Orbital entangled antiferromagnetoc order and spin-orbit-distortion exciton in $\mathrm{S}{\mathrm{r}}_2\mathrm{V}{\mathrm{O}}_4$

With electron filling $n=1$ in the $\mathrm{S}{\mathrm{r}}_2\mathrm{V}{\mathrm{O}}_4$ compound, the octahedrally coordinated $t_{2\mathrm{g}}$ orbitals are strongly active due to tetragonal distortion induced crystal field tuning by external agent such as pressure. Considering the full range of crystal field induced tetragonal splitting in a realistic three-orbital model, collective spin-orbital excitations are investigated using the generalized self consistent and fluctuation approach. The variety of self consistent states obtained including orbital entangled ferromagnetic and antiferromagnetic orders reflects the rich spin-orbital physics resulting from the interplay between the band, spin-orbit coupling, crystal field, and Coulomb interaction terms. The behavior of the calculated energy scales of collective excitations with crystal field is consistent with that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.