Spin-Orbit induced linear magnon-phonon coupling in 2D van der Waals magnets

Standard ab initio treatments of spin and lattice dynamics neglect the coupling between these two degrees of freedom, which turns out to be often a harsh approximation due to the energy overlapping of the respective normal modes. In the context of localized-spin models, the spin-lattice coupling is normally modelled with a non-linear term ---stemming from the dependence of the exchange couplings on the lattice positions--- whose treatment is demanding even in the case of model Hamiltonians and often restricted to the elastic regime only. However, it is known since the late 40es that a linear spin-lattice coupling may arise in the presence of magnetic anisotropies, whose contribution may become dominant with respect to higher order terms. By means of a supercell approach within Density-Functional Theory we provided, to the best of our knowledge, the first ab initio computation of the SOC-induced spin-lattice couplings in a real material. Our calculations for the CrI3 van der Waals magnet ---a recently-synthetized 2D material where a large spin-orbit coupling stabilizes 2D long-range magnetic order and is argued to sustain topological magnetic excitations--- show that a polaritonic-like hybridization between the magnon and the phonon modes may induce ~meV gap in its magnetic excitation spectrum close to the K point of the Brillouin Zone.