in the superconducting state (T = 5K, ν = 5.13 cm−1, Θ = 0.17, Φ = 3.7 rad/cm−1).
Black lines show data for a single film on a substrate (LSAT, dsub = 0.5mm), red lines for
the Fabry-Pérot resonator (LSAT, dgap = 2mm). The line of constant transmission coefficient
is noticeably less steep for the Fabry-Pérot arrangement, meaning that the accuracy to σ1 is
higher, whereas the phase measurement (dashed lines) is more sensitive to σ1 in the case of
the single film on substrate.
different interfaces coincide. These resonances show different dependence on σ1(ω) and
σ2(ω) of the films and the shape of the double-structure is thus very characteristic for a
distinct ratio of these quantities. Thus, in a narrow frequency range, more information is
available than from a spectrum of a single film on a substrate.
Fitting procedure
In order to account for the complex geometry of the Fabry-Pérot resonator, we expanded
our fitting procedure to a five-layer model. Furthermore, we measured the single films
for a temperature T1 > Tc and determine their normal state conductivity σ(T1) (we take
T1 = 30K slightly above Tc ∼ 22K). The found value of σ(T1) is then used to precisely
determine the geometrical parameters of the Fabry-Pérot system: substrate thickness dsub,
space between the films dgap (“gap width”) and “gap absorption”. The latter parameter
160 A THz investigations on Ba 122 thin films
accounts for the non-perfect geometry of the resonator (for example due to the non-
parallelism of interfaces), which can be modelled in first approximation by a finite (but
small) absorption in the gap between the films. Importantly, all spectra are processed
with the same set of geometrical parameters.
Experimental results
We have determined the optical response of three Fabry-Pérot resonators, consisting of
pairs of two identical films (dfilm = 25nm, 30 nm and 50 nm) that are glued via a spacer
(metal or Plexiglas ring, diameter: ∼ 1 cm) face-to-face to each other.
In order to empirically check, whether it is realistic to obtain data of such a Fabry-Pérot
arrangement despite experimental challenges, first, a resonator composed of relatively thin
films (dfilm = 25nm, Tc = 22K, dfilm ∼ 1mm, dgap ∼ 1mm) was examined. We found
that the five-layer model describes the spectra nicely, as depicted in Fig A.2a. However,
as far as physics is concerned, the film quality was rather poor, as indicated by a very
high London penetration depth λL ∼ 1.46 µm (at 5K).
As we expected a higher film quality for thicker samples, further measurements were
carried out on 50 nm films (Tc = 21K, dsub ∼ 1mm, dgap ∼ 1mm). However, for these
thick films the transmission coefficient of the Fabry-Pérot resonator in the superconducting
state was too low, i.e. beyond the resolution limit of the spectrometer (see Fig A.2b).
30 nm films (Tc = 23K, dsub ∼ 0.5mm, dgap ∼ 2mm) were found to satisfy the re-
quirements given by film quality and resolution limit of the spectrometer (see Fig A.2c).
However, we found that an additional factor - the plane-parallelism of the substrates - plays
a crucial role for providing the high quality factor of the Fabry-Pérot resonator. In that
case, the thickness of the substrates was non-uniform in the range 0.487mm to 0.505mm.
Thickness measurements of the complete resonator gave values between 2.934mm and
2.958mm, meaning that the biggest effect causing a non-parallelism of the whole system
came from non-plane-parallel substrates. Since such pronounced non-perfection that leads
to the broadening of the Fabry-Pérot resonance peaks in the spectra is not included in
the model based on Fresnel optics, we were not able to describe the experimental spectra
consistently over a broad frequency and temperature range; the disturbance is too large
to be taken into account by the “gap absorption” mentioned above.
In summary, we have shown that our Fabry-Pérot resonators made out of superconduct-
ing thin films (on substrates) have theoretically the potential to enhance the sensitivity to
the real part of the optical conductivity at very low frequencies. In the experiment, the res-
olution limit of our setup restrains the film thickness in the case of Ba(Fe0.9Co0.1)2As2 to
approximately 30 nm. However, our measurements on 25 nm films proof that the thin film
A.2 Superfluid density 161
Figure A.2: Transmission coefficient spectra (dots) of Ba(Fe0.9Co0.1)2As2 Fabry-Pérot res-
onators measured at 5K, fitted (line) with a five-layer-model for the film thicknesses (a) dfilm
= 25nm, (b) 30 nm and (c) 50 nm.
quality and homogeneity is still a serious issue for iron pnictides that has to be solved be-
fore proceeding with our work. We further note that the success of this approach depends
delicately on the uniform thickness of the substrate. One solution would be to deposit two
films on both sides of a substrate, which is, however, experimentally challenging.
A.2 Superfluid density
As already mentioned in the previous section A.1, a common problem of THz investigations
on superconductors is the rather huge error of σ1(ω) at low frequencies. However, the
162 A THz investigations on Ba 122 thin films
corresponding imaginary part σ2(ω) (which determines the penetration depth) can usually
be extracted with very high accuracy.
Therefore, our collaborator A. Karakozov has analysed the temperature-dependence of
the normalized superfluid density:
ρs(t) = λL(0)2/λL(t)2 (A.1)
with the relative temperature t = T/Tc, using the α-model that describes multiband
superconductors via BCS-like equations with a reduced critical temperature [317, 318].
This model was then applied to fit the optical properties of one of our Ba(Fe0.9Co0.1)2As2
films on LSAT substrate (Tc = 22K, dfilm = 50 nm). Considering the existence of a small
energy gap with 2∆/kBTc ∼ 2 (see Fig. 4.10), the superfluid density can be only described
within a model of at least three weakly interacting condensates with 2∆/kBTc ∼ 2, 3 and
4, as depicted in Fig. A.3. This is an important refinement of the commonly used minimal
model which describes the electrodynamic properties of iron pnictides with two effective
bands.
Figure A.3: Experimental values for the normalized superfluid density ρs(t) = λL(0)2/λL(t)2
(red circles) for a 50 nm Ba(Fe0.9Co0.1)2As2 film with Tc = 22K. Additionally, calculations
for a two-band (blue dotted line) and a three-band fit (red solid line) with a minimum gap
2∆/kBTc ∼ 2 are compared to a BCS one-band approach (adapted from Ref. [317]). The best
description can be obtained by the three-band approach.
A.3 Irradiation studies
In 2011, Efremov et al. predicted that two-band superconductors with s±-symmetry
might undergo a disorder-induced transition to s++-symmetry, with both gaps tending
to the same, finite value [319, 320]. As optical spectroscopy is not sensitive to the phase
A.3 Irradiation studies 163
of the superconducting order parameter, the corresponding zero-crossing of the smaller
energy gap would appear as if the gap first closes and then re-emerges. Such a unique
behaviour constitutes a smoking gun experiment to proof the s±-symmetry for iron-based
superconductors.
Furthermore, manipulating the scattering rate has also the potential to deliver impor-
tant information about the origin of the strong intra-gap absorption: while nodes can be
lifted by increasing scattering [72], pair-breaking should be rather enhanced (as long as
superconductivity is not destroyed too much).
Therefore, we have investigated the effect of proton and α-particle irradiation on the
optical properties of 50 nm thin Ba(Fe0.9Co0.1)2As2 films on CaF2 substrate. The irradi-
ation was performed on the DanFysik-350 at the P. N. Lebedev Physical Institute of the
Russian Academy of Sciences (Moscow) with an energy of 200 keV, which is high enough
to guarantee that all particles pass the film. The dose for one irradiation is 2 · 1014 cm−2,
corresponding to a decrease of Tc by 2K per step for protons (see Fig. A.5c), and a de-
crease of 3.5K per step for α-particles. The latter stronger suppression of Tc is consistent
with the creation of magnetic scattering centres [321]; therefore, we concentrate here on
the results obtained via proton irradiation. The corresponding investigations were super-
vised in the framework of this thesis, and can be found in more detail in Ref. [322] and
Ref. [323].
Intra-gap absorption
The unusual strong non-BCS-like intra-gap absorption can be best visualized, when com-
paring the frequency-dependent conductivity at T > Tc with that at T  Tc. As displayed
in Fig. A.4, even after several irradiation steps that suppress Tc by more than 10K, the
conductivity at lowest frequencies and 5.6K still exceeds the normal state values. Thus,
the intra-gap absorption must originate - at least to some extent - from pair-breaking
interband scattering.
Crossover from s±- to s++-symmetry
In order to observe the crossover from s±- to s++-symmetry of the superconducting order
parameter, we track the position of the coherence peak Tmax for eight irradiation steps1;
the corresponding Tc value is determined by the abrupt onset of frequency-dependent
changes in the measured phase, typical for a superconductor at T < Tc. For the 7th and
1 If its shape resembles rather a plateau than a peak, we consider the temperature where the plateau
sets in as Tmax.
164 A THz investigations on Ba 122 thin films
Figure A.4: Frequency-dependent optical conductivity σ1(ω) at 30K (closed dark symbols)
and 5.6K (open bright symbols) for (a) the unirradiated film (Tc = 26K, blue), (b) the film
after five irradiation steps with protons (Tc = 16K, red), as well as (c) the film after eight
irradiation steps (Tc ∼ 10K, green, adapted from Ref. [322]). In all cases, a strong intra-gap
absorption can be observed below Tc.
8th irradiation, however, the transition is already very weak and possibly smeared out too
much, in order to determine Tc in this way.
As can be seen in Fig. A.5c, the irradiation suppresses Tc and the residual resistivity
ratio (σ(30K)/σ(295K)) at least for the first six irradiation steps linearly, meaning that the
scattering rate is enhanced proportional to the irradiation dose. In parallel, the coherence
peak is quickly suppressed, until it is shifted out of the measured temperature window for
the fifth irradiation (see Fig. A.5a and Fig. A.5c). Interestingly, Tmax is quicker suppressed
than Tc, meaning that the BCS relation between gap value and critical temperature is
violated; this is an important condition to observe the s±- to s++ crossover. Furthermore,
the permittivity is reduced significantly with irradiation, while the penetration depth λL
raises almost linearly, consistent with a smooth decrease of the superfluid density.
