Crystal Structure and Dzyaloshinski–Moriya Micromagnetics

The relationship between atomic-scale and micromagnetic Dzyaloshinski-Moriya (DM) interactions has been investigated. By analyzing the Lifshitz invariants for different point groups, we have found that there is no unique link between the absence of inversion symmetry and DM interactions. The absence of inversion symmetry is a necessary condition for a net DM interaction in crystals, but several noncentrosymmetric point groups have zero DM interactions. In many cases, the key consideration is whether the crystals are polar and/or chiral. For example, MnSi-type spin spirals, which violate helical spin symmetry, are caused by the insertion of chiral atomic-scale building blocks into an achiral cubic lattice, and the scalar interaction parameter D used to describe the spirals is only loosely related to the DM vector D. It contains, in fact, magnetostatic and magnetocrystalline contributions of unknown magnitude. Finally, we discuss some aspects of the micromagnetism of the skyrmionics of nanoparticles and granular nanostructures.