Topological spin excitations induced by an external magnetic field coupled to a surface with rotational symmetry

Abstract

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler-Lagrange static equations, derived from the Hamiltonian lead to the inhomogeneous double sine-Gordon equation (DSG). However, if the magnetic field is coupled with the metric elements of the surface, and consequently, its curvature, the homogeneous DSG appears and a $2\pi$-soliton is obtained as a solution for this model. In order to obey the self-dual equations, surface deformations are predicted at the sector where the spins point in the opposite direction to the magnetic field. The model was used to particularize the characteristic lenght of the 2$\pi$-soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid and the hyperboloid. Fractional 2$\pi$-solitons must appear on finite surfaces, as the sphere, torus and barrels, for example.

15 pages, 1 figure, to appear in volume 43 of the Brazilian Journal of Physics. arXiv admin note: substantial text overlap with arXiv:1206.6228

References in corpus (7)

• Graphene bubbles with controllable curvature
• Ground-state configurations in ferromagnetic nanotori
• On topological spin excitations on a rigid torus
• Heisenberg model on a space with negative curvature: topological spin textures on the pseudosphere
• On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry
• Magnetic vortex-like excitations on a sphere
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Cited by in corpus (5)

• Torsion induced effects in magnetic nanowires
• 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
• Manipulating the shape of flexible magnetoelastic nanodiscs with meron-like magnetic states