For the 7th irradiation, however, the behaviour starts to change. The conductivity in the
normal state, as well as the residual resistivity ratio increase slightly. This might indicate
that the number of defects got so high that an impurity band has formed, contributing
to the overall conductivity. We want to stress, however, that this does not affect our
interpretations concerning the coherence peak, as the conductivity in the normal state is
still perfectly flat in the THz range (see Fig. A.4c). Our remarkable observation is that
at the same time, the coherence peak shifts back to higher frequencies, clearly visible
A.3 Irradiation studies 165
Figure A.5: Optical properties of a 50 nm Ba(Fe0.9Co0.1)2As2 film (Tc = 26K) depen-
dent on the irradiation with protons (dose: 2 · 1014 cm−2 per step; adapted from Ref. [322]).
(a,b) Temperature-dependent (a) optical conductivity σ1(T ) and (b) permittivity 1(T ) for
selected irradiation steps (unirradiated: green closed diamonds, 2nd irradiation: dark cyan
open squares, 5th irradiation: blue closed hexagons, 7th irradiation: purple open circles, 8th
irradiation: red closed stars). (c,d) Residual resistivity ratio RRR σ(30K)/σ(295K) (grey
squares), compared to (c) the suppression of Tc (orange squares) and the maximum of the
coherence peak Tmax, as well as (d) London’s penetration depth at 5 cm−1 (green squares).
Lines and arrows are guides to the eye, stressing that the 8th irradiation clearly deviates from
the trend expected from the first irradiation steps.
166 A THz investigations on Ba 122 thin films
when comparing in Fig. A.5a σ1(T ) of the 7th and 8th irradiation step. Furthermore, the
penetration depth saturates, or even tends to decrease. Those observations may indicate
a re-appearance of the lower superconducting gap in the measured temperature and fre-
quency window, i.e. a crossover from s±- to s++-symmetry of the superconducting order
parameter.
B
ACKNOWLEDGEMENTS
Writing this thesis sometimes felt like a time travel through the last four years and I got
aware once more how lucky I was to have so many people who supported me.
• First of all, I would like to thank my supervisor Prof. Dressel. You always supported
and trusted me - probably in some situations more than I did. Most of all, I want
to thank you for the warm and familiar atmosphere at your institute.
• I would also thank Prof. Keimer and Prof. Basov for kindly accepting to co-referee
this thesis. I always enjoyed discussions with members of your groups.
• Furthermore, I would like to thank Dan Wu. You introduced me with incredible
patience in the field of iron pnictides and infrared spectroscopy. We really miss you
in our team. Thanks also to Neven Barišić. I learnt a lot from our discussions.
• Work at our institute like we know it would not be possible without the great techni-
cal support by Gabi Untereiner, the low temperature and the mechanical workshop,
as well as the motherly care of Agni Schmidt.
168 B Acknowledgements
Furthermore, I want to acknowledge all my collaboration partners, especially:
• The sample growers: H. S. Jeevan in the group of Prof. P. Gegenwart, S. Haindl and
K. Iida in the group of Prof. B. Holzapfel, as well as S. Aswartham in the group of
S. Wurmehl. Without your support, this thesis would not have been possible.
• Boris Gorshunov and Elena Zhukova, our frequent visitors from Moscow. Boris, I
learnt so much more from you than just to “press c”. Elena, I always enjoyed the
“Hühnerstall” with you.
• R. Kremer, as well as Mrs. Siegle and Mrs. Brücher for the technical support
with the specific heat measurements, your confidence concerning the SQUID and
the introduction to the ultra low field option. Mr. Kremer, I really learnt a lot while
revising the first version of our PRL and I always enjoy(ed) our discussions.
• Prof. D. N. Basov and Kirk Post, as well as all the group members and friends in San
Diego: thanks for your great hospitality. Dimitri, I was always inspired, motivated
and full of ideas when I came back from your group to Stuttgart. Kirk, you are the
most positive person I ever met in my life (“... but look, how stable the temperature
is...”) and I really appreciate the work with you, especially your russian-american
cowboy Helium filling technique as well as the surfing lessons.
• My collaborators in Göttingen (now Augsburg). I learnt a lot from our long discus-
sions.
• Prof. I. Eremin and A. Akbari for the theoretical support and the mutual exchange,
as well as Y. Xiao for the discussion of the neutron data; you helped me to survive
my first PRB experiences. Thanks also to Prof. J. Fink, Prof. J. Schmalian, Prof.
R. Hackl, and Prof. I. Fisher for fruitful discussions.
• D. Efremov and O. Dolgov for a lot of fruitful discussions concerning our thin film
measurements.
Furthermore, I have to thank the German Academic Exchange Service, the DFG, as well
as the Baden-Württembergische Landesförderung for financial support.
However, the whole thesis would not have been possible without my great colleagues at
the 1st Physical Institute:
• First of all, I would like to thank all the Infra-Rats, it was a pleasure to work with
all of you. Special thanks for accepting me as “IR Mom” and all the help with the
official stuff in the lab.
169
• Rebecca and Tobi, you were at my side from the first day. Becci, I learnt a lot when
passing your “lessons” (which started on my first day at the institute with changing
the pump oil). Tobi, no one is a more talented “lab dancer” than you...
• David, Andy and Anja, you enriched our team with new energy and always good
mood. David, thanks for the great support in the last two yours, especially while
writing the thesis. Andy, I was really grateful when someone finally took my “Küken”
burden. Anja, please never ever drink again two energy drinks in a row.
• Uwe, although you chose the other side (without breakfast), thanks for working
hardly on re-discovering my optimism.
• Sabrina, Conrad and Eric, thanks for the nice inclusion in your “Team Columbus”.
The worst lab day got better with a good mineral water in the evening... Sabrina,
we should have thrown this cryostat out of the window.
• Kirk, David, Anja and Conrad, the whole magnetic detwinning project would not
have been possible without you and your night shifts.
• My diploma student Felix, my master student Micha, as well as my bachelor students:
Kilian, Fabi, Andreas and Alina - I hope that you could learn from me as much as
I learnt from you and your questions.
• Tomislav, Eva, Julia and Stefano, thanks a lot for the help in the dc and ellipsometry
lab. The work atmosphere was always great.
Special thanks also to my old colleagues from Würzburg, in particular to Prof. Geurts,
Prof. Ossau, Prof. Umbach and Prof. Claessen for the reports that supported me in
getting my scholarships. Although it was quite some work, I would also like to thank
Prof. Honerkamp to suggest me for organizing the SPP summer school.
Finally, I want to thank my family and friends for all the support during the years. I
can not find the words to express how much this means to me. Christian, I will never
forget when you came to my lab with a freshly baked pizza in an improvised delivery box
(and it was still warm). Thanks for all your patience.

Bibliography
[1] M. R. Norman, Science 332, 196 (2011).
[2] W. Buckel and R. Kleiner, Supraleitung, Wiley, Weihnheim (2013).
[3] D. N. Basov and A. V. Chubukov, Nature Physics 7, 272 (2011).
[4] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130,
3296 (2008).
[5] D. C. Johnston, Adv. Phys. 59, 6 (2010).
[6] I. R. Fisher, L. Degiorgi, and Z. X. Shen, Rep. Prog. Phys. 74, 124506 (2011).
[7] Y. Xiao, Y. Su, W. Schmidt, K. Schmalzl, C. M. N. Kumar, S. Price, T. Chatterji,
R. Mittal, L. J. Chang, S. Nandi, N. Kumar, S. K. Dhar, A. Thamizhavel, and T.
Brückel, Phys. Rev. B 81, 220406(R) (2010).
[8] Y. Xiao, Y. Su, M. Meven, R. Mittal, C.M.N. Kumar, T. Chatterji, S. Price, J.
Persson, N. Kumar, S.K. Dhar, A. Thamizhavel, and T. Brückel, Phys. Rev. B 80,
174424 (2009).
[9] S. Zapf, D. Wu, L. Bogani, H. S. Jeevan, P. Gegenwart, and M. Dressel, Phys. Rev.
B 84, 140503 (2011).
[10] S. Zapf, H. S. Jeevan, T. Ivek, F. Pfister, F. Klingert, S. Jiang, D. Wu, P. Gegenwart,
R. K. Kremer, and M. Dressel, Phys. Rev. Lett. 110, 237002 (2013).
[11] A. Akbari, I. Eremin, and P. Thalmeier, Phys. Rev. B 84, 134513 (2011).
[12] P. Marsik, C. N. Wang, M. Rössle, M. Yazdi-Rizi, R. Schuster, K. W. Kim, A.
Dubroka, D. Munzar, T. Wolf, X. H. Chen, and C. Bernhard, Phys. Rev. B 88,
180508(R) (2013).
[13] S. Zapf, C. Stingl, K. W. Post, J. Maiwald, N. Bach, I. Pietsch, D. Neubauer, A.
Löhle, C. Clauss, S. Jiang, H. S. Jeevan, D. N. Basov, P. Gegenwart, and M. Dressel,
Phys. Rev. Lett. 113, 227001 (2014).
172 Bibliography
[14] S. Blundell, Magnetism in Condensed Matter, Oxford University Press Inc., New York
(2001).
[15] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 106, 162 (1957).
[16] H. Fröhlich, Phys. Rev. 79, 845 (1950).
[17] J. Bardeen, Phys. Rev. 80, 567 (1950).
[18] W. L. McMillan, Phys. Rev. 167, 331 (1968).
[19] L. Gao, Y. Y. Xue, F. Chen, Q. Xiong, R. L. Meng, D. Ramirez, C. W. Chu, J. H.
Eggert, and H. K. Mao, Phys. Rev. B 50, 4260 (1994).
[20] J. G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1986).
[21] E. Fradkin and S. A. Kivelson, Nature Phys. 8, 864 (2012).
[22] N. Lavrov, Y. Ando, S. Komiya, and I. Tsukada, Phys. Rev. Lett. 87, 017007 (2001).
[23] A. Lavrov, S. Komiya, and Y. Ando, Nature 418, 385-386 (2002).
[24] J.-H. Chu, J. G. Analytis, D. Press, T. D. Ladd, Y. Yamamoto, and I. R. Fisher,
Phys. Rev. B 81, 214502 (2010).
[25] J.-H. Chu, H.-K. Kuo, J. G. Analytis, and I. R. Fisher, Science 337, 710 (2012).
[26] M. Tegel, M. Rotter, V. Wieß, F. M. Schappacher, R. Pöttgen, and D. Johrendt, J.
