Field-tuned skyrmion crystals: anomalous quantum oscillations induced by Zeeman fields

Recent experiments on chiral magnets have observed skyrmion crystal phases which are stable in the presence of Dzyaloshinsky-Moriya interactions and Zeeman fields. Skyrmion crystal coupled to itinerant electrons manifests itself in electronic transport as the anomalous “topological Hall effect” caused by a real-space Berry-phase mechanism. This also leads a formation of Chern bands which depend on the properties of the skyrmion crystal unit cell. Our study has shown that incorporating quartic spin interactions into a system which hosts a skyrmion crystal results in a field-tunable skyrmion lattice constant. Itinerant electrons coupled to such skyrmion crystals can then be described by a Hofstadter-type model whose Chern bands depend strongly on the Zeeman field coupled to the local moments. Such metallic magnets serve as candidates for observing Zeeman-field-induced anomalous quantum oscillations.