Chiral ferromagnetism beyond Lifshitz invariants

Abstract

We consider a contribution $w_{\text{ch}}$ to the micromagnetic energy density that is linear with respect to the first spatial derivatives of the local magnetization direction. For a generalized 2D Rashba ferromagnet, we present a microscopic analysis of this contribution and, in particular, demonstrate that it cannot be expressed through Lifshitz invariants beyond the linear order in the spin-orbit coupling (SOC) strength. Terms in $w_{\text{ch}}$ beyond Lifshitz invariants emerge as a result of spin rotation symmetry breaking caused by SOC. Effects of these terms on the phase diagram of magnetic states and spin-wave dispersion are discussed. Finally, we present a classification of terms in $w_{\text{ch}}$, allowed by symmetry, for each crystallographic point group.

arXiv comment6 pages, 2 figures + 4 page supplementary information

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Cited by in corpus (10)

• Control of magnetic states and spin interactions in bilayer CrCl${}_3$ with strain and electric fields: an ab initio study
• First Principles Calculation of Dzyaloshinskii-Moriya Interaction: A Green's function Approach
• Current-Induced Dynamics of Chiral Magnetic Structures: Creation, Motion, and Applications
• Antichiral Ferromagnetism
• Non-collinear ground state from a four-spin chiral exchange in a tetrahedral magnet
• Quartic asymmetric exchange for two-dimensional ferromagnets with trigonal prismatic symmetry
• Light-induced Dzyaloshinskii-Moriya interactions in antiferromagnetic metals
• Signatures of quartic asymmetric exchange in a class of two dimensional magnets
• Field-direction-dependent skyrmion crystals in noncentrosymmetric cubic magnets: A comparison between point groups $(O,T)$ and $T_{\mathrm{d}}$
• Non-Lifshitz invariants corrections to Dzyaloshinskii-Moriya interaction energy