Phys.: Condens. Matter 20, 452201 (2008).
[27] H. S. Jeevan, Z. Hossain, D. Kasinathan, H. Rosner, C. Geibel, and P. Gegenwart,
Phys. Rev. B 78, 052502 (2008).
[28] Z. Ren, Z. Zhu, S. Jiang, X. Xu, Q. Tao, C. Wang, C. Feng, G. H. Cao, and Z. A.
Xu, Phys. Rev. B 78, 052501 (2008).
[29] C. F. Miclea, M. Nicklas, H. S. Jeevan, D. Kasinathan, Z. Hossain, H. Rosner, P.
Gegenwart, C. Geibel, and F. Steglich, Phys. Rev. B 79, 212509 (2009).
[30] Z. Ren, Q. Tao, S. Jiang, C. Feng, C. Wang, J. Dai, G. Cao, and Z. Xu, Phys. Rev.
Lett. 102, 137002 (2009).
[31] W. H. Jiao, Q. Tao, J. K. Bao, Y. L. Sun, C. M. Feng, Z. A. Xu, I. Nowik, I. Felner,
and G. H. Cao, Europhys. Lett. 95, 67007 (2011).
Bibliography 173
[32] S. Jiang, H. Xing, G. Xuan, Z. Ren, C. Wang, Z. A. Xu, and G. Cao, Phys. Rev. B
80, 184514 (2009).
[33] U. B. Paramanik, D. Das, R. Prasad, and Z. Hossain, J. Phys.: Condens. Matter 25,
265701 (2013).
[34] H. S. Jeevan, Z. Hossain, D. Kasinathan, H. Rosner, C. Geibel, and P. Gegenwart,
Phys. Rev. B 78, 092406 (2008).
[35] M. Reis, Fundamentals of Magnetism, Academic Press, Amsterdam (2013).
[36] M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).
[37] M. Getzlaff, Fundamentals of Magnetism, Springer, Berlin (2008).
[38] J. A. Mydosh, Spin Glasses: An Experimental Introduction, Taylor & Francis, London
(1993).
[39] M. Gabay and G. Toulouse, Phys. Rev. Lett. 47, 201 (1981).
[40] M. Tinkham, Introduction to Superconductivity, Dover Publications (2012).
[41] C. A. Reynolds, B. Serin, W. H. Wright, and L. B. Nesbitt, Phys. Rev. 78, 487 (1950).
[42] E. Mawell, Phys. Rev. 78, 477 (1950).
[43] R. E. Glover III and M. Tinkham, Phys. Rev. 108, 243 (1957).
[44] G. M. Eliashberg, Sov. Phys. JETP 11, 696 (1960).
[45] L. Boeri, O.V. Dolgov, and A. A. Golubov, Phys. Rev. Lett. 101, 026403 (2008).
[46] M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang,
Y. Q. Wang, and C. W. Chu, Phys. Rev. Lett. 58, 908 (1987).
[47] H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano, Jpn. J. Appl. Phys. 27, L209
(1988).
[48] M. R. Norman, D. Pines, and C. Kallin, Adv. Phys. 54, 8 (2005).
[49] N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J. Levallois, J.-B. Bonnemaison, R. Liang,
D. A. Bonn, W. N. Hardy, and L. Taillefer, Nature 447, 565 (2007).
[50] H.-B. Yang, J. D. Rameau, Z.-H. Pan, G. D. Gu, P. D. Johnson, H. Claus, D. G.
Hinks, and T. E. Kidd, Phys. Rev. Lett. 107, 047003 (2011).
174 Bibliography
[51] N. Harrison and S. E. Sebastian, New J. Phys. 16, 063025 (2014).
[52] M. C. Boyer, W. D. Wise, K. Chatterjee, M. Yi, T. Kondo, T. Takeuchi, H. Ikuta,
and E. W. Hudson, Nature Phys. 3, 802 (2007).
[53] R.-H. He, M. Hashimoto, H. Karapetyan, J. D. Koralek, J. P. Hinton, J. P. Testaud,
V. Nathan, Y. Yoshida, H. Yao, K. Tanaka, W. Meevasana, R. G. Moore, D. H. Lu,
S.-K. Mo, M. Ishikado, H. Eisaki, Z. Hussain, T. P. Devereaux, S. A. Kivelson, J.
Orenstein, A. Kapitulnik, and Z.-X. Shen, Science 331, 1579 (2011).
[54] Y. He, Y. Yin, M. Zech, A. Soumyanarayanan, M. M. Yee, T. Williams, M. C. Boyer,
K. Chatterjee, W. D. Wise, I. Zeljkovic, T. Kondo, T. Takeuchi, H. Ikuta, P. Mistark,
R. S. Markiewicz, A. Bansil, S. Sachdev, E. W. Hudson, and J. E. Hoffman, Science
344, 608 (2014).
[55] C. V. Parker, P. Aynajian, E. H. da Silva Neto, A. Pushp, S. Ono, Jinsheng Wen, Z.
Xu, G. Gu, and A. Yazdani, Nature 468, 677 (2010).
[56] D. H. Torchinsky, F. Mahmood, A. T. Bollinger, I. Boz˘ović, and N. Gedik, Nature
Mater. 12, 387 (2013).
[57] R. Comin, A. Frano, M. M. Yee, Y. Yoshida, H. Eisaki, E. Schierle, E. Weschke, R.
Sutarto, F. He, A. Soumyanarayanan, Yang He, M. Le Tacon, I. S. Elfimov, Jennifer
E. Hoffman, G. A. Sawatzky, B. Keimer, and A. Damascelli, Science 343, 390 (2014).
[58] E. H. da Silva Neto, P. Aynajian, Al. Frano, R. Comin, E. Schierle, E. Weschke, A.
Gyenis, J. Wen, J. Schneeloch, Z. Xu, S. Ono, G. Gu, M. Le Tacon, and A. Yazdani,
Science 343, 393 (2014).
[59] V. Hinkov, D. Haug, B. Fauqué, P. Bourges, Y. Sidis, A. Ivanov, C. Bernhard, C. T.
Lin, and B. Keimer, Science 319, 597 (2008).
[60] M. J. Lawler, K. Fujita, J. Lee, A. R. Schmidt, Y. Kohsaka, C. K. Kim, H. Eisaki, S.
Uchida, J. C. Davis, J. P. Sethna, and E.-A. Kim, Nature 466, 347 (2010).
[61] J. R. Waldram, Superconductivity in metals and cuprates, Institute of Physics Pub-
lishing, London (1996).
[62] N. F. Mott, Philos. Mag. 26, 1015 (1972).
[63] A. F. Yoffe and A. R. Regel, Prog. Semicond. 4, 237 (1960).
[64] T. Moriya and K. Ueda, Rep. Prog. Phys. 66, 1299 (2003).
Bibliography 175
[65] N. L. Wang, H. Hosono, and P. Dai, Iron-based superconductors, Pan Stanford, Sin-
gapore (2013).
[66] F. Ronning, T. Klimczuk, E. D. Bauer, H. Volz, and J. D. Thompson, J. Phys.:
Condens. Matter 20, 322201 (2008).
[67] Q.-Y. Wang, Z. Li, W.-H. Zhang, Z.-C. Zhang, J.-S. Zhang, W. Li, H. Ding, Y.-B.
Ou, P. Deng, K. Chang, J. Wen, C.-L. Song, K. He, J.-F. Jia, S.-H. Ji, Y.-Y. Wang,
L.-L. Wang, X. Chen, X.-C. Ma, and Q.-K. Xue, Chin. Phys. Lett. 29, 037402 (2012).
[68] H. Wadati, I. Elfimov, and G. A. Sawatzky, Phys. Rev. Lett. 105, 157004 (2010).
[69] I. Mazin, Nature 464, 183 (2010).
[70] I. I. Mazin, D. J. Singh, M. D. Johannes, and M.-H. Du, Phys. Rev. Lett. 101, 057003
(2008).
[71] P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Rep. Prog. Phys. 74, 124508
(2011).
[72] V. Mishra, G. Boyd, S. Graser, T. Maier, P. J. Hirschfeld, and D. J. Scalapino, Phys.
Rev. B 79, 094512 (2009).
[73] E. Wiesenmayer, H. Luetkens, G. Pascua, R. Khasanov, A. Amato, H. Potts, B.
Banusch, H.-H. Klauss, and D. Johrendt, Phys. Rev. Lett. 107, 237001 (2011).
[74] P. Cai, X. Zhou, W. Ruan, A. Wang, X. Chen, D.-H. Lee, and Y. Wang, Nature
Commun. 4, 1596 (2012).
[75] M. A. Tanatar, E. C. Blomberg, A. Kreyssig, M. G. Kim, N. Ni, A. Thaler, S. L.
Bud’ko, P. C. Canfield, A. I. Goldman, I. I. Mazin, and R. Prozorov, Phys. Rev. B
81, 184508 (2010).
[76] M. Yi, D. Luc, J.-H. Chu, J. G. Analytis, A. P. Sorini, A. F. Kemper, B. Moritz,
S.-K. Mo, R. G. Moore, M. Hashimoto, W.-S. Lee, Z. Hussain, T. P. Devereaux, I.
R. Fisher, and Z.-X. Shen, PNAS 108, 6878 (2011).
[77] S. Kasahara, H. J. Shi, K. Hashimoto, S. Tonegawa, Y. Mizukami, T. Shibauchi, K.
Sugimoto, T. Fukuda, T. Terashima, A. H. Nevidomskyy, and Y. Matsuda, Nature
Phys. 486, 382 (2012).
[78] C. Dhital, Z. Yamani, W. Tian, J. Zeretsky, A. S. Sefat, Z. Wang, R. J. Birgeneau,
and S. D. Wilson, Phys. Rev. Lett. 108, 087001 (2012).
176 Bibliography
[79] E. P. Rosenthal, E. F. Andrade, C. J. Arguello, R. M. Fernandes, L. Y. Xing, X. C.
Wang, C. Q. Jin, A. J. Millis, and A. N. Pasupathy, Nature Phys. 10, 225 (2014).
[80] R. M. Fernandes, A. V. Chubukov, and J. Schmalian, Nature Phys. 10, 97 (2014).
[81] H. H. Kuo and I. R. Fisher, Phys. Rev. Lett. 112, 227001 (2014).
