Using the multiband $d\text{−}p$ model and unrestricted Hartree-Fock approximation we investigate the electronic structure and spin-orbital order in a three-dimensional ${\mathrm{VO}}_3$ lattice. The main aim of this paper is testing if a simple $d\text{−}p$ model with partly filled $3d$ orbitals (in vanadium ions) and $2p$ orbitals (in oxygen ions) is capable of reproducing correctly nontrivial coexisting spin-orbital order observed in the vanadium perovskites. We point out that the multiband $d\text{−}p$ model has to include partly filled $e_g$ orbitals in vanadium ions. The results suggest weak self-doping as an important correction beyond the ionic model and reproduce the possible ground states with broken spin-orbital symmetry in vanadium ions: either $C$-type alternating orbital order accompanied by $G$-type antiferromagnetic spin order or $G$-type alternating orbital order accompanied by $C$-type antiferromagnetic spin order. Both states are experimentally observed and compete with each other in ${\mathrm{YVO}}_3$ whereas only the latter was observed in ${\mathrm{LaVO}}_3$. Orbital order is induced and stabilized by particular patterns of oxygen distortions arising from the Jahn-Teller effect. In contrast to time-consuming ab initio calculations, the computations using the $d\text{−}p$ model are very quick and should be regarded as very useful in solid-state physics, provided the parameters are selected carefully.

• Received 16 May 2018
• Revised 19 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.085119