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

The motion of a spin excitation across topologically nontrivial magnetic order exhibits a deflection that is analogous to the effect of the Lorentz force on an electrically charged particle in an orbital magnetic field. We used polarized inelastic neutron scattering to investigate the propagation of magnons (i.e., bosonic collective spin excitations) in a lattice of skyrmion tubes in manganese silicide. For wave vectors perpendicular to the skyrmion tubes, the magnon spectra are consistent with the formation of finely spaced emergent Landau levels that are characteristic of the fictitious magnetic field used to account for the nontrivial topological winding of the 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. Description Magnons in a skyrmion lattice Electrons in two-dimensional solids placed in an external magnetic field fill the so-called Landau energy levels. In materials with a nontrivial spin texture, spin excitations (magnons) may have an analogous energy-level structure. However, showing this effect in an experiment is tricky. Weber et al. used inelastic neutron scattering and numerical simulations to demonstrate this effect in the skyrmion lattice phase of the material manganese monosilicide. —JS Inelastic neutron-scattering measurements indicate the formation of Landau levels for magnons in the skyrmion phase of MnSi.