Phase transitions in a ferromagnetic semiconductor. III

We investigate the ferromagnetic phase transition in a heavily doped semiconductor or semimetal containing magnetic ions. The coupling between conduction electrons and magnetic ions is treated in the molecular field approximation. We show that the system undergoes a transition to an ordered state for arbitrarily small concentrations of the magnetic ions and the conduction electrons. In the limitJ/? _F?1 we obtain the Ruderman-Kittel result for the Curie temperature, and forJ/? _F?1 a generalization of Thompson’s strong coupling result. (J is the exchange coupling constant between conduction electrons and magnetic ions and? _F is the kinetic Fermi energy at absolute zero.) The intermediate range is evaluated numerically.