Superexchange operator and crystal-field-like terms for rare-earth-iron interaction in garnets

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Abstract
A superexchange operator for the case of two distinct orbitally degenerate ions is examined in the second-order perturbation theory with the emphasis on the anisotropy of the interaction. In addition to the usual spin-dependent terms, the model is also shown to give rise to the spin-independent terms. In the case of exchange interaction between rare-earth and ferric ions in garnets, the latter are reduced to the single-ion terms which are identical in form to the crystal-field operator. It appears that it is possible to estimate these terms directly from experimentally determined exchange parameters. The significance of these crystal-field-like terms is examined for the case of Er3+ in erbium-iron garnet.

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