[82] G. F. Chen, Z. Li, D. Wu, G. Li, W. Z. Hu, J. Dong, P. Zheng, J. L. Luo, and N. L.
Wang, Phys. Rev. Lett. 100, 247002 (2008).
[83] K. Hashimoto, K. Cho, T. Shibauchi, S. Kasahara, Y. Mizukami, R. Katsumata, Y.
Tsuruhara, T. Terashima, H. Ikeda, M. A. Tanatar, H. Kitano, N. Salovich, R. W.
Giannetta, P. Walmsley, A. Carrington, R. Prozorov, and Y. Matsuda, Science 22,
1554 (2012).
[84] T. Shibauchi, A. Carrington, and Y. Matsuda, Annu. Rev. Condens. Matter Phys. 5,
113 (2014).
[85] D. Manske, Theory of unconventional superconductors, Springer, Berlin (2004).
[86] J. P. Carbotte, E. Schachinger, and D. N. Basov, Nature 401, 354 (1999).
[87] E. G. Maksimov, M. L. Kulić, and O. V. Dolgov, Adv. Cond. Matt. Phys., 423725
(2010).
[88] D. S. Inosov, J. T. Park, P. Bourges, D. L. Sun, Y. Sidis, A. Schneidewind, K. Hradil,
D. Haug, C. T. Lin, B. Keimer, and V. Hinko, Nature Phys. 6, 178 (2010).
[89] A. D. Christianson, E. A. Goremychkin, R. Osborn, S. Rosenkranz, M. D. Lumsden,
C. D. Malliakas, I. S. Todorov, H. Claus, D. Y. Chung, M. G. Kanatzidis, R. I.
Bewley, and T. Guidi, Nature 456, 930 (2008).
[90] C. P. Poole Jr, R. Prozorov, H. A. Farach, and R. J. Creswick, Superconductivity,
Elsevier, Waltham (2014).
[91] M. McElfresh, Fundamentals of magnetism and magnetic materials, Quantum Design
(1994).
[92] C. P. Bean, Phys. Rev. Lett. 8, 250 (1962).
[93] Y. Yeshrun, A. P. Malozemoff, and A. Shaulov, Rev. Mod. Phys. 68, 911 (1996).
[94] S.V. Chong, S. Hashimoto, and K. Kadowaki, Solid State Comm. 150, 1178 (2010).
[95] Y. B. Kim, C. F. Hempstead, and A. R. Strnad, Phys. Rev. Lett. 129, 528 (1963).
Bibliography 177
[96] F. Herlach and N. Miur, High Magnetic Fields - Science And Technology, Vol. 3,
World Scientific, Singapore (2006).
[97] A. M. Clogston, Phys. Rev. Lett. 9, 266 (1962).
[98] B. S. Chandrasekhar, Appl. Phys. Lett. 1, 7 (1962).
[99] N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Phys. Rev. 147, 295 (1966).
[100] E. Müller-Hartmann and J. Zittartz, Phys. Rev. Lett. 26, 428 (1971).
[101] K. Winzer, Solid State Comm. 24, 551 (1977).
[102] K.-H. Müller and V. N. Narozhnyi, Rep. Prog. Phys. 64, 943 (2001).
[103] P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964).
[104] A. I. Larkin and Y. N. Ovchinnikov, Zh. Eksp. Teor. Fiz. 47, 1136 (1964).
[105] A. I. Larkin and Y. N. Ovchinnikov, Sov. Phys. JETP 20, (1965).
[106] H. A. Radovan, N. A. Fortune, T. P. Murphy, S. T. Hannahs, E. C. Palm, S. W.
Tozer, and D. Hall, Nature 425, 51 (2003).
[107] P. W. Anderson and H. Suhl, Phys. Rev. 116, 898 (1959).
[108] M. Tachiki, H. Matsumoto, T. Koyama, and H. Umezawa, Solid State Comm. 34,
19 (1980).
[109] H. S. Greenside, E. I. Blount, and C. M. Varma, Phys. Rev. Lett. 46, 49 (1981).
[110] V. Jaccarino and M. Peter, Phys. Rev. Lett. 9, 290 (1962).
[111] O. Fischer, M. Decroux, S. Roth, R. Chevrel, and M. Sergent, J. Phys. C 8, L474
(1975).
[112] H. W. Meul, C. Rossel, M. Decroux, O. Fischer, G. Remenyi, and A. Briggs, Phys.
Rev. Lett. 53, 497 (1984).
[113] M. Dressel and G. Grüner, Electrodynamics of Solids, Cambridge University Press,
Cambridge (2002).
[114] M. Fox, Optical properties of solids, Oxford University Press, Oxford (2001).
[115] N. L. Wang, H. Hosono, and P. Dai, Iron-based Superconductors, CRC Press, Boca
Raton (2013).
178 Bibliography
[116] D. N. Basov and T. Timusk, Rev. Mod. Phys. 77, 721 (2005).
[117] M. Tinkham, Phys. Rev. 104, 845 (1956).
[118] R. A. Ferrell and R. E. Glover, Phys. Rev. 109, 1398 (1958).
[119] M. Tinkham and R. A. Ferrell, Phys. Rev. Lett. 2, 331 (1959).
[120] D. C. Mattis and J. Bardeen, Phys. Rev. 111, 412 (1958).
[121] W. Zimmermann, E. H. Brandt, M. Bauer, E. Seider, and L. Genzel, Physica C 183,
99 (1991).
[122] U. S. Pracht, E. Heintze, C. Clauss, D. Hafner, R. Bek, D. Werner, S. Gelhorn, M.
Scheffler, M. Dressel, D. Sherman, B. Gorshunov, K. S. Il’in, D. Henrich, and M.
Siegel, IEEE Trans. THz Sci. Technol. 3, 269 (2013).
[123] M. M. Qazilbash, J. J. Hamlin, R. E. Baumbach, L. Zhang, D. J. Singh, M. B.
Maple, and D. N. Basov, Nature Phys. 5, 647 (2009).
[124] J. Dong, H. J. Zhang, G. Xu, Z. Li, G. Li, W. Z. Hu, D. Wu, G. F. Chen, X. Dai,
J. L. Luo, Z. Fang, and N. L. Wang, Europhys. Lett. 83, 27006 (2008).
[125] G. F. Chen, Z. Li, G. Li, J. Zhou, D. Wu, J. Dong, W. Z. Hu, P. Zheng, Z. J. Chen,
H. Q. Yuan, J. Singleton, J. L. Luo, and N. L. Wang, Phys. Rev. Lett. 101, 057007
(2008).
[126] A. Dubroka, K. W. Kim, M. Rössle, V. K. Malik, A. J. Drew, R. H. Liu, G. Wu, X.
H. Chen, and C. Bernhard, Phys. Rev. Lett. 101, 097011 (2008).
[127] G. Li, W. Z. Hu, J. Dong, Z. Li, P. Zheng, G. F. Chen, J. L. Luo, and N. L. Wang,
Phys. Rev. Lett. 101, 107004 (2008).
[128] D. Wu, N. Barišić, P. Kallina, A. Faridian, B. Gorshunov, N. Drichko, L. J. Li, X.
Lin, G. H. Cao, Z. A. Xu, N. L. Wang, and M. Dressel, Phys. Rev. B 81, 100512(R)
(2010).
[129] M. Nakajima, S. Ishida, K. Kihou, Y. Tomioka, T. Ito, Y. Yoshida, C. H. Lee, H.
Kito, A. Iyo, H. Eisaki, K. M. Kojima, and S. Uchida, Phys. Rev. B 81, 104528
(2010).
[130] N. Barišić, D. Wu, M. Dressel, L. J. Li, G. H. Cao, and Z. A. Xu, Phys. Rev. B 82,
054518 (2010).
Bibliography 179
[131] S. J. Moon, A. A. Schafgans, M. A. Tanatar, R. Prozorov, A. Thaler, P. C. Canfield,
A. S. Sefat, D. Mandrus, and D. N. Basov, Phys. Rev. Lett. 110, 097003 (2013).
[132] F. Pfuner, J. G. Analytis, J.-H. Chu, I. R. Fisher, and L. Degiorgi, Eur. Phys. J. B
67, 513 (2009).
[133] E. van Heumen, Y. Huang, S. de Jong, A. B. Kuzmenko, M. S. Golden, and D. van
der Marel, Europhys. Lett. 90, 37005 (2010).
[134] R. P. S. M. Lobo, Y. M. Dai, U. Nagel, T. Rõõm, J. P. Carbotte, T. Timusk, A.
Forget, and D. Colson, Phys. Rev. B 82, 100506(R) (2010).
[135] A. Charnukha, O. V. Dolgov, A. A. Golubov, Y. Matiks, D. L. Sun, C. T. Lin, B.
Keimer, and A. V. Boris, Phys. Rev. B 84, 174511 (2011).
[136] Y. S. Kwon, J. B. Hong, Y. R. Jang, H. J. Oh, Y. Y. Song, B. H. Min, T. Iizuka, S.
Kimura, A. V. Balatsky, and Y. Bang, New J. Phys. 14, 063009 (2012).
[137] Y. M. Dai, B. Xu, B. Shen, H. H. Wen, J. P. Hu, X. G. Qiu, and R. P. S. M. Lobo,
Phys. Rev. B 86, 100501(R) (2012).
[138] S. J. Moon, A. A. Schafgans, S. Kasahara, T. Shibauchi, T. Terashima, Y. Matsuda,
M. A. Tanatar, R. Prozorov, A. Thaler, P. C. Canfield, A. S. Sefat, D. Mandrus, and
D. N. Basov, Phys. Rev. Lett. 109, 027006 (2012).
[139] J. N. Hancock, S. I. Mirzaei, J. Gillett, S. E. Sebastian, J. Teyssier, R. Viennois, E.
Giannini, and D. van der Marel, Phys. Rev. B 82, 014523 (2010).
[140] Y. Imai, F. Nabeshima, D. Nakamura, T. Katase, H. Hiramatsu, H. Hosono, and A.
Maeda, J. Phys. Soc. Jpn. 82, 043709 (2013).
[141] M. Nakajima, S. Ishida, T. Tanaka, K. Kihou, Y. Tomioka, T. Saito, C. H. Lee, H.
