Spin waves in degenerate ferromagnetic semiconductors at low temperatures

The s-d(f) exchange model of a ferromagnetic semiconductor is considered. With the use of the perturbation expansion in the formal parameter (2 S)^-1, S being the magnitude of magnetic ion spin, the magnon Green function is calculated. The spectrum and damping of spin waves in the presence of conduction electrons is investigated. It is demonstrated that the change of sign of the temperature dependent correction to the spin-wave stiffness is possible provided that the Fermi energy exceeds some critical value. This may lead to the increase of the spin-wave stiffness with temperature unlike the case of the Heisenberg ferromagnet. The estimations of this effect for doped EuO and EuS are carried out.