  The search for topological spin excitations in recently discovered
two-dimensional (2D) van der Waals (vdW) magnetic materials is important
because of their potential applications in dissipation-less spintronics. In the
2D vdW ferromagnetic (FM) honeycomb lattice CrI$_3$(T$_C$= 61 K), acoustic and
optical spin waves were found to be separated by a gap at the Dirac points. The
presence of such a gap is a signature of topological spin excitations if it
arises from the next nearest neighbor(NNN) Dzyaloshinskii-Moriya (DM) or
bond-angle dependent Kitaev interactions within the Cr honeycomb lattice.
Alternatively, the gap is suggested to arise from an electron correlation
effect not associated with topological spin excitations. Here we use inelastic
neutron scattering to conclusively demonstrate that the Kitaev interactions and
electron correlation effects cannot describe spin waves, Dirac gap and their
in-plane magnetic field dependence. Our results support the DM interactions
being the microscopic origin of the observed Dirac gap. Moreover, we find that
the nearest neighbor (NN) magnetic exchange interactions along the axis are
antiferromagnetic (AF)and the NNN interactions are FM. Therefore, our results
unveil the origin of the observedcaxisAF order in thin layers of CrI$_3$,
firmly determine the microscopic spin interactions in bulk CrI$_3$, and provide
a new understanding of topology-driven spin excitations in 2D vdW magnets.
