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

TL;DR

This study investigates how curvature in paraboloidal nanoparticles influences magnetic vortex and skyrmion energies, revealing curvature-dependent energy variations that affect vortex pinning and skyrmion size.

Contribution

It provides analytical insights into curvature effects on magnetic energies of vortices and skyrmions, highlighting potential mechanisms for vortex pinning and size modulation.

Findings

Vortex in-plane energy is higher on paraboloids than in planar disks.

Dipolar energy of vortex cores decreases on paraboloidal surfaces.

Skyrmion width shrinks to reduce magnetostatic energy under curvature constraints.

Abstract

Curvature effects are important for a proper description of the properties of magnetic systems. In this paper the exchange and dipolar energy of vortices on a paraboloidal shell is studied. Using analytical calculations it is shown that the in-plane component of vortices has larger energy on a paraboloidal shell than in a planar disk with same thickness. On the other hand, the dipolar energy associated to the vortex core diminishes if the vortex core is on a paraboloidal surface. This reduction in the dipolar energy may cause a vortex pinning mechanism by a paraboloidal shaped defect in a planar nanomagnet. Regarding skyrmions, by using an in-plane anisotropy approximation to the dipolar energy, it is shown that the skyrmion must have its width shrunk in order to diminishes the magnetostatic energy and satisfy geometrical constraints of the system.