The dynamics of skyrmion shrinking

Abstract

When magnetic skyrmions decay, their size in real space decreases in a finite time before they eventually collapse. We construct an effective continuum model and use its dynamics to describe the shrinking behavior of skyrmions before they collapse. Using the Landau-Lifshitz-Gilbert equation and the time derivative of the vector field, we find a set of coupled nonlinear ordinary differential equation for the time dependent effective skyrmion radius and its helicity. In particular, we use a triangular-shaped skyrmion profile of its polar angle. Contrary to the commonly expected simple exponential decrease in size, we reveal a more complicated time dependence, in which the time-dependent radius crosses over from an exponential decay towards a square root decrease, $\sim (t-t_c{)}^{1/2}$, near a critical time $t_c$ at which it collapses. This critical time is found to depend logarithmically on the lattice constant. In addition, we examine the interplay between the shrinking dynamics and an accompanying transformation through different skyrmion configurations, depending on the various system parameters. The findings are verified by numerical studies on the lattice, supporting the predictions from the theoretical continuum model.

References in corpus (5)

• Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
• Theory of current-driven motion of Skyrmions and spirals in helical magnets
• Skyrmions in Magnetic Multilayers
• Magnon-skyrmion scattering in chiral magnets
• Dynamics of the collapse of a ferromagnetic skyrmion in a centrosymmetric lattice

Cited by in corpus (2)

• Proposal for realizing quantum-spin systems on a two-dimensional square lattice with Dzyaloshinskii-Moriya interaction by Floquet engineering using Rydberg atoms
• Dynamics of antiskyrmion shrinking