On the theory of carrier-induced ferromagnetism in diluted magnetic semiconductors

Two different approaches (presented in the literature as alternative approx imations) to the problem of carrier-induced ferromagnetism in the system of disordered magnetic ions of a diluted magnetic semiconductor are analyzed. They are based on a self-consistent procedure for the mean exchange fields and the RKKY interaction. Calculations in the framework of an exactly solv able model are carried out, and it is shown that these approaches stem from two different contributions to the magnetic susceptibility. One stems from the diagonal part of the carrier-ion exchange interaction and corresponds to the mean field approximation. The other one stems from the off-diagonal part of the same interaction and describes the indirect interaction between localized spins via free carriers. These two contributions can give rise t o different magnetic properties. Thus the aforementioned contributions are complementary and not alternative to each other. A general approach is prop osed and compared with different approximations to the problem under consid eration. (C) 2000 American Institute of Physics.[S1063-777X(00)00412-6].