Theory of Superexchange Interaction. I. KMnF3

A calculation of the superexchange integral J in KMnF 3 in made on the basis of Anderson's theory. While previous quantitative treatments have been confined to the `three-orbital four-electron system', the present work takes into account the effect due to other electrons and ions surrounding the system explicitly. It is found that this effect is by no means negligible. All integrals including many-center integrals are evaluated exactly. Covalency parameter dependence of each term which contributes to the superexchange integral is investigated. It is concluded that correct sign and order of magnitude of J can be obtained for reasonable values of covalency parameters.