Magnon scattering across quantum Hall skyrmion crystals

Skyrmion crystals have a rich collective mode spectrum and are hypothesized to appear in quantum Hall ferromagnets in the lowest Landau level at small doping away from one filled level. We develop a model of a ferromagnet-skyrmion crystal-ferromagnet junction, relevant to recent experiments in monolayer graphene, to study the influence of collective modes of skyrmion crystals on the propagation an incoming ferromagnetic magnon[1] – a setup proposed to uncover the nature of the collective modes [2]. We show, using an appropriate set of generalized theta functions, how to smoothly interpolate between regions of zero (ferromagnetic ends) and spatially modulating finite topological charge density (skyrmion crystal). The collective mode equations for such a configuration, from a suitably defined energy functional, map onto the Bogoliubov-de Gennes equation. Using this mapping, along with a slice-wise recursive transfer matrix approach, we calculate the transmission amplitudes of an incoming ferromagnetic magnon. We also show how changing the collective mode spectrum of the skyrmion crystal, by varying the strength of the topological charge density terms in the functional, affects magnon transmission. Our results present unique signatures of skyrmion crystals due to their characteristic collective mode spectrum, and can be used as evidence for their presence in graphene and possibly in twisted bilayer graphene.



[1] N. Chakraborty, R. Moessner, B. Doucot: In prep

[2] H. Zhou et al. Nature Physics (2020)