Skyrmion Jellyfish in Driven Chiral Magnets

TL;DR

This paper demonstrates that skyrmions in chiral magnets can be driven to move by oscillating magnetic fields, with their velocity depending on the field's parameters and internal modes, revealing universal and controllable motion mechanisms.

Contribution

The study provides an analytical framework for understanding skyrmion motion under oscillating fields, highlighting universal behavior and the influence of internal modes and damping.

Findings

Skyrmions move with constant velocity under oscillating magnetic fields.

Velocity depends on field polarization, frequency, and phase.

Two mechanisms: friction-driven at low frequencies and magnon emission at high frequencies.

Abstract

Chiral magnets can host topological particles known as skyrmions, which carry an exactly quantised topological charge $Q=-1$. In the presence of an oscillating magnetic field ${\bf B}_1(t)$, a single skyrmion embedded in a ferromagnetic background will start to move with constant velocity ${\bf v}_{\text{trans}}$. The mechanism behind this motion is similar to the one used by a jellyfish when it swims through water. We show that the skyrmion's motion is a universal phenomenon, arising in any magnetic system with translational modes. By projecting the equation of motion onto the skyrmion's translational modes and going to quadratic order in ${\bf B}_1(t)$, we obtain an analytical expression for ${\bf v}_{\text{trans}}$ as a function of the system's linear response. The linear response and consequently ${\bf v}_{\text{trans}}$ are influenced by the skyrmion's internal modes and scattering states, as well as by the ferromagnetic background's Kittel mode. The direction and speed of ${\bf v}_{\text{trans}}$ can be controlled by changing the polarisation, frequency and phase of the driving field ${\bf B}_1(t)$. For systems with small Gilbert damping parameter $\alpha$, we identify two distinct physical mechanisms used by the skyrmion to move. At low driving frequencies, the skyrmion's motion is driven by friction, and $v_{\text{trans}}\sim\alpha$, whereas at higher frequencies above the ferromagnetic gap, the skyrmion moves by magnon emission, and $v_{\text{trans}}$ becomes independent of $\alpha$.