Self-consistent electronic structures of magnetic semiconductors by a discrete variationalXαcalculation. I. Ferromagnetic spinels, CdCr2S4and CdCr2Se4

Abstract

The electronic band structures of ferromagnetic Cd${\mathrm{Cr}}_{2}$${\mathrm{S}}_{4}$ and Cd${\mathrm{Cr}}_{2}$${\mathrm{Se}}_{4}$ are self-consistently calculated by using the discrete variational $X\ensuremath{\alpha}$ method. The general features of the band structures are quite similar between sulfide and selenide; each structure consists of relatively narrow valence bands, fairly wide conduction bands, and very narrow $d$ bands. The $3d\ensuremath{\epsilon}$ and $3d\ensuremath{\gamma}$ bands for up spin lie in the energy region near the top of the valence bands and around the bottom of the lowest conduction band, respectively, and both $d$ bands for down spin fall in the conduction bands. The maximum point of the valence bands has ${\ensuremath{\Sigma}}_{4}$ symmetry for both compounds, and the minimum point of the conduction band has ${\ensuremath{\Lambda}}_{1}$ for sulfide and ${\ensuremath{\Gamma}}_{1}$ for selenide. The fundamental energy gap at the $\ensuremath{\Gamma}$ point is 2.6 eV for sulfide and 2.3 eV for selenide. The spin polarization of the $3d$ orbitals of Cr is about 3.5, in which 0.5 comes from the $3d\ensuremath{\gamma}$ components mixed with the valence bands, while the spin polarization of the outermost $p$ orbitals of chalcogen ion has the opposite sign, the magnitude of which is about 0.3.