First-Principles Evaluation of the Dzyaloshinskii–Moriya Interaction

Abstract

We review recent developments of formulations to calculate the Dzyaloshinskii-Moriya (DM) interaction from first principles. In particular, we focus on three approaches. The first one evaluates the energy change due to the spin twisting by directly calculating the helical spin structure. The second one employs the spin gauge field technique to perform the derivative expansion with respect to the magnetic moment. This gives a clear picture that the DM interaction can be represented as the spin current in the equilibrium within the first order of the spin-orbit couplings. The third one is the perturbation expansion with respect to the exchange couplings and can be understood as the extension of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction to the noncentrosymmetric spin-orbit systems. By calculating the DM interaction for the typical chiral ferromagnets Mn 1−x Fe x Ge and Fe 1−x Co x Ge, we discuss how these approaches work in actual systems.

Ab initio analysis of magnetic properties of the prototype B20 chiral magnet FeGe

“…For instance, theoretical predictions for the spiralization in FeGe yield D = −4.5 meVÅ 39 and D = −6.5 meVÅ 34 based on the dispersion of spin spirals, whereas a relativistic multiple-scattering framework provides a value of D = −9.0 meVÅ 40 . Moreover, representing the spiralization by intrinsic spin currents leads to D = −7.0 meVÅ 41 , and theoretical studies focusing on the spin susceptibility report the two distinct values D = −10.1 meVÅ 42 and D = −1.0 meVÅ 43 . This large variation of the spiralization in FeGe is complemented by electronic-structure works that provide the values A = 700 meVÅ 243 and A = 855 meVÅ 244 for the spin stiffness, using the energy relation of non-collinear magnetic states or an approach based on Green's functions.…”

Complex magnetism of B20-MnGe: from spin-spirals, hedgehogs to monopoles

“…Informed by the canonical micromag-netic theory, most attention has focused on the D parameter. An approach by Koretsune et al based on taking the limit of the static non-uniform spin susceptibility constructed from a Wannier representation resulted in the value D = 107 meVÅ 38 , with a revised value of D ≈ 27 meVÅ computed by the same method being reported in a recent review 39 . Different approaches, based on the DFT energies of spin spirals or a different derivation of the spiralization tensor, resulted in the values D = 1.2 meVÅ 42 , D ≈ −1.8 meVÅ 43 , and D ≈ 1 meVÅ 40,41 .…”

Data-driven design of B20 alloys with targeted magnetic properties guided by machine learning and density functional theory

“…Alloy design using computational methods have not attracted a lot of attention. Most of the computational efforts that involve density functional theory (DFT) calculations have focused on either providing an explanation of the observed properties from the viewpoint of the band theory or extracting properties such as the strength of the DM term as a function of alloy substitutions and epitaxial strain [14,15,16,17,18,19,20,21,22]. In this work, a novel computational approach, built on the foundations of machine learning (ML) and DFT, is developed to accelerate the design of B20-based chiral magnets with improved T C .…”