Impact of curvature-induced Dzyaloshinskii-Moriya interaction on magnetic vortex texture in spherical caps

TL;DR

This paper investigates how the curvature-induced Dzyaloshinskii-Moriya interaction affects magnetic vortex textures in spherical caps, revealing unique edge tilts and core size variations due to curvature effects.

Contribution

It derives equations describing vortex profiles in spherical caps and highlights the distinct influence of curvature-induced DMI on vortex core size and magnetization tilt.

Findings

Edge tilt of magnetization increases surface energy.

Curvature-induced DMI enlarges vortex core size.

Differences from planar disk DMI effects are demonstrated.

Abstract

Geometric curvature of nanoscale magnetic shells brings about curvature-induced anisotropy and Dzyaloshinskii-Moriya interaction (DMI). Here, we derive equations to describe the profile of the magnetic vortex state in a spherical cap. We demonstrate that the azimuthal component of magnetization acquires a finite tilt at the edge of the cap, which results in the increase of the magnetic surface energy. This is different compared to the case of a closed spherical shell, where symmetry of the texture does not allow any tilt of magnetization at the equator of the sphere. Furthermore, we analyze the size of the vortex core in a spherical cap and show that the presence of the curvature-induced DMI leads to the increase of the core size independent of the product of the circulation and polarity of the vortex. This is in contrast to the case of planar disks with intrinsic DMI, where the preferred direction of circulation as well as the decrease or increase of the size of vortex core is determined by the sign of the product of the circulation and polarity with respect to the sign of the constant of the intrinsic DMI.