Curvature effects in statics and dynamics of low dimensional magnets

Abstract

We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature induces two effective magnetic interactions: effective magnetic anisotropy and effective Dzyaloshinskii-like interaction. We derive an equation of magnetisation dynamics and propose a general static solution for the limit case of strong anisotropy. To illustrate our approach we consider the magnetisation structure in a ring wire and a cone surface: ground states in both systems essentially depend on the curvature excluding strictly tangential solutions even in the case of strong anisotropy. We derive also the spectrum of spin waves in such systems.

LaTeX, 17 pages, 3 figures

References in corpus (5)

• Two-Dimensional Matter: Order, Curvature and Defects
• Magnetochiral symmetry breaking in a Möbius ring
• Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry
• Domain-wall structure of a classical Heisenberg ferromagnet on a Mobius strip
• Stability of magnetic nanowires against spin-polarized current

Cited by in corpus (27)

• Magnetochiral symmetry breaking in a Möbius ring
• Curved Magnetism in CrI${}_3$
• Oscillatory behavior of the domain wall dynamics in a curved cylindrical magnetic nanowire
• The effect of curvature on the eigenexcitations of magnetic skyrmions
• Curvature induced drift and deformation of magnetic skyrmions: comparison of ferro- and antiferromagnetic cases
• Micromagnetic modelling of magnetic domain walls in curved cylindrical nanotubes and nanowires
• Curvature-driven homogeneous Dzyaloshinskii-Moriya interaction and emergent weak ferromagnetism in anisotropic antiferromagnetic spin chains
• Curvature control of the superconducting proximity effect in diffusive ferromagnetic nanowires
• Curvature-induced long ranged supercurrents in diffusive SFS Josephson Junctions, with dynamic $0-\pi$ transition
• Control of magnetic response in curved stripes by tailoring cross-section
• Curvilinear manipulation of polarized spin wave
• Curvature induced magnetization of altermagnetic films
• Manipulation by magnetic frustration in ferrotoroidal spin chains via curvature and torsion
• Dynamics of domain walls in curved antiferromagnetic wires
• Non-constant geometric curvature for tailored spin-orbit coupling and chirality in superconductor-magnet heterostructures
• Chiral breakdown engineered by mesoscale Dzyaloshinskii-Moriya interaction in biaxial magnetic nanotubes
• Electrical control of superconducting spin valves using ferromagnetic helices
• Field-induced spin reorientation transitions in antiferromagnetic ring-shaped spin chains
• Exploration of magnetoelastic deformations in spin-chain compound CuBr${}_2$
• Spin-orbit torque driven motion of chiral domain walls induced by radial magnetization in nanotube geometry
• Magnetoelectricity of Topological Solitons in 2D Magnets
• Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study
• Topology-induced symmetry breaking demonstrated in antiferromagnetic magnons on a Möbius strip
• Mode splitting of spin waves in magnetic nanotubes with discrete symmetries
• Observation of compact ferrimagnetic skyrmions in DyCo${}_3$ film
• Torsion-induced Dzyaloshinskii-Moriya interaction in helical magnets
• Impact of curvature-induced Dzyaloshinskii-Moriya interaction on magnetic vortex texture in spherical caps