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In two dimensional honeycomb ferromagnets, bosonic magnon quasiparticles(spin waves) may either behave as massless Dirac fermions or form topologicallyprotected edge states. The key ingredient defining their nature is thenext-nearest neighbor Dzyaloshinskii-Moriya (DM) interaction that breaks theinversion symmetry of the lattice and discriminates chirality of the associatedspin-wave excitations. Using inelastic neutron scattering, we find that spinwaves of the insulating honeycomb ferromagnet CrI$_3$ ($T_C=61$ K) have twodistinctive bands of ferromagnetic excitations separated by a $\sim$4 meV gapat the Dirac points. These results can only be understood by considering aHeisenberg Hamiltonian with DM interaction, thus providing experimentalevidence that spin waves in CrI$_3$ can have robust topological propertiesuseful for dissipationless spintronic applications.

Topological spin excitations in honeycomb ferromagnet CrI$_3$