Vanadium sesquioxide $\left({\mathrm{V}}_2{\mathrm{O}}_3\right)$ is an antiferromagnetic insulator below $T_{\mathrm{N}}\approx 155\text{K}$. The magnetic order does not consist of only antiferromagnetic nearest-neighbor bonds, possibly excluding the interplane vanadium pairs, as one would infer from the bipartite character of the hexagonal basal plane in the high-temperature corundum structure. In fact, a magnetic structure with one ferromagnetic bond and two antiferromagnetic ones in the honeycomb plane is known experimentally to be realized, accompanied by a monoclinic distortion that makes the ferromagnetic bond inequivalent from the other two. We show here that the magnetic ordering, the accompanying monoclinic structural distortion, the magnetic anisotropy, and also the recently discovered high-pressure nonmagnetic monoclinic phase, can all be accurately described by conventional electronic structure calculations within GGA and GGA+$U$. Remarkably, our calculations yield that the corundum phase would be unstable to a monoclinic distortion even without magnetic ordering, thus suggesting that magnetism and lattice distortion are independent phenomena, though they reinforce each other. By means of GGA+$U$, we find a metal-to-insulator transition at a critical $U_c$. Both metal at $U\le U_c$ and insulator above $U_c$ have the same magnetic order as that actually observed below $T_{\mathrm{N}}$, but different monoclinic distortions. Reassuringly, the distortion on the insulating side agrees with the experimental one. Our results are in line with DMFT calculations for the paramagnetic phase [A. I. Poteryaev et al., Phys. Rev. B 76, 085127 (2007)], which predict that the insulating character is driven by a correlation-enhanced crystal-field splitting between $e_g^{\pi }$ and $a_{1g}$ orbitals that pushes the latter above the chemical potential. We find that the $a_{1g}$ orbital, although almost empty in the insulating phase, is actually responsible for the unusual magnetic order as it leads to magnetic frustration whose effect is similar to a next-nearest-neighbor exchange in a Heisenberg model on a honeycomb lattice.

• Received 17 February 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075121