Vortex motion in a finite-size easy-plane ferromagnet and application to a nanodot

TL;DR

This paper investigates vortex dynamics in a finite-size easy-plane ferromagnet, revealing how magnetic fields influence vortex motion and proposing a control method for vortices in nanodots using ac magnetic fields.

Contribution

It introduces a new collective variable theory including mode coupling, accurately describing vortex orbits and their dependence on system parameters.

Findings

Vortex follows a spiral orbit without magnetic field.

A stable limit cycle emerges under rotating magnetic fields.

Orbit radius scales with system size and field amplitude.

Abstract

We study the motion of a non-planar vortex in a circular easy-plane ferromagnet, which imitates a magnetic nanodot. Analysis was done using numerical simulations and a new collective variable theory which includes the coupling of Goldstone-like mode with the vortex center. Without magnetic field the vortex follows a spiral orbit which we calculate. When a rotating in-plane magnetic field is included, the vortex tends to a stable limit cycle which exists in a significant range of field amplitude B and frequency $\omega$ for a given system size L. For a fixed $\omega$, the radius R of the orbital motion is proportional to L while the orbital frequency $\Omega$ varies as 1/L and is significantly smaller than $\omega$. Since the limit cycle is caused by the interplay between the magnetization and the vortex motion, the internal mode is essential in the collective variable theory which then gives the correct estimate and dependency for the orbit radius $R\sim B L/\omega$. Using this simple theory we indicate how an ac magnetic field can be used to control vortices observed in real magnetic nanodots.