Vortex mechanics in planar nano-magnets

TL;DR

This paper introduces a collective-variable approach to analyze non-linear magnetic texture dynamics in planar nano-magnets, deriving equations that match experimental and simulation results without extra assumptions.

Contribution

It presents a novel analytical method for deriving non-linear equations of motion for magnetic textures using arbitrary parameters in a complex function.

Findings

Derived equations match Landau-Lifshitz-Gilbert dynamics

Analytical solutions for vortex motion are obtained

Results agree with experiments and simulations

Abstract

A collective-variable approach for the study of non-linear dynamics of magnetic textures in planar nano-magnets is proposed. The variables are just arbitrary parameters (complex or real) in the specified analytical function of a complex variable, describing the texture in motion. Starting with such a function, a formal procedure is outlined, allowing a (non-linear) system of differential equations of motion to be obtained for the variables. The resulting equations are equivalent to Landau-Lifshitz-Gilbert dynamics as far as the definition of collective variables allows it. Apart from the collective-variable specification, the procedure does not involve any additional assumptions (such as translational invariance or steady-state motion). As an example, the equations of weakly non-linear motion of a magnetic vortex are derived and solved analytically. A simple formula for the dependence of the vortex precession frequency on its amplitude is derived. The results are verified against special cases from the literature and agree quantitatively with experiments and simulations.