Tailoring spin-exchange interactions and topological magnons in 2D ferromagnetic van der Waals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>CrI</mml:mi>

Magnetism and magnon excitation in the two-dimensional van der Waals CrI${}_{3}$ is driven by not only the isotropic spin-exchange interactions, but also the anisotropic spin-exchange interactions, where the nonmagnetic ligand Iodine atoms play important roles. This allows indirect modulation of interactions between Chromium atoms by tuning the electronic states of Iodine atoms via stacking order control. Here, combining first-principles calculation and linear spin-wave theory, the authors theoretically demonstrate that multiple stacking orders between monolayer CrI${}_{3}$ and Chromium host different modulation of spin-exchange interactions and topological magnon phases, identified by the existence of chiral edge states. The modulation of spin-exchange interactions is mainly driven by the interfacial charge transfer from the Chromium atoms to the Iodine atoms, which indirectly changes the electronic states of Chromium $d$ orbitals from symmetry point of view.