The electronic band structure of a ferromagnetic semiconducting spinel Hg${\mathrm{Cr}}_2$${\mathrm{Se}}_4$ is self-consistently calculated by using the discrete variational $X\alpha$ method. The overall features of the band structure are quite similar to those of Cd${\mathrm{Cr}}_2$${\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 $d\epsilon$ and $d\gamma$ bands, and its width is 0.4 eV, much smaller than those of the Cd compounds. The top of the valence bands has the ${\Sigma }_4$ symmetry and the bottom of the conduction bands ${\Gamma }_1$. 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.

• Received 9 December 1980

DOI:https://doi.org/10.1103/PhysRevB.24.3441