Non-Lifshitz invariants corrections to Dzyaloshinskii-Moriya interaction energy

Abstract

We study the continuum limit of two-dimensional chiral magnets in which Dzyaloshinskii-Moriya interaction (DMI) is due to the interplay between a smooth magnetic texture and spin-orbit coupling. The resulting free-energy density of the system contains linear terms in the spatial gradient of the magnetic texture, which mark an instability of the system towards the formation of nontrivial magnetic orders such as skyrmions or chiral domain walls. We perform a microscopic analysis of DMI tensors responsible for this contribution to free energy based on a Berry phase formulation in the mixed space of momentum and position, and reveal that they exhibit non-Lifshitz invariants features. In particular, a perturbation theory shows in the case of Rashba spin-orbit interactions the presence of non-Lifshitz invariants to third order in the small spin-orbit interaction and fourth order in the small exchange coupling. The higher-order terms may even lead to an enhancement of DMI interaction at strong spin-orbit coupling due to divergences in the density of states at the bottom of the conduction band. Finally, we also study the DMI free energy generated from Rashba spin-orbit interaction in different symmetry groups.

arXiv comment17 pages, 2 figures

References in corpus (33)

• Skyrmion Lattice in a Chiral Magnet
• Spontaneous Skyrmion Ground States in Magnetic Metals
• Current-driven dynamics of chiral ferromagnetic domain walls
• Blowing Magnetic Skyrmion Bubbles
• Spin Transfer Torques in MnSi at Ultra-low Current Densities
• Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films
• Emergent Phenomena Induced by Spin-Orbit Coupling at Surfaces and Interfaces
• Interface-Induced Phenomena in Magnetism
• Model Hamiltonian for Topological Insulators
• Current-induced skyrmion dynamics in constricted geometries
• Hexagonal Warping Effects in the Surface States of Topological Insulator Bi${}_2$Te${}_3$
• Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles
• Berry phase correction to electron density of states in solids
• Electric field driven switching of individual magnetic skyrmions
• Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure
• The skyrmion switch: turning magnetic skyrmion bubbles on and off with an electric field
• Physical foundations and basic properties of magnetic skyrmions
• Twisted exchange interaction between localized spins embedded in a one- or two-dimensional electron gas with Rashba spin-orbit coupling
• Laser-Induced Skyrmion Writing and Erasing in an Ultrafast Cryo-Lorentz Transmission Electron Microscopy
• Long-range crystalline nature of the skyrmion lattice in MnSi
• Cubic Rashba spin-orbit interaction of two-dimensional hole gas in strained-Ge/SiGe quantum well
• Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques
• Phase-Space Berry Phases in Chiral Magnets: Dzyaloshinskii-Moriya Interaction and the Charge of Skyrmions
• The chiral biquadratic pair interaction
• Domain wall of a ferromagnet on a three-dimensional topological insulator
• Asymmetric and symmetric exchange in a generalized 2D Rashba ferromagnet
• Spin and Orbital Magnetic Response on the Surface of a Topological Insulator
• Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry
• Chiral ferromagnetism beyond Lifshitz invariants
• Symmetry and topology of two-dimensional noncentrosymmetric superconductors
• Non-collinear ground state from a four-spin chiral exchange in a tetrahedral magnet
• Antichiral Ferromagnetism
• Quartic asymmetric exchange for two-dimensional ferromagnets with trigonal prismatic symmetry