Carrier induced ferromagnetism in diluted local-moment systems
  The electronic and magnetic properties of concentrated and diluted ferromagnetic semiconductors are investigated by using the Kondo lattice model, which describes an interband exchange coupling between itinerant conduction electrons and localized magnetic moments. In our calculations, the electronic problem and the local magnetic problem are solved separately. For the electronic part an interpolating self-energy approach together with a coherent potential approximation (CPA) treatment of a dynamical alloy analogy is used to calculate temperature-dependent quasiparticle densities of states and the electronic self-energy of the diluted local-moment system. For constructing the magnetic phase diagram we use a modified RKKY theory by mapping the interband exchange to an effective Heisenberg model. The exchange integrals appear as functionals of the diluted electronic self-energy being therefore temperature- and carrier-concentration-dependent and covering RKKY as well as double exchange behavior. The disorder of the localized moments in the effective Heisenberg model is solved by a generalized locator CPA approach. The main results are: 1) extremely low carrier concentrations are sufficient to induce ferromagnetism; 2) the Curie temperature exhibits a strikingly non-monotonic behavior as a function of carrier concentration with a distinct maximum; 3) $T_C$ curves break down at critical $n/x$ due to antiferromagnetic correlations and 4) the dilution always lowers $T_C$ but broadens the ferromagnetic region with respect to carrier concentration. 
Guixin Tang and Wolfgang Nolting