Ferromagnetism in a dilute magnetic semiconductor: Generalized RKKY interaction and spin-wave excitations

Carrier-mediated ferromagnetism in a dilute magnetic semiconductor has been studied using (i) a single-impurity based generalized Ruderman-Kittel-Kasuya-Yosida (RKKY) approach which goes beyond linear response theory, and (ii) a mean-field-plus-spin-fluctuation approach within a (purely fermionic) Hubbard-model representation of the magnetic impurities, which incorporates dynamical effects associated with finite frequency spin correlations in the ordered state. Due to a competition between the magnitude of the carrier spin polarization and its oscillation length scale, the ferromagnetic spin coupling is found to be optimized with respect to both hole doping concentration and impurity-carrier spin coupling energy J (or equivalently U). The ferromagnetic transition temperature T_c, deteremined within the spin-fluctuation theory, corresponds closely with the observed T_c values. Positional disorder of magnetic impurities causes significant stiffening of the high-energy spin-wave modes. We also explicitly study the stability/instability of the mean-field ferromagnetic state, which highlights the role of competing antiferromagnetic interactions causing spin twisting and noncollinear ferromagnetic ordering.