We introduce a model to study magnon scattering in skyrmion crystals,
sandwiched between ferromagnets which act as the source of magnons. Skyrmions
are topological objects while skyrmion crystals break internal and
translational symmetries, thus our setup allows us to study the interplay of
topology and symmetry breaking. Starting from a basis of holomorphic theta
functions, we construct an analytical ansatz for such a junction with finite
spatially modulating topological charge density in the central region and
vanishing in the leads. We then construct a suitably defined energy functional
for the junction and derive the resulting equations of motion, which resemble a
Bogoliubov-de Gennes-like equation. Using analytical techniques, field theory,
heuristic models and microscopic recursive transfer-matrix numerics, we
calculate the spectra and magnon transmission properties of the skyrmion
crystal. We find that magnon transmission can be understood via a combination
of low-energy Goldstone modes and effective emergent Landau levels at higher
energies. The former manifests in discrete low-energy peaks in the transmission
spectrum which reflect the nature of the Goldstone modes arising from symmetry
breaking. The latter, which reflect the topology, lead to band-like
transmission features, from the structure of which further details of the
excitation spectrum of the skyrmion crystal can be inferred. Such
characteristic transmission features are absent in competing phases of the
quantum Hall phase diagram, and hence provide direct signatures of skyrmion
crystal phases and their spectra. Our results directly apply to quantum Hall
heterojunction experiments in monolayer graphene with the central region doped
slightly away from unit filling, a ν=1:1±δν:1 junction and
are also relevant to junctions formed by metallic magnets or in junctions with
artificial gauge fields.Comment: 20+6 pages, 9+2 figures, comments welcom