Discovery of two-dimensional ferromagnetic van der Waals chromium triiodide (${\mathrm{CrI}}_3$) opens new avenues toward tunable terahertz topological magnon via stacking order control in a multilayer system. We theoretically simulated magnetism and topological magnon modulation in multiple ${\mathrm{CrI}}_3/\mathrm{As}$ stacking orders by means of first-principles and linear spin-wave theory calculations. The first-nearest-neighbor spin-exchange interactions are enhanced up to 100% from those in monolayer ${\mathrm{CrI}}_3$ due to degeneracy lifting in $\mathrm{Cr} d$ orbitals induced by broken symmetry from the addition of $\mathrm{As}$ monolayer. Furthermore, interfacial charge transfer from the $\mathrm{As}$ monolayer to $\mathrm{I}$ atom in the bottom sublayer induces finite Dzyaloshinskii-Moriya interactions of first-nearest-neighboring $\mathrm{Cr}$ atoms and enhances those of second-nearest-neighboring $\mathrm{Cr}$ atoms. Magnon Dirac gaps in bilayer ${\mathrm{CrI}}_3/\mathrm{As}$ are open wider than those in monolayer ${\mathrm{CrI}}_3$ at the edge of the Brillouin zone, attributed to the enhanced second-nearest-neighbor Dzyaloshinskii-Moriya interactions. The magnon dispersion in a nanoribbon geometry exhibits localized magnon edge states, and the existence of localized edge states is unique to a certain periodicity direction relative to the crystallographic direction in the stacking order with broken rotational symmetry.

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• Dzyaloshinskii-Moriya interaction
• Exchange interaction
• Magnons
• Topological materials
• van der Waals systems