On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

Abstract

We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and $\pi$-solitons are predicted. The second one is given by the XY model, leading to a vortex turning around the surface. Helical states are also considered, however, topological arguments can not be used to ensure its stability. The energy and the anisotropy parameter which stabilizes the vortex state are explicitly calculated for two surfaces: catenoid and hyperboloid. The results show that the anisotropy and the vortex energy depends on the underlying geometry.

10 pages, 2 figures, Accepted for publication in Phys. Lett A (2013)

References in corpus (8)

• Stability of magnetic configurations in nanorings
• 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
• Magnetic vortex-like excitations on a sphere
• Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry
• Hyperbolic Interfaces
• Phase transition of two-dimensional generalized XY model