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With electron filling $n=1$ in the $\rm Sr_2VO_4$ compound, the octahedrallycoordinated $t_{\rm 2g}$ orbitals are strongly active due to tetragonaldistortion induced crystal field tuning by external agent such as pressure.Considering the full range of crystal field induced tetragonal splitting in arealistic three-orbital model, collective spin-orbital excitations areinvestigated using the generalized self consistent and fluctuation approach.The variety of self consistent states obtained including orbital entangledferromagnetic and antiferromagnetic orders reflects the rich spin-orbitalphysics resulting from the interplay between the band, spin-orbit coupling,crystal field, and Coulomb interaction terms. The behavior of the calculatedenergy scales of collective excitations with crystal field is consistent withthat of the transition temperatures with pressure as obtained fromsusceptibility and resistivity anomalies in high-pressure studies.

Orbital entangled antiferromagnetoc order and spin-orbit-distortion exciton in $\rm Sr_2VO_4$