s-f Scattering in ferromagnetic semiconductors at low temperatures

The states of current carriers in ferromagnetic semiconductors in the spin-wave region are constructed, the ratio of s-f exchange parameter to the bandwidth being an arbitrary quantity. These states are close to the true eigenstates of the s-f exchange model Hamiltonian. The transition probabilities between the states both due to the nonsecular part of the s-f Hamiltonian and the interaction with defects are calculated. The temperature dependence of the electron spectrum and the electron contribution to the magnon frequency are found. It is shown that the effective Hamiltonian describing the interaction between the true carriers and the magnons may be introduced, the effective interaction vanishing when the electron and magnon momenta become zero. It is demonstrated that the magnetoresistance due to scattering by charged impurities may be appreciable when the renormalization of electron states is taken into account.