Topological magnetic solitons on a paraboloidal shell

Abstract

We study the influence of curvature on the exchange energy of skyrmions and vortices on a paraboloidal surface. It is shown that such structures appear as excitations of the Heisenberg model, presenting topological stability, unlike what happens on other simply-connected geometries such as pseudospheres. We also show that the skyrmion width depends on the geometrical parameters of the paraboloid. The presence of a magnetic field leads to the appearance of $2\pi$-skyrmions, introducing a new characteristic length into the system. Regarding vortices, the geometrical parameters of the paraboloid play an important role in the exchange energy of this excitation.

References in corpus (9)

• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Scaling relations for magnetic nanoparticles
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
• 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
• Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry
• Scattering of charge carriers in graphene induced by topological defects

Cited by in corpus (1)

• Curvature-induced changes in the magnetic energy of vortices and skyrmions in paraboloidal nanoparticles