Magnons in 2D magnetic materials and the role of spin-orbit coupling in the topological properties

Magnetism in 2D materials is accompanied by novel phenomena related to the properties of spin-waves (the so-called magnons). Magnons exhibit topological properties in the family of the layered chromium trihalides like in the case of the paradigmatic CrI₃. In this work we present an ab initio approach to calculate magnons within the framework of many-body perturbation theory and solving the Bethe-Salpeter Equation. The approach is implemented with full spinorial wave functions, accounting for the spin-orbit interaction. The resulting magnon dispersions do not rely on any assumptions of the microscopic magnetic interactions. We characterize the magnon dispersion for the family of monolayers chromium trihalides and we compare the results with the spin wave dispersion obtained from the Heisenberg model. We find clear differences between ab initio results and the spin wave model. Moreover, we focus on the bandgap at the K point of the dispersion. We rationalize the topological bandgap in terms of the spin-orbit coupling originated by the halide atoms.