An effective Kugel–Khomskii-type model that can be applied to analyze the magnetic and orbital order in the Sr2VO4 compound is formulated. For the case of infinitely large crystal field splitting (the difference of the energy of the \(xy\) state from the energies of the xz and yz states), the phase diagram describing the ground state of the model in the variables of spin–orbit coupling and Hund’s exchange is determined. A quantum phase transition is described, and an equation for the phase boundary between a state exhibiting both the hidden magnetic and orbital long-range orders and a weakly ferromagnetic state with concurrent antiferro-orbital order with the same amplitude is derived. These long-range orders are described in terms of octupole moments constructed from the components of the total magnetic moment.
