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