A Note on the Theory of Superexchange Interaction

Abstract

The expressions of the coefficients appearing in the interaction \(\mathscr{J}_{ij,kl}(\textbf{\itshape s}_{i}{\cdot}\textbf{\itshape s}_{j})\) ( s k · s l ) between unpaired spins have been derived together with the expressions for the ordinary superexchange integral J i j . The latter expressions include some new terms which have been overlooked in previous derivations. Consideration of the former interaciton seems to solve, at least qualitatively, the difficulties encountered before. The results were also applied in the derivation of the expressions of the coupling constant in the interaction between a paramagnetic ion pair and an electric field. Finally, an attempt is made to calculate the superexchange integral in the three center four electron problem by using the values obtained in the calculation on KMnF 3 . The relation between Anderson's recent theory and the older based upon Heitler-London model is studied. Numerical results are given and analyzed from both points of view.