Fukazawa, Y. Kohori, T. Kakeshita, A. Iyo, T. Ito, H. Eisaki, and S. Uchida, Sci Rep.
4, 5873 (2014).
[142] J. J. Tu, J. Li, W. Liu, A. Punnoose, Y. Gong, Y. H. Ren, L. J. Li, G. H. Cao, Z.
A. Xu, and C. C. Homes, Phys. Rev. B 82, 174509 (2010).
[143] E. G. Maksimov, A. E. Karakozov, B. P. Gorshunov, A. S. Prokhorov, A. A.
Voronkov, E. S. Zhukova, V. S. Nozdrin, S. S. Zhukov, D. Wu, M. Dressel, S. Haindl,
K. Iida, and B. Holzapfel, Phys. Rev. B 83, 140502(R) (2011).
180 Bibliography
[144] E. G. Maksimov, A. E. Karakozov, A. A. Voronkov, B. P. Gorshunov, S. S. Zhukov,
E. S. Zhukova, V. S. Nozdrin, A. S. Prokhorov, S. Haindl, B. Holzapfel, L. Schultz,
D. Wu, M. Dressel, K. Iida, P. Kallina, and F. Kurth, JETP 93, 736 (2011).
[145] A. Akrap, J. J. Tu, L. J. Li, G. H. Cao, Z. A. Xu, and C. C. Homes, Phys. Rev. B
80, 180502(R) (2009).
[146] S. J. Moon, J. H. Shin, D. Parker, W. S. Choi, I. I. Mazin, Y. S. Lee, J. Y. Kim, N.
H. Sung, B. K. Cho, S. H. Khim, J. S. Kim, K. H. Kim, and T. W. Noh, Phys. Rev.
B 81, 205114 (2010).
[147] Z. G. Chen, T. Dong, R. H. Ruan, B. F. Hu, B. Cheng, W. Z. Hu, P. Zheng, Z.
Fang, X. Dai, and N. L. Wang, Phys. Rev. Lett. 105, 097003 (2010).
[148] B. Gorshunov, D. Wu, A. A. Voronkov, P. Kallina, K. Iida, S. Haindl, F. Kurth, L.
Schultz, B. Holzapfel, and M. Dressel, Phys. Rev. B 81, 060509(R) (2010).
[149] A. Perucchi, L. Baldassarre, S. Lupi, J. Y. Jiang, J. D.Weiss, E. E. Hellstrom, S.
Lee, C. W. Bark, C. B. Eom, M. Putti, I. Pallecchi, C. Marini, and P. Dore, Eur.
Phys. J. B 77, 25 (2010).
[150] R. V. Aguilar, L. S. Bilbro, S. Lee, C. W. Bark, J. Jiang, J. D. Weiss, E. E. Hellstrom,
D. C. Larbalestier, C. B. Eom, and N. P. Armitage, Phys. Rev. B 82, 180514 (R)
(2010).
[151] T. Fischer, A. V. Pronin, J. Wosnitza, K. Iida, F. Kurth, S. Haindl, L. Schultz, B.
Holzapfel, and E. Schachinger, Phys. Rev. B 82, 224507 (2010).
[152] Y. A. Aleshchenko, A. V. Muratov, V. M. Pudalov, E. S. Zhukova, B. P. Gorshunov,
F. Kurth, and K. Iida, JETP 94, 719 (2012).
[153] A. Perucchi, L. Baldassarre, B. Joseph, S. Lupi, S. Lee, C. B. Eom, J. Jiang, J. D.
Weiss, E. E. Hellstrom, and P. Dore, Eur. Phys. J. B 86, 274 (2013).
[154] K. W. Kim, M. Rössle, A. Dubroka, V. K. Malik, T. Wolf, and C. Bernhard, Phys.
Rev. B 81, 214508 (2010).
[155] D. Wu, N. Barišić, M. Dressel, G. H. Cao, Z-A. Xu, J. P. Carbotte, and E.
Schachinger, Phys. Rev. B 82, 184527 (2010).
[156] Y. M. Dai, B. Xu, B. Shen, H. H.Wen, X. G. Qiu, and R. P. S. M. Lobo, Europhys.
Lett. 104, 47006 (2013).
Bibliography 181
[157] B. B. Jin, T. Dahm, A. I. Gubin, Eun-Mi Choi, Hyun Jung Kim, Sung-IK Lee, W.
N. Kang, and N. Klein, Phys. Rev. Lett. 91, 127006 (2003).
[158] A. Charnukha , P. Popovich , Y. Matiks, D. L. Sun, C. T. Lin, A. N. Yaresko, B.
Keimer, and A. V. Boris, Nature Commun. 2, 219 (2011).
[159] J. Yang, D. Hüvonen, U. Nagel, T. Rõõm, N. Ni, P. C. Canfield, S. L. Bud’ko, J. P.
Carbotte, and T. Timusk, Phys. Rev. Lett. 102, 187003 (2009).
[160] D. Wu, N. Barišić, M. Dressel, G. H. Cao, Z-A. Xu, E. Schachinger, and J. P.
Carbotte, Phys. Rev. B 82, 144519 (2010).
[161] Y. M. Dai, B. Xu, B. Shen, H. Xiao, H. H. Wen, X. G. Qiu, C. C. Homes, and R.
P. S. M. Lobo, Phys. Rev. Lett. 111, 117001 (2013).
[162] A. Lucarelli, A. Dusza, F. Pfuner, P. Lerch, J. G. Analytis, J.-H. Chu, I. R. Fisher,
and L. Degiorgi, New J. Phys. 12, 073036 (2010).
[163] A. A. Schafgans, S. J. Moon, B. C. Pursley, A. D. LaForge, M. M. Qazilbash, A.
S. Sefat, D. Mandrus, K. Haule, G. Kotliar, and D. N. Basov, Phys. Rev. Lett. 108,
147002 (2012).
[164] N. L. Wang, W. Z. Hu, Z. G. Chen, R. H. Yuan, G. Li, G. F. Chen, and T. Xiang,
J. Phys.: Condens. Matter 24, 294202 (2012).
[165] Z. G. Chen, R. H. Yuan, T. Dong, and N. L. Wang, Phys. Rev. B 81, 100502(R)
(2010).
[166] M. Nakajima, T. Tanaka, S. Ishida, K. Kihou, C. H. Lee, A. Iyo, T. Kakeshita, H.
Eisaki, and S. Uchida, Phys. Rev. B 88, 094501 (2013).
[167] A. Dusza, A. Lucarelli, F. Pruner, J.-H. Chu, I.R. Fisher, and L. Degiorgi, Europhys.
Lett. 93, 37002 (2011).
[168] Z. P. Yin, K. Haule, and G. Kotliar, Nature Phys. 7, 294 (2011).
[169] M. Nakajima, T. Liang, S. Ishida, Y. Tomioka, K. Kihou, C. H. Lee, A. Iyo, H.
Eisaki, T. Kakeshita, T. Ito, and S. Uchida, PNAS 108, 12238 (2011).
[170] A. Dusza, A. Lucarelli, A. Sanna, J.-H. Chu, I.R. Fisher, and L. Degiorgi, New J.
of Phys. 14, 023020 (2012).
[171] M. Nakajima, S. Ishida, Y. Tomioka, K. Kihou, C. H. Lee, A. Iyo, T. Ito, T.
Kakeshita, H. Eisaki, and S. Uchida, Phys. Rev. Lett. 109, 217003 (2012).
182 Bibliography
[172] A. Dusza, A. Lucarelli, J.-H. Chu, I.R. Fisher, and L. Degiorgi, J. Supercond. Nov.
Magn. 26, 2603 (2013).
[173] C. Mirri, A. Dusza, S. Bastelberger, J.-H. Chu, H.-H. Kuo, I. R. Fisher, and L.
Degiorgi, Phys. Rev. B 89, 060501(R) (2014).
[174] A. A. Schafgans, B. C. Pursley, A. D. LaForge, A. S. Sefat, D. Mandrus, and D. N.
Basov, Phys. Rev. B 84, 052501 (2011).
[175] C. Clauß, Optical investigations on the charge ordered state of two dimensional con-
ductors, Diplomarbeit am 1. Physikalischen Institut, Stuttgart (2008).
[176] J. Merz, Infrarotspektroskopie an Eisenpniktiden, Bachelorarbeit am 1. Physikalis-
chen Institut, Stuttgart (2014).
[177] A. D. LaForge, A. Frenzel, B. C. Pursley, T. Lin, X. Liu, J. Shi, and D. N. Basov,
Phys. Rev. B 81, 125120 (2010).
[178] W. G. Jenks, I. M. Thomas, and J. P. Wikswo Jr., EAP 19, 457 (1997).
[179] D. Martien, Introduction to AC susceptibility, Quantum Design (2002).
[180] K. Iida, J. Hänisch, R. Hühne, F. Kurth, M. Kidszun, S. Haindl, J. Werner, L.
Schultz, and B. Holzapfel, Appl. Phys. Lett. 95, 192501 (2009).
[181] C. Krellner, N. Caroca-Canales, A. Jesche, H. Rosner, A. Ormeci, and C. Geibel,
Phys. Rev. B 78, 100504(R) (2008).
[182] S. Jiang, Y. Luo, Z. Ren, Z. Zhu, C. Wang, X. Xu, Q. Tao, G. Cao, and Z. A. Xu,
New J. Phys. 11 025007 (2009).
[183] J. Herrero-Martín, V. Scagnoli, C. Mazzoli, Y. Su, R. Mittal, Y. Xiao, T. Brückel,
N. Kumar, S.K. Dhar, A. Thamizhavel, and L. Paolasini, Phys. Rev. B. 80, 134411
(2009).
[184] D. Wu, N. Barišić, N. Drichko, S. Kaiser, A. Faridian, M. Dressel, S. Jiang, Z. Ren,
L. J. Li, G. H. Cao, Z. A. Xu, H. S. Jeevan, and P. Gegenwart, Phys. Rev. B 79,
155103 (2009).
[185] D. Kasinathan, A. Ormeci, K. Koch, U. Burkhardt, W. Schnelle, A. Leithe-Jasper,
and H. Rosner, New J. Phys. 11 025023 (2009).
[186] W. Z. Hu, J. Dong, G. Li, Z. Li, P. Zheng, G. F. Chen, J. L. Luo, and N. L. Wang,
Front. Phys. China 4, 459 (2009).
