Surface anisotropy in a magnetic cylinder induced by the displacement of a vortex core

TL;DR

This paper models how displacing a vortex core in a magnetic cylinder induces a surface anisotropy, simplifying the analysis of dipolar energy effects in magnetic nanostructures.

Contribution

It introduces a simple surface anisotropy model proportional to the cylinder's demagnetizing factor, enhancing analytical and numerical studies of vortex core displacement.

Findings

Surface anisotropy is proportional to the in-plane demagnetizing factor.

The model simplifies the dipolar energy calculation.

Results improve efficiency of vortex core displacement analysis.

Abstract

In this article we investigate the induction of a surface anisotropy due to the displacement of the vortex core in a cylindrical nanostructure. In fact, the effect of the displacement of the vortex core in the dipolar energy can be modeled simply as a surface anisotropy of the form $E_s = K_s \int_{\mathcal{S}_m} d\mathcal{S} \, (\hat{n} \cdot \hat{m})^2/2$. Moreover, the surface anisotropy constant $K_s$ is proportional to the cylinder in-plane demagnetizing factor in the direction of the core deviation, $N_y(L/R)$, i.e., $K_s = \mu_0 M_0^2 R \, N_y(L/R)$, where $R$ and $L$ are the radius and the thickness of the cylinder, respectively. Our results show that the term of the nontrivial dipolar energy caused by the charges in the cylinder mantle can be replaced by a simple integral $E_s$ that increases the efficiency of the numerical calculations in the analytical study of the displacement of the vortex core in magnetic vortices.