Magnetic systems can host topological spin textures, with skyrmions being a well-known example. I will begin with a pedagogical discussion of how topological descriptions naturally arise in magnetic systems, with particular attention to skyrmions [1,2] and domain walls. I then report our recent findings on the behavior of magnetic textures in altermagnets, which can be traced to the existence of an anisotropic spin-transfer torque effect [3]. We find that the spin-splitter adiabatic torque can induce domain wall precession, slowing down domain wall motion. The domain wall response also becomes anisotropic, reflecting the d-wave symmetry of the altermagnet. Furthermore, we observe that the spin-splitter adiabatic torque modifies skyrmion dynamics, inducing an anisotropic skyrmion Hall effect. In the second part of my talk, I will discuss how topological domain walls can lead to nonreciprocal, superfluid-like topological spin transport [4]. I will also give an overview of our other findings related to skyrmion modifications that can occur in certain magnets, such as the appearance of antiskyrmions, elongated skyrmions, and skyrmions with arbitrary helicity—which is relevant to van der Waals materials [5] and CoPt single-layer gradient alloys [6].

[1] Kovalev, Li, Schwartz, Phys. Rev. B 110, 045122 (2024)
[2] Kovalev, Sandhoefner, Front. Phys. 6, 98 (2018)
[3] Vakili, Schwartz, Kovalev Phys. Rev. Lett. 134, 176401 (2025)
[4] Kovalev, Li, Schwartz, Phys. Rev. B 110, 045122 (2024)
[5] Huang, Schwartz, Shao, Kovalev, Tsymbal, Phys. Rev. B 109, 024426 (2024)
[6] Ericson et al, ACS Nano 2024, 18, 45, 31261–31273