Carrier Induced Ferromagnetism in Concentrated and Diluted Local-Moment Systems

For modeling the magnetic properties of concentrated and diluted magnetic semiconductors, we use the Kondo-lattice model. The magnetic phase diagram is derived by inspecting the static susceptibility of itinerant band electrons, which are exchange coupled to localized magnetic moments. It turns out that rather low band occupations favor a ferromagnetic ordering of the local moment systems due to an indirect coupling mediated by a spin polarization of the itinerant charge carriers. The disorder in diluted systems is treated by adding a CPA-type concept to the theory. For almost all moment concentrations $x$, ferromagnetism is possible, however, only for carrier concentrations $n$ distinctly smaller than $x$. The charge carrier compensation in real magnetic semiconductors (in ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ by, e.g., antisites) seems to be a necessary condition for getting carrier induced ferromagnetism.