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.

arXiv commentinvited review paper

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• Controlling the helicity of magnetic skyrmions in a $\beta$-Mn-type high-temperature chiral magnet
• Ab initio analysis of magnetic properties of prototype B20 chiral magnet FeGe
• Short period magnetization texture of B20-MnGe explained by thermally fluctuating local moments
• Ab initio exploration of short-pitch skyrmion materials: Role of orbital frustration
• Critical metrology of minimally accessible anisotropic spin chains
• Tuning skyrmion Hall effect via engineering of spin-orbit interaction
• Complex magnetism of B20-MnGe: from spin-spirals, hedgehogs to monopoles
• Skyrmion instabilities and distorted spiral states in a frustrated chiral magnet
• Onset of a skyrmion phase by chemical substitution in MnGe chiral magnet
• Theory of chiral effects in magnetic textures with spin-orbit coupling
• Dominant orbital magnetization in the prototypical altermagnet MnTe
• Impurity-induced orbital magnetization in a Rashba electron gas
• Theoretical study on stabilization and destabilization of magnetic skyrmions by uniaxial-strain-induced anisotropic Dzyaloshinskii--Moriya interactions
• Dzyaloshinskii-Moriya interaction in strongly spin-orbit-coupled systems: General formula and application to topological and Rashba materials
• Direct observations of spin fluctuations in spin-hedgehog-anti-hedgehog lattice states in MnSi${}_{1-x}$Ge${}_x$ ($x=0.6$ and $0.8$) at zero magnetic field
• Dzyaloshinskii-Moriya spin density by skew scattering
• Dzyaloshinskii-Moriya Interaction between Multipolar Moments in $5d^1$ Systems
• Modulated phases in a spin model with Dzyaloshinskii-Moriya interactions
• Optical responses induced by spin gauge field at the second order
• General spin models from noncollinear spin density functional theory and spin-cluster expansion