Topological magnons in CrI₃ monolayers: an itinerant fermion description

Magnons dominate the magnetic response of ferromagnetic two-dimensional crystals such as CrI3. Because of the arrangement of Cr spins in a honeycomb lattice, magnons in CrI3 bear a strong resemblance with electrons in graphene. Neutron scattering experiments carried out in bulk CrI3 show the existence of a gap at the Dirac points, conjectured to have a topological nature. We propose a theory for magnons in CrI3 monolayers based on an itinerant fermion picture, with a Hamiltonian derived from first principles. We obtain the magnon dispersion for 2D CrI3 with a gap at the Dirac points with the same Berry curvature in both valleys. For CrI3 ribbons, we find chiral in-gap edge states. Analysis of the magnon wave functions in momentum space confirms their topological nature. Importantly, our approach does not require a spin Hamiltonian, and can be applied to insulating and conducting 2D materials with any type of magnetic order.