Abstract
A brief review of theory of ferromagnetism of diluted magnetic semiconductors of the form (A, Mn) B based on the double-exchange model is first given. A systematic investigation of the phenomena extending the current theory is outlined. We begin with an investigation of regions of instability of the non-magnetic towards the ferromagnetic state of a system of Mn atoms doped in an AB-type semiconductor. A self-consistent many-body theory of the ferromagnetic state is then developed, going beyond the mean-field approaches by including fluctuations of the Mn spins and the itinerant hole gas. A functional theory suitable for computation of system properties such as the Curie temperature as a function of the hole and the Mn concentrations, the spin current, etc., is formulated.