Intrinsic spin currents in bulk noncentrosymmetric ferromagnets

Intrinsic spin currents are encountered in noncentrosymmetric crystals without any external electric fields; these currents are caused by spin–orbit interaction. In this paper, various theoretical aspects of this phenomenon in bulk ferromagnets are studied by using group theory, perturbation expansion, and calculations for model and real systems. The group-theoretical analysis of the spin-current tensor shows that the absence of space-inversion symmetry is not a sufficient condition for appearance of the intrinsic spin currents. The perturbation expansion proves that in the regime of exchange splitting dominating over spin–orbit interaction, the spin polarization of the intrinsic currents is nearly perpendicular to the direction of magnetization. First-principles calculations are carried out for NiMnSb and CoMnFeSi ferromagnetic compounds, both featured by a tetrahedral crystallographic point group. The dependence of the spin-current tensor on the direction of magnetization is approximated by a simple quadratic formula containing two constants; the relative error of this approximation is found as small as a few percent for both compounds.