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)

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• Multiplet of skyrmion states on a curvilinear defect: skyrmion lattices as a ground state
• 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
• Topological magnetic solitons on a paraboloidal shell
• Curvature control of the superconducting proximity effect in diffusive ferromagnetic nanowires
• Curvature-Induced Skyrmion Mass
• Topological spin excitations induced by an external magnetic field coupled to a surface with rotational symmetry
• Non-constant geometric curvature for tailored spin-orbit coupling and chirality in superconductor-magnet heterostructures
• Berry phases and zero-modes in toroidal topological insulator
• Impact of curvature-induced Dzyaloshinskii-Moriya interaction on magnetic vortex texture in spherical caps