Stacking-dependent topological magnons in bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CrI</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

Motivated by the potential of atomically thin magnets towards achieving tunable high-frequency magnonics, we detail spin-wave dispersion bilayer ${\mathrm{CrI}}_{3}$. We demonstrate that magnonic behavior strongly depends on its stacking configuration and interlayer magnetic ordering, where a topological band gap opens in caused Dzyaloshinskii-Moriya Kitaev interactions, classifying ${\mathrm{CrI}}_{3}$ as magnon insulator. further reveal both size topology with an antiferromagnetic ordering are external field.