Skyrmion Hall Effect in D-Wave Altermagnets

Altermagnetism recently gained a lot of attention due to its unique characteristics of combining the time-reversal symmetry breaking nature of ferromagnets with the stray-field free nature of antiferromagnets. Altermagnets can host skyrmions, which, in ferromagnets, are known for their remarkable dynamics in form of the skyrmion Hall effect. This Hall effect is absent in antiferromagnets, as the topological charge responsible for this effect vanishes. The same argument also holds for altermagnets, but simulations nonetheless show a Hall response. In this work, we show by discussing the finite difference discretization used in many numerical solvers, that the Hall signal seen in simulations can be attributed to a numerical error that appears due to the particular symmetries of altermagnets.