Two different approaches (presented in the literature as alternative approximations) 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 Ruderman - Kittel - Kasuya - Yosida interaction. Calculations in the framework of exactly solvable model are carried out, and it shows 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 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 carries. These two contributions can be responsible for the different magnetic properties. Thus, the aforementioned contributions are complementary but not alternative to each other. A general approach is proposed and compared with different approximations to the problem under consideration.

• Рябченко Сергій Михайлович (1940–) (фізико-математичні науки)

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