Mechanisms of Carrier-Induced Ferromagnetism in Diluted Magnetic Semiconductors

Two different approaches to the problem of carrier-induced ferromagnetism in the system of the disordered magnetic ions, one bases on self-consistent procedure for the exchange mean fields, other one bases on the RKKY interaction, used in present literature as the alternative approximations is analyzed. Our calculations in the framework of exactly solvable model show that two different contributions to the magnetic characteristics of the system represent these approaches. One stems from the diagonal part of carrier-ion exchange interaction that corresponds to mean field approximation. Other one stems from the off-diagonal part that describes the interaction between ion spins via free carriers. These two contributions can be responsible for the different magnetic properties, so aforementioned approaches are complementary, not alternative. A general approach is proposed and compared with different approximations to the problem under consideration.