Self-consistent electronic structures of magnetic semiconductors by a discrete variationalXαcalculation. III. Chalcopyrite CuFeS2

The electronic band structure of chalcopyrite CuFe${\mathrm{S}}_2$ in the antiferromagnetic phase is calculated by spin-polarized self-consistent-charge discrete-variational $X\alpha$ method. The valence bands consist of many rather narrow bands constructed from S $3p$, Cu $3d$, and majority-spin Fe $3d$ orbitals. The upper valence bands are constituted mainly of Cu $3d$ and Fe $3d$ orbitals. The top of the valence band is at the $X$ point. The conduction bands composed mainly of $4s$ and $4p$ orbitals of Cu and Fe have the bottom at the $\Gamma$ point and the direct gap is 3.1 eV. The narrow bands composed mainly of minority-spin Fe $3d$ orbitals are in the so-called fundamental gap. The direct minimum gap of these $d$ bands is 0.7 eV at the $X$ point. These gap energies are in good agreement with the observed optical spectra. The minimum gap of the minority-spin $d$ bands is indirect and about 0.3 eV. The magnetic moment of an Fe ion is $3.88{\mu }_B$, which agrees with the observed value.