Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry

Abstract

We study the nonlinear $\sigma$-model in an external magnetic field applied on curved surfaces with rotational symmetry. The Euler-Lagrange equations derived from the Hamiltonian yield the double sine-Gordon equation (DSG) provided the magnetic field is tuned with the curvature of the surface. A $2\pi$ skyrmion appears like a solution for this model and surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. We also study some specific examples by applying the model on three rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. The coupling between a magnetic field and the curvature of the substract is an interesting result and we believe that this issue may be relevant to be applied in condensed matter systems, e.g., superconductors, nematic liquid crystals, graphene and topological insulators.

arXiv commentTo be published in Physics Letters A

References in corpus (16)

• Spectroscopy of nanoscopic semiconductor rings
• Magnetoelastic nonlinear metamaterials
• Graphene bubbles with controllable curvature
• Magnetic bistability and controllable reversal of asymmetric ferromagnetic nanorings
• Anomalous coupling between topological defects and curvature
• Out-of-surface vortices in spherical shells
• Ground-state configurations in ferromagnetic nanotori
• On topological spin excitations on a rigid torus
• Chiral symmetry breaking of magnetic vortices by sample roughness
• A model for structural defects in nanomagnets
• Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere
• Heisenberg spins on a cone: an interplay between geometry and magnetism
• Geometrical pinning of magnetic vortices induced by a deficit angle on a surface: anisotropic spins on a conic space background
• Magnetic vortex-like excitations on a sphere
• Heisenberg Spins on an Elastic Torus Section
• Pseudospherical functions on a hyperboloid of one sheet

Cited by in corpus (8)

• Curvature effects in statics and dynamics of low dimensional magnets
• Topologically stable magnetization states on a spherical shell: curvature stabilized skyrmions
• Vortex-antivortex pairs induced by curvature in toroidal nanomagnets
• Stability of skyrmions on curved surfaces in the presence of a magnetic field
• Analysis on the stability of in-surface magnetic configurations in toroidal nanoshells
• On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry
• Topological magnetic solitons on a paraboloidal shell
• Topological spin excitations induced by an external magnetic field coupled to a surface with rotational symmetry