Crystal Structure and Dzyaloshinski–Moriya Micromagnetics

Abstract

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.

Gauge theory applied to magnetic lattices

“…( 24) automatically implies that all centrosymmetric crystallographic point groups exclude the possibility to have DMI. Furthermore, we notice how the above-discussed method also correctly predicts the absence of DMI on some non-centrosymmetric crystal systems such as T d , C 3h , D 3h in accordance with the literature [19]. We can now proceed and discuss three examples of a non-vanishing DMI tensor.…”

“…On a micromagnetic level, the traditional approach relies on phenomenological thermodynamic arguments and spin wave expansions of the micromagnetic energy functional [16][17][18], but disregards the underlying Heisenberg model in favor of a pure field (a) E-mail: g.durin@inrim.it (corresponding author) theoretical approach. The generalized expression of the micromagnetic energy functional that one finds in the literature is [5,19,20] E ex [m, ∇m] = ΩV {A | ∇m | 2 + QM(m)}d 3 r, (1) where QM(m) = A,C QAC M AC constitutes the DMI energy of the system [21] and is represented as the contraction of the DMI tensor QAC and the chirality M(m) = ∇m × m of the material. The above-mentioned approaches, while extremely powerful, are phenomenological in nature and neglect the fact that higher order interactions are intimately related to lower order ones as they come from the low energy limit of a more general energy functional [10].…”

Comparative study of topological Hall effect and skyrmions in NiMnIn and NiMnGa

“…Point-group analysis clarifies the situation and outlines the occurrence of crystal-specific spin structures. 17,18 For example, some compounds with noncentrosymmetric point groups, such as inverse cubic Heusler and half-Heusler compounds, do not support DM interactions. 17 Our focus is on a specific aspect of this relationship, namely, on the distinction between cubic and noncubic crystal structures.…”

Possible Topological Hall Effect in a Spin Gapless Semiconducting Mn2CoAl Heusler Compound

“…[ 47 ] Although the Mn 2 CoAl compound is non‐centrosymmetric (space group F3m) but the space group does not support bulk DMI (similar to the centrosymmetric magnets) as per the reported analysis on the point group dependency of micromagnetic DMI. [ 48 ] Interestingly, the literature suggests a strong magnetic frustration due to the presence of both ferro‐ and antiferromagnetic‐type Heisenberg exchange interaction along with the disorder in the Mn 2 CoAl compound. [ 49–51 ] Therefore, the competition between the cubic MCA, which is expected in the cubic crystal systems, [ 42 ] and the Heisenberg exchange interactions may create the noncoplanar spin texture.…”