Recent neutron-diffraction experiments in honeycomb CrI3โ quasi-2D
ferromagnets have evinced the existence of a gap at the Dirac point in their
spin-wave spectra. The existence of this gap has been attributed to strong
in-plane Dzyaloshinskii-Moriya or Kitaev (DM/K) interactions and suggested to
set the stage for topologically protected edge states to sustain
non-dissipative spin transport. We perform state-of-the-art simulations of the
spin-wave spectra in monolayer CrI3โ, based on time-dependent
density-functional perturbation theory (TDDFpT) and fully accounting for
spin-orbit couplings (SOC) from which DM/K interactions ultimately stem. While
our results are in qualitative agreement with experiments, the computed TDDFpT
magnon gap at the Dirac point is found to be 0.47~meV, roughly 6 times smaller
than the most recent experimental estimates, so questioning that intralayer
anisotropies alone can explain the observed gap. Lattice-dynamical
calculations, performed within density-functional perturbation theory (DFpT),
indicate that a substantial degeneracy and a strong coupling between
vibrational and magnetic excitations exist in this system, providing a possible
additional gap-opening mechanism in the spin-wave spectra. In order to pursue
this path, we introduce an interacting magnon-phonon Hamiltonian featuring a
linear coupling between lattice and spin fluctuations, enabled by the magnetic
anisotropy induced by SOC. Upon determination of the relevant interaction
constants by DFpT and supercell calculations, this model allows us to propose
magnon-phonon interactions as an important microscopic mechanism responsible
for the enhancement of the gap in the range of โ4~meV around the Dirac
point of the CrI3โ monolayer