  Two-dimensional (2D) honeycomb ferromagnets, such as monolayer
chromium-trihalides, are predicted to behave as topological magnon insulators -
characterized by an insulating bulk and topologically protected edge states,
giving rise to a thermal magnon Hall effect. Here we report the behavior of the
topological magnons in monolayer CrI$_3$ under external stimuli, including
biaxial and uniaxial strain, electric gating, as well as in-plane and
out-of-plane magnetic field, revealing that one can thereby tailor the magnetic
states as well as the size and the topology of the magnonic bandgap. These
findings broaden the perspective of using 2D magnetic materials to design
topological magnonic devices.
