  We propose that localized defects in magnetic semiconductors act as deep
impurities and can be described by the Anderson model. Within this model,
hybridization of d-orbitals and p-orbitals gives rise to a non-RKKY indirect
exchange mechanism, when the localized d-electrons are exchanged through both
conduction and valence bands. For semiconductors with indirect band gap the
non-RKKY part of exchange integral is antiferromagnetic, which suppresses
ferromagnetism. In case of direct band gap, this exchange mechanism can, under
certain conditions, lead to enhancement of ferromagnetism. The indirect
exchange intergral is much stronger than RKKY, and can be sufficiently long
range. Thus, a potentially new class of high-temperature magnetic
semiconductors emerges, where doped carriers are not necessary to mediate
ferromagnetism. Curie temperatures in such magnetic semiconductors are
determined mostly by the interaction between localized impurities, not Zener
mechanism. This effect could also be responsible for unusually high Curie
temperatures in some magnetic semiconductors with direct band gap, such as
GaMnAs.
