Conduction-band structure of a ferromagnetic semiconductor

We use the s-f model to investigate the energy spectrum, the spectral weights, and the lifetimes of the electronic quasiparticles in a ferromagnetic semiconductor. Starting from two-pole Gaussian Ans\"atze for a complete set of relevant spectral densities and fitting free parameters by exactly calculable spectral moments of these functions, we find a result which reproduces all exactly solvable limiting cases of the s-f model. It is shown that the conduction band splits into several quasiparticle subbands as a consequence of the s-f exchange interaction between conduction electrons and localized magnetic moments. This splitting takes place in principle for all temperatures, i.e., it is not at all due to the onset of ferromagnetism. The spectacular red shifts of the optical absorption edge, observed for EuO, EuS, and EuSe, are almost qualitatively explained by a broadening of the lowest {↑} subband with decreasing temperature.