Insulating phase ofV2O3: An attempt at a realistic calculation

The problem of the highly correlated electron gas ${\mathrm{V}}_2$ ${\mathrm{O}}_3$ consisting of a filled $a_{1g}$ and a quarterly full $e_g$ band is treated on the basis of a Hartree-Fock calculation with spin and orbit unrestriction. The values of the effective hopping integrals which include covalency effects (due to the overlap of the $2p_{\pi }$ orbitals of the oxygens with the $3d$ wave functions of the vanadium atoms) are assessed on the bases of available bandstructure calculations and experimental results measuring covalency contributions. For reasonable values of the Hubbard parameters $U_{\mathrm{mm}}\simeq 2$ eV, $U_{\mathrm{mn}}\simeq 1.6$ eV, and $J_{\mathrm{mn}}\simeq 0.2$ eV [the interatomic Coulomb repulsion of electrons on the same orbit ($m, m$) on different orbits ($m, n$) and the exchange integral $J_{\mathrm{mn}}$] it is found that the observed spin structure of ${\mathrm{V}}_2$ ${\mathrm{O}}_3$ together with an antiferromagnetic orbital order gives the lowest Hartree-Fock ground-state energy amongst a large class of solutions which we considered and shows a gap in the density of states of the order of 0.2-0.3 eV. Since this gap appears already in the trigonal phase, we feel confident that the monoclinic distortion in the low-temperature phase is of magnetostrictive origin and not a primary cause of the metal-insulator transition. The peculiar value of $1.2{\mu }_B$ per V atom as observed by neutron scattering is interpreted as a strongly covalency-enhanced moment on the V atom. The atomic limit value of $1{\mu }_B$ due to one magnetic $e_g$ electron per V atom is reduced to $\simeq 0.75{\mu }_B$ in an itinerant picture. The covalency mechanism providing the extra $0.4{\mu }_B$ is known as back-bonding effect and leads at the same time to a negative spin density on the oxygen ions which are therefore no longer diamagnetic. Negative ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ NMR shift in the insulating antiferromagnetic phase should be able to verify this conjecture.