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.

中文翻译：

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层状蜂窝铁磁体中的拓扑外尔磁子和热霍尔效应

在这项工作中，我们研究了 ABC 堆叠蜂窝晶格中三维铁磁体的拓扑特性和磁振子霍尔效应，受最近非弹性中子散射研究的启发。 $铬{\mathrm{一世}}_3$. 我们表明，层间耦合显着影响了磁振子分支的磁振子能带结构和陈数$J_C$，此外，与其他作者采用的 AA 堆叠相比，它在 ABC 堆叠中具有性质不同的效果。最低磁振子带的非平凡陈数由每个蜂窝层中的下一个最近邻 Dzyaloshinskii-Moriya 相互作用稳定，导致跳跃项类似于石墨烯电子霍尔丹模型中的跳跃项。然而，我们还发现了几个无间隙的 Weyl 点，将非等效的 Chern 绝缘相分开，通过层间耦合的比率进行调整$J_C$ 和第三邻居海森堡相互作用 $J_3$. 我们进一步表明，磁子带的拓扑特征导致非零热霍尔传导率，其符号和大小取决于$J_C$和层内耦合。由于层间耦合强度$J_C$ 可以通过对准二维材料施加压力来轻松调整，例如 $铬{\mathrm{一世}}_3$，这提供了在实验中调整磁振子热霍尔效应的潜在途径。