Spin wave spectra in doped ferromagnetic semiconductors

Abstract

We present a theory of the magnetic excitation spectrum of ferromagnetic semiconductors and semimetals. The calculations are performed up to second order in the exchange coupling between the localized spin array Si and the free carrier spin density s(ri), using the functional differentiation technique and Green functions. A high frequency spin wave mode is found, in addition to the usual low frequency spin wave branch. The damping of both modes is found to be small at low temperatures when the free carriers are spin polarized, in which case the bottleneck limit is applicable. At high temperature where 〈sz〉→0, the spin dynamics is described by the Hasegawa equations and the Korringa relaxation term which governs the width of the magnetic resonance is recovered.