Bibliography 183
[187] E. Dengler, J. Deisenhofer, H. A. Krug von Nidda, S. Khim, J. S. Kim, K. H. Kim,
F. Casper, C. Felser, and A. Loidl, Phys. Rev. B 81, 024406 (2010).
[188] T. Terashima, N. Kurita, A. Kikkawa, H. S. Suzuki, T. Matsumoto, K. Murata, and
S. Uji, J. Phys. Soc. Jpn. 79, 103706 (2010).
[189] J. Koo, J. Park, S. K. Cho, K. D. Kim, S.-Y. Park, Y. H. Jeong, Y. J. Park T. Y.
Koo, K.-P. Hong, C.-H. Lee, J.-Y. Kim, B.-K. Cho, K. B. Lee, and H.-J. Kim, J.
Phys. Soc. Jpn. 79, 114708 (2010).
[190] M. Tokunaga, I. Katakura, N. Katayama, and K. Ohgushi, J. Low Temp. Phys. 159,
601) (2010).
[191] S. de Jong, E. van Heumen, S. Thirupathaiah, R. Huisman, F. Massee, J. B. Goed-
koop, R. Ovsyannikov, J. Fink, H. A. Dürr, A. Gloskovskii, H. S. Jeevan, P. Gegen-
wart, A. Erb, L. Patthey, M. Shi, R. Follath, A. Varykhalov, and M. S. Golden,
Europhys. Lett. 89, 27007 (2010).
[192] B. Zhou, Y. Zhang, L. X. Yang, M. Xu, C. He, F. Chen, J. F. Zhao, H. W. Ou, J.
Wei, B. P. Xie, T. Wu, G. Wu, M. Arita, K. Shimada, H. Namatame, M. Taniguchi,
X. H. Chen, and D. L. Feng, Phys. Rev. B 81, 155124 (2010).
[193] M. S. Kim, N. H. Sung, Y. Son, M. S. Ko, and B. K. Cho, Appl. Phys. Lett. 98,
172509 (2011).
[194] H. Kobayashi, S. Ikeda, Y. Yoda, H. Nakamura, and M. Machida, Phys. Rev. B 84,
184304 (2011).
[195] J. Herrero-Martín, C. Mazzoli, V. Scagnoli, L. Paolasini, H. Walker, Y. Xiao, T.
Brückel, R. Mittal, N. Kumar, S. K. Dhar, A. Thamizhavel, and Y. Su, J. Supercond.
Nov. Mag. 24, 705 (2011).
[196] A. Blachowski, K. Ruebenbauer, J. Zukrowski, K. Rogacki, Z. Bukowski, and J.
Karpinski, Phys. Rev. B 83, 134410 (2011).
[197] J. J. Ying, X. F. Wang, T. Wu, Z. J. Xiang, R. H. Liu, Y. J. Yan, A. F. Wang, M.
Zhang, G. J. Ye, P. Cheng, J. P. Hu, and X. H. Chen, Phys. Rev. Lett. 107, 067001
(2011).
[198] Y. Xiao, Y. Su, S. Nandi, S. Price, B. Schmitz, C. M. N. Kumar, R. Mittal, T.
Chatterji, N. Kumar, S. K. Dhar, A. Thamizhavel, and T. Brückel, Phys. Rev. B 85,
094504 (2012).
184 Bibliography
[199] L. Rettig, R. Cortés, S. Thirupathaiah, P. Gegenwart, H. S. Jeevan, M. Wolf, J.
Fink, and U. Bovensiepen, Phys. Rev. Lett. 108, 097002 (2012).
[200] M. Ikeda, K. Yoshida, and T. Kobayashi, J. Phys. Soc. Jpn.. 81, 033703 (2012).
[201] S. K. Mohanta, S. N. Mishra, S. M. Davane, S. Layek, and Z. Hossain, Mod. Phys.
Lett. B 27, 1350234 (2013).
[202] M. Ikeda, M. Hagiwara, T. Kobayashi, W. Hirata, S. Miyasaka, and S. Tajima, J.
Korean Phys. Soc. 62, 2007 (2013).
[203] A. Dutta, Anupam, Z. Hossain, and A. K. Gupta, J. Phys.: Condens. Matter 25,
375602 (2013).
[204] G. Adhikary, N. Sahadev, D. Biswas, R. Bindu, N. Kumar, A. Thamizhavel, S. K.
Dhar, and K. Maiti, J. Phys.: Condens. Matter 25, 225701 (2013).
[205] I. Avigo, R. Cortés, L. Rettig, S. Thirupathaiah, H. S. Jeevan, P. Gegenwart, T.
Wolf, M. Ligges, M. Wolf, J. Fink, and U. Bovensiepen, J. Phys.: Condens. Matter
25, 094003 (2013).
[206] A. V. Tsvyashchenko, V. A. Sidorov, L. N. Fomicheva, K. Gofryk, R. A. Sadykov,
and J. D. Thompson, Phys. Status Solidi B 250, 589 (2013).
[207] F. Drief, S. Kacimi, and A. Zaoui, Comput. Mater. Sci. 84, 97 (2013).
[208] C. W. Kwang-Hua, Chemical Physics 415, 186 (2013).
[209] P. F. S. Rosa, B. Zeng, C. Adriano, T. M. Garitezi, T. Grant, Z. Fisk, L. Balicas,
R. R. Urbano, and P. G. Pagliuso, arXiv:1402.2412.
[210] H. Raffius, E. Mörsen, B. D. Mosel, and W. Müller-Warmuth, J. Phys. Chem. Solids
49, 785 (1988).
[211] C. Feng, Z. Ren, S. Xu, S. Jiang, Z. A. Xu, G. Cao, I. Nowik, I. Felner, K. Matsub-
ayashi, and Y. Uwatoko, Phys. Rev. B 82, 094426 (2010).
[212] D. H. Ryan, J. M. Cardogan, S. Xu, Z. A. Xu, and G. H. Cao, Phys. Rev. B 83,
132403 (2011).
[213] L. Hua, J. M. Shen, Q. L. Zhu, and L. Chen, Physica B 406, 47 (2011).
[214] J. Ballinger, L. E. Wenger, Y. K. Vohra, and A. S. Sefat, J. Appl. Phys. 111, 07E106
(2012).
Bibliography 185
[215] W. H. Jiao, I. Felner, I. Nowik, and G. H. Cao, J. Supercond. Nov. Magn. 25, 441
(2012).
[216] H. Raffius, E. Mörsen, B. D. Mosel, W. Müller-Warmuth, W. Jeitschko, L. Ter-
büchte, and T. Vomhof, J. Phys. Chem. Solids 54, 135 (1993).
[217] M. Reehuis, W. Jeitschko, M. H. Möller, and P. J. Brown, J. Phys. Chem. Solids
53, 687 (1992) .
[218] S. Nandi, A. Kreyssig, Y. Lee, Yogesh Singh, J. W. Kim, D. C. Johnston, B. N.
Harmon, and A. I. Goldman, Phys. Rev. B 79, 100407 (2009).
[219] A. Akbari, P. Thalmeier, and I. Eremin New J. Phys. 15 033034 (2013).
[220] T. Terashima, M. Kimata, H. Satsukawa, A. Harada, K. Hazama, S. Uji, H. S.
Suzuki, T. Matsumoto, and K. Murata, J. Phys. Soc. Jpn. 78, 083701 (2009).
[221] W. Uhoya, G. Tsoi, Y. K. Vohra, M. A. McGuire, A. S. Sefat, B. C. Sales, D.
Mandrus, and S. T. Weir, J. Phys.: Condens. Matter 22 292202 (2010).
[222] K. Matsubayashi, K. Munakata, N. Katayama, M. Isobe, K. Ohgushi, Y. Ueda, N.
Kawamura, M. Mizumaki, N. Ishimatsu, M. Hedo, I. Umehara, and Y. Uwatoko,
Phys. Rev. B 84, 024502 (2011).
[223] W. Uhoya, G. Tsoi, Y. K. Vohra, M. A. McGuire, and A. S. Sefat, J. Phys.: Condens.
Matter 22 292202 (2010).
[224] N. Kurita, M. Kimata, K. Kodama, A. Harada, M. Tomita, H. S. Suzuki, T. Mat-
sumoto, K. Murata, S. Uji, and T. Terashima, Phys. Rev. B 83, 214513 (2011).
[225] N. Kurita, M. Kimata, K. Kodama, A. Harada, M. Tomita, H. S. Suzuki, T. Mat-
sumoto, K. Murata, S. Uji, and T. Terashima, Phys. Rev. B 83, 100501(R) (2011).
[226] H. B. Banks, W. Bi, L. Sun, G. F. Chen, X. H. Chen, and J. S. Schilling, Physica C
471, 476 (2011).
[227] N. Kurita, M. Kimata, K. Kodama, A. Harada, M. Tomita, H. S. Suzuki, T. Mat-
sumoto, K. Murata, S. Uji, and T. Terashima, J. Phys.: Conf. Ser. 273, 012098
(2011).
[228] N. Kurita, M. Kimata, K. Kodama, A. Harada, M. Tomita, H. S. Suzuki, T. Mat-
sumoto, K. Murata, S. Uji, and T. Terashima, J. Phys.: Conf. Ser. 391, 012132
(2012).
186 Bibliography
[229] N. Kurita, M. Kimata, K. Kodama, A. Harada, M. Tomita, H. S. Suzuki, T. Mat-
sumoto, K. Murata, S. Uji, and T. Terashima, Phys. Rev. B 88, 224510 (2013).
[230] H. S. Jeevan, D. Kasinathan, H. Rosner, and P. Gegenwart, Phys. Rev. B 83, 054511
(2011).
[231] A. Ahmed, M. Itou, S. Xu, Z. Xu, G. Cao, Y. Sakurai, J. Penner-Hahn, and A. Deb,
Phys. Rev. Lett. 105, 207003 (2010).
[232] L. Sun, J. Guo, G. Chen, X. Chen, X. Dong, W. Lu, C. Zhang, Z. Jiang, Y. Zou,
S. Zhang, Y. Huang, Q. Wu, X. Dai, Y. Li, J. Liu, and Z. Zhao, Phys. Rev. B 82,
134509 (2010).
