Calculation of the Rare-Earth—Iron Superexchange Interaction in the Garnets

The exchange potential for the rare earth—iron interaction in the garnets depends on ten theoretical parameters. Since experiments provide only six splittings, the potential has been simplified in past treatments by various drastic assumptions which are highly implausible on physical grounds. By treating directly the superexchange mechanism involved we obtain a potential whose parameters are physically well-defined exchange and transfer integrals. By invoking the ``orthogonality requirement'' the number of these parameters is greatly reduced. A preliminary calculation for ytterbium shows that a good fit can be obtained by assuming the interaction of the rare earth with its nearest iron neighbor to predominate.