Magnon-phonon interactions enhance the gap at the Dirac point in the spin-wave spectra of CrI$_3$ two-dimensional magnets

TL;DR

This study investigates the origin of the Dirac point gap in CrI3 monolayers, revealing that magnon-phonon interactions significantly enhance the gap beyond what intralayer anisotropies alone can explain.

Contribution

The paper introduces a combined theoretical approach showing that magnon-phonon coupling plays a crucial role in the spin-wave gap in CrI3, challenging previous assumptions about anisotropy effects.

Findings

Computed magnon gap is smaller than experimental estimates.

Lattice vibrations strongly couple with magnetic excitations.

Magnon-phonon interactions can increase the gap to approximately 4 meV.

Abstract

Recent neutron-diffraction experiments in honeycomb CrI$_3$ 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 CrI$_3$, 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 $\approx 4$~meV around the Dirac point of the CrI$_3$ monolayer.