The conduction-electron state in a ferromagnetic semiconductor is studied theoretically by applying the coherent-potential approximation to the s-f model. In order to consider multiple scattering at ferromagnetic temperatures, we first derive the t-matrix elements of the s-f exchange interaction for a single f spin embedded in the effective medium, where a conduction electron is subjected to complex potential, ${\mathrm{\Sigma }}_{\mathrm{\uparrow }}$ or ${\mathrm{\Sigma }}_{\mathrm{\downarrow }}$, according to the orientation of its spin. Using the mean-field theory for fluctuating f spins, the variation of the density of states with temperature is investigated for various values of IS/W. Here IS is the exchange interaction energy and W is the bandwidth of the conduction band. The anomalous redshift of the optical-absorption edge and the temperature dependence of the electron-spin polarization, experimentally observed in EuO and EuS, can be explained consistently within this approximation. © 1996 The American Physical Society.

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