Point-Group Dependence of Dzyaloshinski-Moriya Micromagnetics*

The micromagnetic realization of Dzyaloshinski-Moriya interactions (DMI) is investigated, with particular reference to spin spirals and skyrmions in crystals with cubic symmetry. The analysis starts with a group-theoretical analysis and explains the micromagnetism by a magnetic gyration tensor that is loosely related to the vector D of the DMI. In contrast to conventional wisdom, the DM free-energy term D M.(▽×M) is not caused by broken inversion symmetry but reflects the presence of chiral building blocks (motifs) in the crystal structure. The scalar D includes not only DMI but also magnetocrystalline and magnetostatic contributions. In micromagnetic calculations, this D should never be used for noncubic structures, such as uniaxial tetragonal, rhombohedral, and hexagonal crystals. Furthermore, D = 0 for the cubic point groups T_h, O_h, and T_d, which include half- and inverse Heusler alloys (T_d), in spite of their broken inversion symmetry and nonzero atomic-scale DMI. The theoretical findings are used to discuss skyrmions in a range of related alloys: MnNiGa and MnNiSn, which crystallize in the centrosymmetric hexagonal Ni₂In structure (point group D_6h), and Heusler-type cubic compounds MnNiIn and MnNiAl.