Topological Weyl magnons and thermal Hall effect in layered honeycomb ferromagnets

In this work, we study the topological properties and magnon Hall effect of a three-dimensional ferromagnet in the ABC stacking honeycomb lattice, motivated by the recent inelastic neutron scattering study of $\mathrm{Cr}{\mathrm{I}}₃$. We show that the magnon band structure and Chern numbers of the magnon branches are significantly affected by the interlayer coupling ${J}_c$, which moreover has a qualitatively different effect in the ABC stacking compared to the AA stacking adopted by other authors. The nontrivial Chern number of the lowest magnon band is stabilized by the next-nearest-neighbor Dzyaloshinskii-Moriya interaction in each honeycomb layer, resulting in the hopping term similar to that in the electronic Haldane model for graphene. However, we also find several gapless Weyl points, separating the nonequivalent Chern insulating phases, tuned by the ratio of the interlayer coupling ${J}_c$ and the third-neighbor Heisenberg interaction ${J}₃$. We further show that the topological character of magnon bands results in nonzero thermal Hall conductivity, whose sign and magnitude depend on ${J}_c$ and the intralayer couplings. Since the interlayer coupling strength ${J}_c$ can be easily tuned by applying pressure to the quasi-2D material such as $\mathrm{Cr}{\mathrm{I}}₃$, this provides a potential route to tuning the magnon thermal Hall effect in an experiment.