Dynamics of a vortex domain wall in a magnetic nanostrip: an application of the collective coordinate approach

TL;DR

This paper models the complex dynamics of vortex domain walls in ferromagnetic nanostrips under magnetic fields using a collective coordinate approach, capturing different motion regimes and validating with simulations.

Contribution

It introduces a simplified two-mode collective coordinate model that describes vortex domain wall dynamics across various regimes, extending to high fields with additional modes.

Findings

The model accurately predicts low and intermediate field dynamics.

Vortex wall motion transitions from viscous to oscillatory regimes.

Additional modes are necessary to describe high-field behavior.

Abstract

The motion of a vortex domain wall in a ferromagnetic strip of submicron width under the influence of an external magnetic field exhibits three distinct dynamical regimes. In a viscous regime at low fields the wall moves rigidly with a velocity proportional to the field. Above a critical field the viscous motion breaks down giving way to oscillations accompanied by a slow drift of the wall. At still higher fields the drift velocity starts rising with the field again but with a much lower mobility dv/dH than in the viscous regime. To describe the dynamics of the wall we use the method of collective coordinates that focuses on soft modes of the system. By retaining two soft modes, parametrized by the coordinates of the vortex core, we obtain a simple description of the wall dynamics at low and intermediate applied fields that describes both the viscous and oscillatory regimes below and above the breakdown. The calculated dynamics agrees well with micromagnetic simulations at low and intermediate values of the driving field. In higher fields, additional modes become soft and the two-mode approximation is no longer sufficient. We explain some of the significant features of vortex domain wall motion in high fields through the inclusion of additional modes associated with the half-antivortices on the strip edge.