Chromium-based diluted magnetic semiconductors

The Zeeman splitting of the valence band of a cubic Cr-based diluted magnetic semiconductor is studied within an effective Hamiltonian for the hybridization-induced hole-ion interaction that includes orbital coupling terms. The static Jahn-Teller distortion tends to quench the orbital contribution. The subband ordering is the same as in the Kondo-like spin-exchange model, but the overall splitting is reduced. We also compute the magnetization. Comparison with recently published magnetoreflectance and magnetization data in ${\mathrm{Zn}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Cr}}_{\mathit{x}}$Se shows excellent agreement. The anomalous sign (ferromagnetic) of the effective p-d exchange is explained.