Conduction-electron states in ferromagnetic semiconductors above the Curie temperature.

Abstract

Theoretical studies on the states of conduction electrons in ferromagnetic semiconductors have been made above the Curie temperature (${\mathit{T}}_{\mathit{C}}$). The conduction electron states are strongly affected by the magnetic ordering of localized moments (f spins), the direction of which is completely random in the high-temperature limit and is strongly correlated between different sites around ${\mathit{T}}_{\mathit{C}}$. We take the self-energy diagram with an electron propagator to second order in the exchange interaction between the conduction electron and f spins, together with the static two-spin correlation function, to calculate the density of states and the self-energy \ensuremath{\Sigma}(k,\ensuremath{\omega}) for the conduction electron by the Green's function technique, where the k dependence of the self-energy is directly taken into account. The effect of the sum rule for a spin-correlation function is also considered. Comparing the results of the present theory and those obtained with the coherent-potential approximation, it is revealed that the present method is suitable for (IS/W)\ensuremath{\lesssim}0.1, where W is the bandwidth of the conduction band, and the product IS is the exchange interaction energy. As the temperature approaches ${\mathit{T}}_{\mathit{C}}$, the bottom of the conduction band in the paramagnetic region is lowered due to the exchange scattering which depends on the f-spin correlation between different sites. The effect of the sum rule for the spin-spin corelation function reduces the lowering of the bottom of the band, especially at T=${\mathit{T}}_{\mathit{C}}$. The result compares reasonably well with the temperature dependence of the absorption edge of EuO reported by Schoenes and Wachter [Phys. Rev. B 7, 3097 (1974)]. The present results are also compared with the results reported by Sinkkonen [Phys. Rev. B 19, 6407 (1979)].