Spin-orbit coupling and magnetism in $\rm Sr_2CrO_4$

With octahedrally coordinated $t_{\rm 2g}$ orbitals which are active at filling $n=2$, the $\rm Sr_2CrO_4$ compound exhibits rich interplay of spin-orbital physics with tetragonal distortion induced crystal field tuning by external agent such as pressure. Considering both reversed and restored crystal field regimes, collective spin-orbital excitations are investigated in the antiferromagnetic state using the generalized self consistent + fluctuations approach including spin-orbit coupling (SOC). A transition is found from staggered to entangled orbital order at critical SOC value in the realistic regime. Behavior of the calculated energy scales of collective excitations with crystal field is in striking similarity to that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.