Stacking-dependent topological magnons in bilayer CrI$_3$

Motivated by the potential of atomically-thin magnets towards tunable high-frequency magnonics, we detail the spin-wave dispersion of bilayer CrI$_3$. We demonstrate that the magnonic behavior of the bilayer strongly depends on its stacking configuration and the interlayer magnetic ordering, where a topological bandgap opens in the dispersion caused by the Dzyaloshinskii-Moriya and Kitaev interactions, classifying bilayer CrI$_3$ as a topological magnon insulator. We further reveal that both size and topology of the bandgap in a CrI$_3$ bilayer with an antiferromagnetic interlayer ordering are tunable by an external magnetic field.