Spin-orbit coupled states arising in the half-filled t2g shell

Abstract

Strongly correlated and spin-orbit coupled t2g systems have been extensively investigated. By coupling orbital and spin angular momentum into one quantity, spin-orbit coupling (SOC) tends to reduce orbital degeneracy, e.g. for the widely studied case of one hole in the t2g shell. However, the opposite has to be expected at half filling. Without spin-orbit coupling, all orbitals are half filled, no orbital degree of freedom is left and coupling to the lattice can be expected to be small. At dominant spin-orbit coupling, in contrast, one of the j=3/2 states is empty and the system couples to the lattice. We investigate this issue. One finding is that the low-energy manifold evolves smoothly from the four S=3/2 states in the absence of SOC to the four j=3/2 states with dominant SOC. These four states are always separated from other states by a robust gap. We then discuss a relevant superexchange mechanism to assess the interplay between spin-orbit coupling and coupling to the lattice.