Exchange Interaction between Nearest-Neighbor Ion Pairs. II.V2+in MgO

The configuration-interaction method is applied to the (right-angle) exchange interaction between nearest-neighbor ${\mathrm{V}}^{2+}$ ion pairs in MgO. Specific configurations under consideration are the ionic configuration, all allowed anion-to-cation charge-transfer configurations, and the most important cation-to-cation charge-transfer configuration. Numerical calculations are performed for the exchange interactions between individual $3d$-electron pairs. The exchange coupling constant $J_{\mathrm{AB}}$ associated with the exchange energy $-2\mathrm{}{J}_{\mathrm{AB}}{\mathrm{S}}_A·{\mathrm{S}}_B$ between total spins of two ${\mathrm{V}}^{2+}$ ions is deduced by projecting the single electronic spin onto the total spin. Its value is found to be 8.2°K (ferromagnetic). The lack of orthogonality between neighboring cation $3d$ orbitals is shown to be very important for the exchange coupling between two magnetic ions at right angles to an intervening anion. The sign of the contribution to the exchange integral arising from this nonorthogonality depends on the symmetry of electron orbitals. For the specific cases under consideration, these contributions are found to be of overriding numerical importance.