Self-consistent electronic structures of magnetic semiconductors by a discrete variationalXαcalculation. II. HgCr2Se4

Abstract

The electronic band structure of a ferromagnetic semiconducting spinel Hg${\mathrm{Cr}}_{2}$${\mathrm{Se}}_{4}$ is self-consistently calculated by using the discrete variational $X\ensuremath{\alpha}$ method. The overall features of the band structure are quite similar to those of Cd${\mathrm{Cr}}_{2}$${\mathrm{S}}_{4}$ and Cd${\mathrm{Cr}}_{2}$${\mathrm{Se}}_{4}$ which have been calculated in the first paper of this series [T. Oguchi, T. Kambara, and K.I. Gondaira, Phys. Rev. B 22, 872 (1980)]. The fundamental energy gap is 1.8 eV, somewhat narrower than those of the Cd compounds. The narrowest band gap appears between the $d\ensuremath{\epsilon}$ and $d\ensuremath{\gamma}$ bands, and its width is 0.4 eV, much smaller than those of the Cd compounds. The top of the valence bands has the ${\ensuremath{\Sigma}}_{4}$ symmetry and the bottom of the conduction bands ${\ensuremath{\Gamma}}_{1}$. The spin polarization of the $3d$ orbitals of Cr is about 3.5, of which 0.5 comes from the $3d$ components mixed in the valence bands, while the spin polarization of the $4p$ orbitals of Se has the opposite sign, the magnitude of which is about 0.3.