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

TL;DR

This study investigates how thermal fluctuations suppress effective spin-orbit coupling in antiferromagnetic Mott insulators, revealing a crossover from spin-orbit dominated behavior at low temperatures to a regime with minimal spin-orbit effects at higher temperatures.

Contribution

It introduces a finite-temperature variational cluster approach to analyze spin-orbit coupling effects in strongly correlated materials, highlighting the temperature-dependent crossover in orbital and spin-orbital correlations.

Findings

Spin-orbit coupling effects diminish at high temperatures.

One-particle spectra become more one-dimensional at high T.

The orbital-order phase transition is linked to the onset of spin-orbital correlations.

Abstract

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 Ca$_2$RuO$_4$, 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 onsite 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 $T\approx 260\;K$, as the signature of the onset of spin-orbital correlations.