CONDUCTION-ELECTRON STATES IN FERROMAGNETIC SEMICONDUCTORS ABOVE THE CURIE-TEMPERATURE

Theoretical studies on the states of conduction electrons in ferromagn etic semiconductors have been made above the Curie temperature (T(C)). The conduction electron states are strongly affected by the magnetic ordering of localized moments (f spins), the direction of which is com pletely random in the high-temperature limit and is strongly correlate d between different sites around T(C). We take the self-energy diagram with an electron propagator to second order in the exchange interacti on between the conduction electron and f spins, together with the stat ic two-spin correlation function, to calculate the density of states a nd the self-energy SIGMA(k,omega) for the conduction electron by the G reen's function technique, where the k dependence of the self-energy i s directly taken into account. The effect of the sum rule for a spin-c orrelation function is also considered. Comparing the results of the p resent theory and those obtained with the coherent-potential approxima tion, it is revealed that the present method is suitable for (IS/W) le ss than or similar to 0.1, where W is the bandwidth of the conduction band, and the product IS is the exchange interaction energy. As the te mperature approaches T(C), the bottom of the conduction band in the pa ramagnetic region is lowered due to the exchange scattering which depe nds on the f-spin correlation between different sites. The effect of t he sum rule for the spin-spin correlation function reduces the lowerin g of the bottom of the band, especially at T = T(C). The result compar es reasonably well with the temperature dependence of the absorption e dge of EuO reported by Schoenes and Wachter [Phys. Rev. B 7, 3097 (197 4)]. The present results are also compared with the results reported b y Sinkkonen [Phys. Rev. B 19, 6407 (1979)].