Dynamics and Pinning for Skyrmions in Altermagnets

Abstract

We examine the dynamics, Hall angle, and pinning for N{\'e}el skyrmions in an altermagnet. Using an atomistic model, we show that skyrmion velocity and Hall angle dependence is anisotropic with respect to the direction of the drive, due to the fourfold symmetry implied by the two sublattices of the altermagnet. The skyrmion Hall angle and velocity at fixed drive show strong variations for increasing ratios of the exchange constant of the sublattices, $J_2/J_1$. This fourfold anisotropy of altermagnetic (ATM) skyrmions also leads to anisotropic pinning effects for an ATM skyrmion interacting with isotropic circular pinning sites. We also propose a simple particle model for this system that takes into account this anisotropy and find that it captures both the variations of the ATM skyrmion Hall angle and velocity as a function of drive direction, as also found in the atomistic simulations. Using this particle model, we examine ATM skyrmions interacting with a periodic array of pinning sites. For increasing ratios of $J_2/J_1$, we find a strongly non-monotonic ATM skyrmion velocity, where there is a minimum in the velocity where the skyrmion locks to different symmetry directions of the periodic pinning lattice. For a random array, we find that ATM skyrmions show strongly anisotropic depinning thresholds and velocity responses for different drive directions, and that the Hall angle is nearly constant with drive. In comparison, for the same parameters, the depinning threshold for a ferromagnetic (FM) skyrmion is lower, and the skyrmion Hall angle shows a strong velocity dependence. The lower depinning threshold for FM skyrmions is due to stronger Magnus forces.