We propose that localized defects in magnetic semiconductors act as deepimpurities and can be described by the Anderson model. Within this model,hybridization of d-orbitals and p-orbitals gives rise to a non-RKKY indirectexchange mechanism, when the localized d-electrons are exchanged through bothconduction and valence bands. For semiconductors with indirect band gap thenon-RKKY part of exchange integral is antiferromagnetic, which suppressesferromagnetism. In case of direct band gap, this exchange mechanism can, undercertain conditions, lead to enhancement of ferromagnetism. The indirectexchange intergral is much stronger than RKKY, and can be sufficiently longrange. Thus, a potentially new class of high-temperature magneticsemiconductors emerges, where doped carriers are not necessary to mediateferromagnetism. Curie temperatures in such magnetic semiconductors aredetermined mostly by the interaction between localized impurities, not Zenermechanism. This effect could also be responsible for unusually high Curietemperatures in some magnetic semiconductors with direct band gap, such asGaMnAs.
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