Skyrmion dynamics in chiral ferromagnets under spin-transfer torque

TL;DR

This paper investigates the dynamics of skyrmions and skyrmioniums in chiral ferromagnets under spin-transfer torque, revealing their steady-state behaviors, velocities, and the effects of current cessation through analytical and numerical methods.

Contribution

It provides new analytical and numerical insights into the motion and steady states of skyrmions and skyrmioniums under spin-transfer torque, including exact solutions and velocity limits.

Findings

Skyrmionium accelerates and reaches a steady velocity or elongates infinitely.

Topological skyrmions converge to a steady velocity at an angle to current.

Skyrmionium continues propagation after current stops.

Abstract

We study the dynamics of skyrmions under spin-transfer torque in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. In particular, we study the motion of a topological skyrmion with skyrmion number $Q=1$ and a non-topological skyrmionium with $Q=0$ using their linear momentum, virial relations, and numerical simulations. The non-topological $Q=0$ skyrmionium is accelerated in the direction of the current flow and it either reaches a steady state with constant velocity, or it is elongated to infinity. The steady-state velocity is given by a balance between current and dissipation and has an upper limit. In contrast, the topological $Q=1$ skyrmion converges to a steady-state with constant velocity at an angle to the current flow. When the spin current stops the $Q=1$ skyrmion is spontaneously pinned whereas the $Q=0$ skyrmionium continues propagation. Exact solutions for the propagating skyrmionium are identified as solutions of equations given numerically in a previous work. Further exact results for propagating skyrmions are given in the case of the pure exchange model. The traveling solutions provide arguments that a spin-polarized current will cause rigid motion of a skyrmion or a skyrmionium.