Topological Magnons and Altermagnetism in Stacked van der Waals Bilayer CrI3

Abstract Stacked van der Waals magnets provide a tunable route to altermagnetism, a compensated magnetic order characterized by momentum-dependent spin splitting, and to the topological magnetic excitations that such order can host. In bilayer CrI$_3$, first-principles calculations and linear spin-wave theory reveal stacking-controlled altermagnetic order and associated magnon band topology. Combining band-representation analysis with calculations of the dynamic structure factor relevant to inelastic neutron scattering, we further characterize the chirally split topological magnons and quantify their energy corrections and lifetimes using a many-body Green's-function approach. The interlayer magnetic ground state is highly sensitive to the stacking geometry, thereby controlling the magnon band topology and transport responses. We further show that magnon--magnon interactions renormalize the magnon dispersion and dynamic structure factor, with a particular focus on magnon decay. Using van der Waals bilayer CrI$_3$ as a representative platform, our results establish stacking engineering as a structural route for tuning altermagnetism and associated topological magnon excitations, opening avenues toward stacking-controlled spintronic and magnonic devices.