Critical behavior of the band gap in ferromagnetic semiconductors

Abstract
The shift of the band gap in ferromagnetic semiconductors due to magnetization and critical fluctuations is determined in detail using recent results of the theory of critical phenomena. The band shift ΔE is expressed in terms of the reduced magnetic field h and the reduced temperature t. The dominant contributions to ΔE are found to be the following: In the critical region, both above and below the critical temperture T c , ΔE∝−h 1/δ−B h 1−α)/βδ for large h. For small h, ΔE∝ (−‖t‖β−b 0‖t‖1−α) for T<T c and ΔE∝−1.7t −γ h+B 0 t 1−α for T≳T c . Outside the critical region, below T c , ΔE∝ (−‖t‖1/2) for small h and ΔE∝−h 1/3 for large h; above T c , ΔE∝−h/t+B 0 t 1/2 for small h and ΔE∝−h 1/3+B 0 h 1/3 for large h. Here α, β and δ are the usual critical exponents and B 0?1.