arXiv:2107.07214v2 [cond-mat.str-el] 17 Dec 2021 Spin-orbit coupling induced staggered-to-entangled orbital order transition in a three-orbital model for Sr 2 CrO 4 Shubhajyoti Mohapatra, 1 Dheeraj Kumar Singh, 2 and Avinash Singh 1, ∗ 1 Department of Physics, Indian Institute of Technology, Kanpur - 208016, India 2 Thapar Institute of Engineering and Technology, Patiala - 147004, India (Dated: December 20, 2021) With octahedrally coordinated t 2g orbitals which are active at filling n = 2, the Sr 2 CrO 4 compound exhibits rich interplay of spin-orbital physics with tetragonal dis- tortion 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 (AFM) state of a realistic three-orbital model using the generalized self consistent + fluctuation approach including spin- orbit coupling (SOC). Important effects of SOC and Coulomb interaction induced orbital mixing terms are highlighted, including staggered-to-entangled orbital order transition. Behavior of the calculated energy scales of collective excitations with crys- tal field is in striking similarity to that of the transition temperatures with pressure as obtained from susceptibility and resistivity anomalies in high-pressure studies.