[233] D. Wu, G. Chanda, H. S. Jeevan, P. Gegenwart, and M. Dressel, Phys. Rev. B 83,
100503(R) (2011).
[234] I. Nowik, I. Felner, Z. Ren, G. H. Cao, and Z. A. Xu, J. Phys.: Condens. Matter
23, 065701 (2011).
[235] S. Thirupathaiah, E. D. L. Rienks, H. S. Jeevan, R. Ovsyannikov, E. Slooten, J.
Kaas, E. van Heumen, S. de Jong, H. A. Duerr, K. Siemensmeyer, R. Follath, P.
Gegenwart, M. S. Golden, and J. Fink, Phys. Rev. B 84, 014531 (2011).
[236] G. Cao, S. Xu, Z. Ren, S. Jiang, C. Feng, and Z. A. Xu, J. Phys.: Condens. Matter
23, 464204 (2011)
[237] Z. Guguchia, A. Shengelaya, A. Maisuradze, L. Howald, Z. Bukowski, M. Chikovani,
H. Luetkens, S. Katrych, J. Karpinski, and H. Keller, J. Supercon. Nov. Magn. 26,
285 (2012).
[238] Y. Tokiwa, S.-H. Hübner, O. Beck, H. S. Jeevan, and P. Gegenwart, Phys. Rev. B
86, 220505(R) (2012).
[239] W. Li, J. X. Zhu, Y. Chen, and C. S. Ting, Phys. Rev. B 86, 155119 (2012).
[240] S. Jiang, H. S. Jeevan, J. Dong, and P. Gegenwart, Phys. Rev. Lett. 110, 067001
(2013).
[241] S. Nandi, W. T. Jin, Y. Xiao, Y. Su, S. Price, D. K. Shukla, J. Strempfer, H. S.
Jeevan, P. Gegenwart, and T. Brückel, Phys. Rev. B 89, 014512 (2014).
[242] S. Nandi, W. T. Jin, Y. Xiao, Y. Su, S. Price, W. Schmidt, K. Schmalzl, T. Chatterji,
H. S. Jeevan, P. Gegenwart, and T. Brückel, Phys. Rev. B 90, 094407 (2014).
Bibliography 187
[243] J. Munevar, H. Micklitz, M. Alzamora, C. Argüello, T. Goko, F. L. Ning, T. Munsie,
T. J. Williams, A. A. Aczel, G. M. Luke, G.F. Chen, and W. Yu, Solid State Commun.
187, 18 (2014).
[244] X. Xu, W. H. Jiao, N. Zhou, Y. K. Li, B. Chen, C. Cao, J. Dai, A. F. Bangura, and
G. Cao, Phys. Rev. B. 89, 104517 (2014).
[245] W. H. Jiao, J. K. Bao, Q. Tao, H. Jiang, C. M. Feng, Z. A. Xu, and G. H. Cao, J.
Phys.: Conf. Ser. 400, 022038 (2012).
[246] S. Sharma, A. Bharathi, K. Vinod, C. S. Sundar, V. Srihari, S. Sen, H. Ghosh, A.
K. Sinha, and S. K. Deb, arXiv:1312.7055
[247] S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes, D. K. Pratt, A. Thaler, N. Ni,
S. L. Bud’ko, P. C. Canfield, J. Schmalian, R. J. McQueeney, and A. I. Goldman,
Phys. Rev. Lett. 104, 057006 (2010).
[248] J. J. Ying, T. Wu, Q. J. Zheng, Y. He, G. Wu, Q. J. Li, Y. J. Yan, Y. L. Xie, R. H.
Liu, X. F. Wang, and X. H. Chen, Phys. Rev. B 81, 052503 (2010).
[249] X. B. Chen, Z. A. Ren, H. S. Ding, and L. H. Liu, Sci. China 53, 1212 (2010).
[250] M. Nicklas, M. Kumar, E. Lengyel, W. Schnelle, and A. Leithe-Jasper, J. Phys.:
Conf. Ser. 273, 012101 (2011).
[251] I. Nowik, I. Felner, Z. Ren, G. H. Cao, and Z. A. Xu, New J. Phys. 13, 023033
(2011).
[252] Z. Guguchia, J. Roos, A. Shengelaya, S. Katrych, Z. Bukowski, S. Weyeneth, F.
Murányi, S. Strässle, A. Maisuradze, J. Karpinski, and H. Keller, Phys. Rev. B 83,
144516 (2011).
[253] Z. Guguchia, S. Bosma, S. Weyeneth, A. Shengelaya, R. Puzniak, Z. Bukowski, J.
Karpinski, and H. Keller, Phys. Rev. B 84, 144506 (2011).
[254] A. Blachowski, K. Ruebenbauer, J. Zukrowski, Z. Bukowski, K. Rogacki, P. J. W.
Moll, and J. Karpinski, Phys. Rev. B 84, 174503 (2011).
[255] M. Matusiak, Z. Bukowski, and J. Karpinski, Phys. Rev. B 83, 224505 (2011).
[256] V. H. Tran, T. A. Zaleski, Z. Bukowski, L. M. Tran, and A. J. Zaleski, Phys. Rev.
B 85, 052502 (2012).
[257] V. H. Tran, Z. Bukowski, L. M. Tran, and A. J. Zaleski, New J. Phys. 14, 073052
(2012).
188 Bibliography
[258] F. A. Garcia, A. Leithe-Jasper, W. Schnelle, M. Nicklas, H. Rosner, and J.
Sichelschmidt, New J. Phys. 14, 063005 (2012).
[259] W. T. Jin, S. Nandi, Y. Xiao, Y. Su, O. Zaharko, Z. Guguchia, Z. Bukowski, S.
Price, W. H. Jiao, G. H. Cao, and T. Brückel, Phys. Rev. B 88, 214516 (2013).
[260] C. Rumble, M. Itou, S. Jiang, Z. A. Xu, G. Cao, Y. Sakurai, J. Penner-Hahn, and
A. Deb, J. Appl. Phys. 113, 013907 (2013).
[261] Z. Ren, X. Lin, Q. Tao, S. Jiang, Z. Zhu, C. Wang, G. Cao, and Z. Xu, Phys. Rev.
B 79, 094426 (2009).
[262] I. Nowik, I. Felner, Z. Ren, Z. A. Xu, and G. H. Cao, J. Phys.: Conf. Ser. 217,
012121 (2010).
[263] W. H. Jiao, H. F. Zhai, J. K. Bao, Y. K. Luo, Q. Tao, C. M. Feng, Z. A. Xu, and
G. H. Cao, New J. Phys. 15, 113002 (2013).
[264] U. B. Paramanik, P. L. Paulose, S. Ramakrishnan, A. K. Nigam, C. Geibel, and Z.
Hossain, Supercond. Sci. Technol. 27, 075012 (2014).
[265] L. J. Li, Y. K. Luo, Q. B. Wang, H. Chen, Z. Ren, Q. Tao, Y. K. Li, X. Lin, M. He,
Z. W. Zhu, G. H. Cao, and Z. A. Xu, New J. Phys. 11, 025008 (2008).
[266] W. Z. Hu, J. Dong, G. Li, Z. Li, P. Zheng, G. F. Chen, J. L. Luo, and N. L. Wang,
Phys. Rev. Lett. 101, 257005 (2008).
[267] A. Mitsuda, T. Matoba, F. Ishikawa, Y. Yamada, and H. Wada, J. Phys. Soc. Jpn.
79, 073704 (2010).
[268] A. Mitsuda, S. Seike, T. Matoba, H. Wada, F. Ishikawa, and Y. Yamada, J. Phys.:
Conf. Ser. 273, 012100 (2011).
[269] P. F. S. Rosa, C. Adriano, W. Iwamoto, T. M. Garitezi, T. Grant, Z. Fisk, and P.
G. Pagliuso, Phys. Rev. B 86, 165131 (2012)
[270] Y. He, T. Wu, G. Wu, Q. J. Zheng, Y. Z. Liu, H. Chen, J. J. Ying, R. H. Liu, X. F.
Wang, Y. L. Xie, Y. J. Yan, J. K. Dong, S. Y. Li, and X. H. Chen, J. Phys.: Condens.
Matter 22, 235701 (2010).
[271] R. Hu, S. L. Bud’ko, W. E. Straszheim, and P. C. Canfield, Phys. Rev. B 83, 094520
(2011).
Bibliography 189
[272] H. A. Krug von Nidda, S. Kraus, S. Schaile, E. Dengler, N. Pascher, M. Hemmida,
M. J. Eom, J. S. Kim, H. S. Jeevan, P. Gegenwart, J. Deisenhofer, and A. Loidl,
Phys. Rev. B 86, 094411 (2012).
[273] R. Sarkar, R. Nath, P. Khuntia, H. S. Jeevan, P. Gegenwart, and M. Baenitz, J.
Phys.: Condens. Matter 24, 045702 (2012).
[274] R. Hu, E. D. Mun, M. M. Altarawneh, C. H. Mielke, V. S. Zapf, S. L. Bud’ko, and
P. C. Canfield, Phys. Rev. B 85, 064511 (2012).
[275] Anupam, P. L. Paulose, H. S. Jeevan, C. Geibel, and Z. Hossain, J. Phys.: Condens.
Matter 21, 265701 (2009).
[276] V. A. Gasparov, H. S. Jeevan, and P. Gegenwart, JETP Letters 89, 294 (2009).
[277] N. Pascher, J. Deisenhofer, H.-A. Krug von Nidda, M. Hemmida, H. S. Jeevan, P.
Gegenwart, and A. Loidl, Phys. Rev. B 82, 054525 (2010).
[278] H. S. Jeevan and P. Gegenwart, J. Phys.: Conf. Ser. 200, 012060 (2010).
[279] Anupam, P. L. Paulose, S. Ramakrishnan, and Z. Hossain, J. Phys.: Condens. Matter
23, 455702 (2011).
[280] J. Maiwald, H. S. Jeevan, and P. Gegenwart, Phys. Rev. B 85, 024511 (2012).
[281] T. Dey, P. Khuntia, A. V. Mahajan, Anupam, and Z. Hossain, Europ. Phys. J. B
86, 458 (2013).
[282] V. A. Gasparov, A. Audouard, L. Drigo, A. I. Rodigin, C. T. Lin, W. P. Liu, M.
