Topological magnetic solitons on a paraboloidal shell

TL;DR

This paper investigates how the curvature of a paraboloidal shell affects the properties and stability of magnetic topological solitons like skyrmions and vortices, revealing geometry-dependent behaviors and new magnetic excitations.

Contribution

It demonstrates the influence of paraboloidal geometry on skyrmion and vortex energies and introduces field-induced $2\pi$-skyrmions as new magnetic excitations.

Findings

Skyrmions on paraboloids are topologically stable, unlike on pseudospheres.

Skyrmion width varies with paraboloid parameters.

Magnetic field induces $2\pi$-skyrmions, adding a new length scale.

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.