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We introduce a model to study magnon scattering in skyrmion crystals,sandwiched between ferromagnets which act as the source of magnons. Skyrmionsare topological objects while skyrmion crystals break internal andtranslational symmetries, thus our setup allows us to study the interplay oftopology and symmetry breaking. Starting from a basis of holomorphic thetafunctions, we construct an analytical ansatz for such a junction with finitespatially modulating topological charge density in the central region andvanishing in the leads. We then construct a suitably defined energy functionalfor the junction and derive the resulting equations of motion, which resemble aBogoliubov-de Gennes-like equation. Using analytical techniques, field theory,heuristic models and microscopic recursive transfer-matrix numerics, wecalculate the spectra and magnon transmission properties of the skyrmioncrystal. We find that magnon transmission can be understood via a combinationof low-energy Goldstone modes and effective emergent Landau levels at higherenergies. The former manifests in discrete low-energy peaks in the transmissionspectrum which reflect the nature of the Goldstone modes arising from symmetrybreaking. The latter, which reflect the topology, lead to band-liketransmission features, from the structure of which further details of theexcitation spectrum of the skyrmion crystal can be inferred. Suchcharacteristic transmission features are absent in competing phases of thequantum Hall phase diagram, and hence provide direct signatures of skyrmioncrystal phases and their spectra. Our results directly apply to quantum Hallheterojunction experiments in monolayer graphene with the central region dopedslightly away from unit filling, a $\nu = 1:1 \pm \delta \nu: 1$ junction andare also relevant to junctions formed by metallic magnets or in junctions withartificial gauge fields.

Riemann meets Goldstone: magnon scattering off quantum Hall skyrmion crystals probes interplay of symmetry breaking and topology