Magnons in a Strongly Spin-Orbital Coupled Magnet*

We present the non-linear spin-wave theory calculations of the dynamical response of an extended Kitaev-Heisenberg model for the parameters applicable to α-RuCl₃. We argue that large anisotropic terms of spin-orbit nature necessarily imply strong anharmonic coupling of magnons. Subsequently, the overlap of one- and two-magnon states must lead to broad spectral features in magnon spectrum. These are accompanied by a significant longitudinal component of the structure factor from the two-magnon states that are also broadened. We calculate magnon decay rates due to anharmonic coupling within a self-consistent approach and find our results for the dynamical structure factor to be in a good agreement with both exact diagonalization results for the same set of parameters and experiment.