s−fmodel in magnetic semiconductors

In the $s-f$ model electrons in the conduction band are coupled with the lattice of localized magnetic moments by exchange interaction. In this paper the influence of the exchange interaction on electron bands and electrical resistivity is studied. An intermediate-coupling theory is presented, valid up to the region where the level broadening exceeds the average thermal energy but is small compared to the bandwidth. Using the functional-derivative method the spin correlations are expressed in terms of the connected correlation functions. The functional-derivative method also provides a decoupling recipe for the electron Green's functions. Concentrating on the two-spin correlations the single-particle Green's function is derived by a decoupling method and is shown to be equivalent to a perturbation expansion. The finite lifetime is obtained for all band energies. The absorption edge, derived from density of states, shows in ferromagnetic semiconductors the familiar red shift and in addition a blue shift of magnetic origin in the paramagnetic region. Mobility is derived from the two-particle Green's function calculated by a decoupling method. Level broadening affects both the acceleration and the scattering part, resulting generally in smaller mobilities than predicted by the weak-coupling theory. In addition, corrections to the ordinary acceleration term are obtained. Results for the ferromagnetic semiconductors EuS and EuO are presented. The narrow mobility minimum occurring at $T_C$ in the weak-coupling case is considerably broadened in temperature. The minimum mobilities are around 3 ${\mathrm{cm}}^2$/Vsec in both materials. The low mobility near $T_C$ is partly caused by the intense scattering and partly by the decrease in the acceleration term. The results compare reasonably well with experiments.