Zhang, A. F. Wang, X. H. Chen, H. S. Jeevan, J. Maiwald, and P. Gegenwart, Phys.
Rev. B 87, 094508 (2013).
[283] K. Sasmal, B. Lv, B. Lorenz, A. M. Guloy, F. Chen, Y.-Y. Xue, and C.-W. Chu,
Phys. Rev. Lett. 101, 107007 (2008).
[284] Y. Qi, Z. Gao, L. Wang, D. Wang, X. Zhang, and Y. Ma, New J. Phys. 10 123003
(2008).
[285] Y. Qi, L. Wang, Z. Gao, X. Zhang, D. Wang, C. Yao, C. Wang, C. Wang, and Y.
Ma, New J. Phys. 14, 033011 (2012).
[286] Anupam, V. K. Anand, P. L. Paulose, S. Ramakrishnan, C. Geibel, and Z. Hossain,
Phys. Rev. B 85, 144513 (2012).
190 Bibliography
[287] Y. R. Jang, J. B. Hong, B. H. Min, M. A. Jung, Y. Y. Song, H. J. Oh, K. J. Lee,
M. H. Jung, S. Kanematsu, K. Imura, K. Deguchi, N. K. Sato, and Y. S. Kwon,
Supercond. Sci. Technol. 24, 085017 (2011).
[288] T. Wu, G. Wu, H. Chen, Y. L. Xie, R. H. Liu, X. F. Wang, and X. H. Chen, J.
Magn. Magn. Mater 321, 3870 (2009).
[289] F. A. Garcia, E. M. Bittar, C. Adriano, T. M. Garitezi, C. Rettori, and P. G.
Pagliuso, J. Phys.: Conf. Ser. 273, 012093 (2011).
[290] B. Zhou, L. X. Yang, F. Chen, M. Xu, T. Wu, G. Wu, X. H. Chen, and D. L. Feng,
J. Phys. Chem. Solids 72, 474 (2011).
[291] M. Zhang, J. J. Ying, Y. J. Yan, A. F. Wang, X. F. Wang, Z. J. Xiang, G. J. Ye, P.
Cheng, X. G. Luo, J. Hu, and X. H. Chen, Phys. Rev. B 85, 092503 (2012).
[292] T. Moriya and K. Ueda, Adv. in Phys. 49, 555 (2000).
[293] P. Richard, C. Capan, J. Ma, P. Zhang, N. Xu, T. Qian, J. D. Denlinger, G.-F. Chen,
A. S. Sefat, Z. Fisk, and H. Ding, J. Phys.: Condens. Matter 26, 035702 (2014).
[294] M. Xia, W. H. Jiao, Z. R. Ye, Q. Q. Ge, Y. Zhang, J. Jiang, R. Peng, X. P. Shen,
Q. Fan, G. H. Cao, T. Zhang, B. P. Xie, and D. L. Feng, J. Phys.: Condens. Matter
26, 265701 (2014).
[295] X. Xu, W. H. Jiao, N. Zhou, Y. K. Li, B. Chen, C. Cao, J. Dai, A. F. Bangura, and
G. Cao, Phys. Rev. B 89, 104517 (2014).
[296] F. Klingert, Magnetic Investigations on EuFe2As2 - Superconductors, Diplomarbeit
am 1. Physikalischen Institut, Stuttgart (2012).
[297] B. Maji, K. G. Suresh and A. K. Nigam, J. Phys.: Condens. Matter 23, 506002
(2011).
[298] A. C. D. van Enter and J. L. van Hemmen, Phys. Rev. B 31, 603 (1985).
[299] K. Jonason, J. Mattsson, and P. Nordblad, Phys. Rev. B 53, 6507 (1996).
[300] A. M. Campbell and J. E. Evetts, Adv. i. Phys. 21, 199 (1972).
[301] J. Giapintzakis, R. L. Neiman, D. M. Ginsberg, and M. A. Kirk, Phys. Rev. B 50,
16001 (1994).
[302] M. C. Frischherzt, F. M. Sauerzopft, H. W. Webert, M. Murakamit, and G. A.
Emel’chenko, Supercond. Sci. Technd. 8, 485 (1995).
Bibliography 191
[303] G. Prando, P. Carretta, R. De Renzi, S. Sanna, A. Palenzona, M. Putti, and M.
Tropeano, Phys. Rev. B 83, 174514 (2011).
[304] W. Braunisch, N. Knauf, V. Kataev, S. Neuhausen, A. Grütz, A. Kock, B. Roden,
D. Khomskii, and D. Wohlleben, Phys. Rev. Lett. 68, 1908 (1992).
[305] F. Pfister, Anisotroper Transport in eisenbasierten Supraleitern, Bachelorarbeit am
1. Physikalischen Institut, Stuttgart (2013).
[306] M. Colarieti-Tosti, S. I. Simak, R. Ahuja, L. Nordström, O. Eriksson, D. Åberg, S.
Edvardsson, and M. S. S. Brooks, Phys. Rev. Lett. 91, 157201 (2003).
[307] L. Bauernfeind, W. Widder, and H. F. Braun, Physica C 254, 151 (1995).
[308] C. A. Cardoso, F. M. Araujo-Moreira, V. P. S. Awana, E. Takayama-Muromachi, O.
F. de Lima, H. Yamauchi, and M. Karppinen, Phys. Rev. B 67, 020407(R) (2003).
[309] S. Garcia, L. Ghivelder, and I. Felner, Phys. Rev. B 79, 054506 (2009).
[310] S. Lausberg, J. Spehling, A. Steppke, A. Jesche, H. Luetkens, A. Amato, C. Baines,
C. Krellner, M. Brando, C. Geibel, H.-H. Klauss, and F. Steglich, Phys. Rev. Lett.
109, 216402 (2012).
[311] Private communication with Prof. J. Fink, IFW Dresden.
[312] Private communication with Prof. J. Schmalian, KIT.
[313] Private communication with Prof. I. Fisher, Stanford.
[314] U. Pracht, THz Spectroscopy on Quantum Phase Transition in Ultra-Thin Films of
Titanium Nitride, Masterarbeit am 1. Physikalischen Institut, Stuttgart (2012).
[315] S. Zapf, B. Gorshunov, D. Wu, E. Zhukova, V. S. Nozdrin, S. Haindl, K. Iida, and
M. Dressel, J. Supercond. Nov. Magn. 21, 1557 (2013).
[316] A. S. Prokhorov, E. S. Zhukova, A. A. Boris, I. E. Spektor, B. P. Gorshunov, V. S.
Nozdrin, E. A. Motovilova, L. S. Kadyrov, S. Zapf, S. Haindl, K. Iida, M. Dressel, K.
V. Chizh, M. S. Storozhevykh, L. V. Arapkina, V. A. Chapnin, O. V. Uvarov, V. P.
Kalinushkin, and V. A. Yuryev, Radiophys. Quant. Electr. 56, 620 (2014).
[317] A. E. Karakozov, S. Zapf, B. Gorshunov, Y. G. Ponomarev, M. V. Magnitskaya,
E. Zhukova, A. S. Prokhorov, V. B. Anzin, and S. Haindl, Phys. Rev. B 90, 014506
(2014).
192 Bibliography
[318] A. E. Karakozov, B. P. Gorshunov, Y. G. Ponomarev, A. S. Prokhorov, M. V.
Magnitskaya, E. Zhukova, K. Iida, M. Dressel, S. Zapf, and S. Haindl, JETP Letters
100, to be translated (2014).
[319] D. V. Efremov, M. M. Korshunov, O. V. Dolgov, A. A. Golubov, and P. J. Hirschfeld,
Phys. Rev. B 84, 180512(R) (2011).
[320] D. V. Efremov, A. A. Golubov, and O. V. Dolgov, New J. Phys. 15, 013002 (2013).
[321] C. Tarantini, M. Putti, A. Gurevich, Y. Shen, R. K. Singh, J. M. Rowell, N. Newman,
D. C. Larbalestier, P. Cheng, Y. Jia, and H.-H. Wen, Phys. Rev. Lett. 104, 087002
(2010).
[322] M. Schilling, THz investigation on iron-based superconductors, Masterarbeit am 1.
Physikalischen Institut, Stuttgart (2014).
[323] A. Baumgartner, THz Untersuchungen an eisenbasierten Supraleitern, Bachelorar-
beit am 1. Physikalischen Institut, Stuttgart (2013).
CURRICULUM VITAE
Education
1996–2005 Friedrich-Dessauer-Gymnasium Aschaffenburg
2005–2010 Julius-Maximilians-Universität Würzburg, elite program “FOKUS Phy-
sik”
since 06/2010 PhD project, Prof. Dressel, University of Stuttgart
Experience
09/2007–10/2007 MPI FKF Stuttgart, Department Kern, Dr. Vogelgesang, Bache-
lor thesis: Wavelength Dependent Optoelectronic Characterization of
Carbon Nanotube Based Field Effect Transistors
08/2008–09/2008 University of Würzburg, EP3 Molenkamp, Prof. Geurts, internship:
Infrared-Spectroscopy on GdMnO3
01/2009–04/2009 UC Berkeley, Department of Chemistry, Prof. Pines, co-worker on the
project: Imaging a Temperature Gradient via NMR
04/2009-04/2010 University of Würzburg, EP3 Molenkamp, Prof. Geurts, Master thesis:
Spinflip-Raman-Spectroscopy on CdMnTe / CdMgZnTe - Quantum
Well Structures
since 06/2010 University of Stuttgart, 1st Physical Institute, Prof. Dressel: infrared
and THz spectroscopy, SQUID magnetometry, dc resistivity, teach-
ing (laboratory courses), supervision of four Bachelor and two Master
students
04/2013-09/2013 Several visits at the UC San Diego, Department of Physics, Prof.
Basov: magneto-optical investigations on EuFe2As2
194 Curriculum Vitae
Selected scholarships and Awards
09/2010–04/2012 Scholarship of the Postgraduate Research Grants Program of Baden-
Württemberg
03/2012 Best Poster Award at the International Conference on Magnetism and
Superconductivity, Istanbul
03/2014 Düker Award for the best scientific presentation of a research project
for school students
DECLARATION OF ORIGINALITY
I hereby declare that this thesis and the work reported herein was composed by and
originated entirely from me. Information derived from the published and unpublished
work of others has been acknowledged in the text and references.