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

TL;DR

This paper investigates carrier-mediated ferromagnetism in dilute magnetic semiconductors using advanced theoretical models, revealing optimal doping conditions, the impact of impurity disorder, and the stability of ferromagnetic states.

Contribution

It introduces a generalized RKKY approach beyond linear response and a mean-field-plus-spin-fluctuation method within a Hubbard model to analyze ferromagnetism in dilute magnetic semiconductors.

Findings

Ferromagnetic transition temperature matches experimental values.

Impurity disorder stiffens high-energy magnon modes.

Competing antiferromagnetic interactions lead to noncollinear ordering.

Abstract

Carrier-mediated ferromagnetism in a dilute magnetic semiconductor has been studied using i) a single-impurity based generalized RKKY approach which goes beyond linear response theory, and ii) a mean-field-plus-spin-fluctuation (MF+SF) 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 magnon modes. We also explicitly study the stability/instability of the mean-field ferromagnetic state, which highlights the role of competing AF interactions causing spin twisting and noncollinear ferromagnetic ordering.