Suppression of effective spin-orbit coupling by thermal fluctuations in spin-orbit coupled antiferromagnets

We apply the finite-temperature variational cluster approach to a strongly correlated and spin-orbit coupled model for four electrons (i.e., two holes) in the t(2g) subshell. We focus on parameters suitable for antiferromagnetic Mott insulators, in particular, Ca2RuO4, and identify a crossover from the low-temperature regime, where spin-orbit coupling is essential, to the high-temperature regime where it leaves few signatures. The crossover is seen in one-particle spectra, where xz and yz spectra are almost one dimensional (as expected for weak spin-orbit coupling) at high temperature. At lower temperature, where spin-orbit coupling mixes all three orbitals, they become more two dimensional. However, stronger effects are seen in two-particle observables like the weight in states with definite on-site angular momentum. We thus identify the enigmatic intermediate-temperature "orbital-order phase transition," which has been reported in various x-ray diffraction and absorption experiments at T approximate to 260 K, as the signature of the onset of spin-orbital correlations.