Topological spin excitations in honeycomb ferromagnet CrI${}_3$

In two dimensional honeycomb ferromagnets, bosonic magnon quasiparticles (spin waves) may either behave as massless Dirac fermions or form topologically protected edge states. The key ingredient defining their nature is the next-nearest neighbor Dzyaloshinskii-Moriya (DM) interaction that breaks the inversion symmetry of the lattice and discriminates chirality of the associated spin-wave excitations. Using inelastic neutron scattering, we find that spin waves of the insulating honeycomb ferromagnet CrI${}_3$ ($T_C=61$ K) have two distinctive bands of ferromagnetic excitations separated by a $\sim$4 meV gap at the Dirac points. These results can only be understood by considering a Heisenberg Hamiltonian with DM interaction, thus providing experimental evidence that spin waves in CrI${}_3$ can have robust topological properties useful for dissipationless spintronic applications.