Energy dissipation of moved magnetic vortices

TL;DR

This paper investigates energy dissipation caused by magnetic vortices moved by a dipolar tip in a ferromagnetic substrate, combining numerical simulations with analytical models to understand size dependence and nonlinear effects.

Contribution

It introduces an analytical expression for magnetic vortex friction force and explores size effects, including the concept of an effective vortex size and a magnetic friction number.

Findings

Friction force diverges in the thermodynamic limit according to the analytical model.

Dissipation depends logarithmically on system size for small systems.

Friction saturates at a velocity-dependent value, defining an effective vortex size.

Abstract

A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. The dipolar tip stabilises a vortex structure which is dragged through the system and dissipates energy. An analytical expression for the friction force in the v$\rightarrow$0-limit based on the Thiele equation is presented. The limitations of this result which predicts a diverging friction force in the thermodynamic limit, are demonstrated by a study of the size dependence of the friction force. While for small system sizes the dissipation depends logarithmically on the system size, it saturates at a specific velocity dependent value. This size can be regarded as an effective vortex size and it is shown how this effective vortex size agrees with the infinite extension of a vortex in the thermodynamic limit. A magnetic friction number is defined which represents a general criterion for the validity of the Thiele equation and quantifies the degree of nonlinearity in the response of a driven spin configuration.