Engineered Chiral Skyrmion and Skyrmionium States by the Gradient of Curvature

TL;DR

This paper introduces a novel mechanism for stabilizing chiral skyrmion states in curvilinear nanomagnets by utilizing the gradient of curvature, enabling control over skyrmion properties through surface engineering.

Contribution

It proposes a new curvature-gradient-based method to stabilize and manipulate chiral skyrmions in magnetic thin films with curved geometries.

Findings

Chiral skyrmions and skyrmionium states can be stabilized by curvature gradients.

The skyrmion radius can be tuned by the position of the bend in the nanostructure.

A general method to reduce curved surface problems to planar problems is developed.

Abstract

Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose a new mechanism to stabilize chiral N\'{e}el skyrmion states relying on the \textit{gradient} of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers $\pm 1$ and a skyrmionium state with a winding number $0$. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii--Moriya interaction. The latter emerges due to the gradient of the local curvature at a bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables one to reduce a magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii--Moriya interaction.