A Deformable Model for Magnetic Vortex Pinning

TL;DR

This paper introduces a two-parameter analytical model for magnetic vortices in thin disks that accurately predicts vortex behavior and interactions with pinning sites, aiding in the quantitative analysis of vortex pinning energies.

Contribution

It presents a novel two-parameter analytical model that describes vortex interactions with pinning sites, improving upon previous one-parameter models.

Findings

Accurately predicts magnetization and vortex position.

Replicates hysteretic transitions and vortex displacement.

Matches numerical simulations closely.

Abstract

A two-parameter analytical model of the magnetic vortex in a thin disk of soft magnetic material is constructed. The model is capable of describing the change in evolution of net vortex state magnetization and of core position when the vortex core interacts with a magnetic pinning site. The model employs a piecewise, physically continuous, magnetization distribution obtained by the merger of two extensively used one-parameter analytical models of the vortex state in a disk. Through comparison to numerical simulations of ideal disks with and without pinning sites, the model is found to accurately predict the magnetization, vortex position, hysteretic transitions, and 2-D displacement of the vortex in the presence of pinning sites. The model will be applicable to the quantitative determination of vortex pinning energies from measurements of magnetization.