Collinear Superexchange Interaction between Inequivalent Ions:V2+andNi2+in MgO

The Dirac-Van Vleck-Serber method of configuration interaction is applied to formulate the collinear superexchange interaction between ${\mathrm{V}}^{2+}$ and ${\mathrm{Ni}}^{2+}$ ions. The major terms of the exchange integral derived by using this method are found to be equivalent to the result of Anderson's mechanism of potential exchange. The dominant contribution to the superexchange interaction is found to arise from the spin polarization of the ligand $p_{\sigma }$ orbitals via covalent mixing with ${\mathrm{Ni}}^{2+}$ ions, in cooperation with the direct exchange between the spins of ${\mathrm{V}}^{2+}$ ions and the polarized $p_{\sigma }$ orbitals. The strength of the interaction is computed to be 7.3°K (ferromagnetic) for ${\mathrm{V}}^{2+}$ and ${\mathrm{Ni}}^{2+}$ ions in MgO, a value which is expected to be too small by a factor of about 2. A semiempirical estimate for the exchange integral is performed for ${\mathrm{V}}^{2+}$ and ${\mathrm{Ni}}^{2+}$ ions in KMg${\mathrm{F}}_3$ by using the measured values for the unpaired spin densities in KNi${\mathrm{F}}_3$ and ${\mathrm{V}}^{2+}$:KMg${\mathrm{F}}_3$. The strength of collinear superexchange is expected to be roughly 15°K for this case.