Long range superexchange - an exchange interaction through empty bands

TL;DR

This paper generalizes the RKKY interaction to semiconductors, revealing a superexchange mechanism mediated by impurity electron excitations, which is significant for understanding magnetic interactions in diluted magnetic semiconductors.

Contribution

It introduces a theoretical framework for superexchange interactions in semiconductors, extending the RKKY model to cases with empty bands and no free carriers.

Findings

Identifies an oscillating anti-ferromagnetic coupling mediated by impurity electrons.

Derives a superexchange interaction analogous to RKKY for semiconductors.

Highlights relevance for magnetic properties of diluted magnetic semiconductors.

Abstract

We derive a generalization of the RKKY interaction to semiconductors using perturbation theory on a non-degenerated two-impurity Anderson model. In metals the interaction is mediated by excitations of free carriers over the Fermi-energy. In semiconductors, where no carriers are present, the only possible excitations are those of the localized impurity electrons (or holes) themselves. Thus a possible interaction is closely related to superexchange. We find an oscillating anti-ferromagnetic spin-spin coupling due to impurity electron (hole) excitations. By treating the coupling through empty bands (superexchange) along the same route as carrier mediated interactions (RKKY) it is easy to compare these two kinds of spin-spin coupling. The interaction derived here is of special interest for diluted magnetic semiconductors.