  We reveal the rich magnon topology in honeycomb bilayer ferromagnets (HBF)
induced by the combined effect of interlayer exchange, Dzyaloshinskii-Moriya
interaction (DMI), and electrostatic doping (ED). In particular, we present a
systematic study of the Hamiltonian non-adiabatic evolution in the HBF
parametric space, spanned by the symmetry-breaking terms (DMI and ED) and
interlayer exchange. We determine the band closure manifolds which are found to
divide the parametric space into six distinct regions, matched with five
distinct topological phases and one topologically trivial phase. The
characteristic Chern numbers and thermal Hall conductivities are calculated for
the topological phases. Edge spectra, dictated by the bulk-edge correspondence,
are also analyzed in the nanoribbon version of the model. Both bulk and edge
spectra are found to be nonreciprocal as a consequence of ED and edge magnons
are observed to counter propagate on opposite edges. The predicted results
offer new insights on the manipulation of magnonic Chern numbers and magnon
topological transport via experimentally tunable parameters.
