Effects of the spin-orbit interaction in Heusler compounds: Electronic structures and Fermi surfaces of NiMnSb and PtMnSb

Electronic structures of the Heusler compounds, NiMnSb and PtMnSb, are investigated by using the linearized-muffin-tin-orbital band method. Equilibrium properties such as lattice constants and bulk moduli are obtained from total energy calculations and effects of the spin-orbit interaction on electronic structures and Fermi surfaces are explored. In the semirelativistic band calculations, NiMnSb is half-metallic, i.e., metallic for majority spin while semiconducting for minority spin bands, but PtMnSb is normal metallic at the experimental lattice constant. PtMnSb becomes a half metal if we take into account the spin-orbit interaction explicitly in the calculation. Equilibrium lattice constants obtained in the ferromagnetic band calculations agree very well with experimental values. The magnitudes of the energy gap in the minority spin bands are found to be sensitive to the variation of the lattice constants for NiMnSb and PtMnSb. The effect of the spin-orbit interaction is substantial in PtMnSb, in contrast to NiMnSb in which it is negligible. A large spin-orbit splitting at Γ in PtMnSb is due to Pt 6p states near ${\mathit{E}}_{\mathit{F}}$, which may be involved in optical transitions to generate a large magneto-optical Kerr effect. Further, the itinerant electrons that mediate the Ruderman-Kittel-Kasuya-Yosida interaction between Mn magnetic moments in NiMnSb and PtMnSb are identified as those on the nearly spherical hole Fermi surfaces of the 12th majority spin bands centered at Γ.