Ferromagnetism and spin waves in diluted magnetic semiconductors

We present a theory of carrier-induced ferromagnetism in diluted magnetic semiconductors (III,Mn)V which allows for arbitrary itinerant-carrier spin polarization and dynamic correlations. Both ingredients, which are absent in an RKKY description, are essential in identifying the systemʹs elementary excitations and describing their properties. We find a branch of gapped collective modes, in addition to the spin waves and Stoner continuum which occur in metallic ferromagnets. We determine the low-temperature spin stiffness and derive, in different regimes, its dependence on the exchange coupling between magnetic ions and free carriers, as well as on the effective band mass.