Propagating two-dimensional magnetic droplets

TL;DR

This paper studies moving magnetic droplet solutions in thin films, extending stationary droplets to dynamic cases, analyzing their properties, stability, and numerical verification within the Landau-Lifshitz framework.

Contribution

It introduces a numerical and analytical study of propagating magnetic droplets, generalizing stationary solutions to moving frames and confirming their stability and properties.

Findings

Propagating droplets have a limited speed and frequency range.

Numerical methods accurately compute droplet structures.

Droplets are stable within certain parameter ranges.

Abstract

Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films are investigated. These localized, nontopological wave structures, parametrized by their precessional frequency and propagation speed, extend the stationary, coherently precessing "magnon droplet" to the moving frame, a non-trivial generalization due to the lack of Galilean invariance. Propagating droplets move on a spin wave background with a nonlinear droplet dispersion relation that yields a limited range of allowable droplet speeds and frequencies. An iterative numerical technique is used to compute the propagating droplet's structure and properties. The results agree with previous asymptotic calculations in the weakly nonlinear regime. Furthermore, an analytical criterion for the droplet's orbital stability is confirmed. Time-dependent numerical simulations further verify the propagating droplet's robustness to perturbation when its frequency and speed lie within the allowable range.