Topological magnon band structure of emergent Landau levels in a skyrmion lattice*

The discovery of magnetic skyrmions —particle-like magnetic textures with non-trivial topology — has attracted increasing scientific interest due to their large potential for future applications. Notably, it has been shown that electrons flowing through the skyrmion texture experience a fictitious magnetic field and an associated topological Hall effect. In return the skyrmion experiences the skyrmion Hall effect, which allows us to efficiently move skyrmion textures through materials and devices with ultra-low current densities, resulting in suggestions to use them in low-power memory devices stabilized by topology. Using polarized neutron spectroscopy, we now demonstrate that collective spin excitations known as magnons similarly feel a virtual magnetic field when moving across a skyrmion texture. The resulting net magnon motion is analogous to the effect of the Lorentz force acting on electrically charged particles that is at the heart of the Hall effect. Our study reveals that the magnon spectrum shows emergent Landau levels that are characteristic of the virtual magnetic field used to account for the nontrivial topological winding of a skyrmion lattice. This provides evidence of a topological magnon band structure in reciprocal space, which is borne out of the nontrivial real-space topology of a magnetic order. Our result also has important implications for applications in magnonics showcasing that topological magnetic textures may be used to manipulate that direction of magnons.