Using magnons in insulating magnets as information carriers is a highly promising approach for low-power consumption devices free of Joule heating. Recently, spatially periodic skyrmionic textures have been postulated to be novel platforms for topological magnons [1-3]. We predict that the control of robust magnon spin currents could be achieved in ferromagnetic skyrmion crystals. Taking advantage of a topological phase transition in the magnon spectrum, we show that an external magnetic field allows one to turn on and off chiral magnon currents carried by topological edge states [2]. Furthermore, we uncover that magnetic antiskyrmion crystals can realize a magnonic quadrupole topological insulator, whose hallmark signature are robust magnonic corner states. Tuning an applied magnetic field induces the self-assembly of fractional antiskyrmions along the sample edges, which, remarkably, restore the protecting symmetries that allow the formation of magnonic corner states [3].

[1] S. A. Díaz, J. Klinovaja, and D. Loss, Phys. Rev. Lett. 122, 187203 (2019).
[2] S. A. Díaz, T. Hirosawa, J. Klinovaja, and D. Loss, Phys. Rev. Research 2, 013231 (2020).
[3] T. Hirosawa, S. A. Díaz, J. Klinovaja, and D. Loss, arXiv:2005.05884