Magnon interaction effects in Kitaev–Heisenberg-\(\Gamma \) model: a mean-field spin-wave analysis

Abstract

We study the effects of magnon interactions in the magnetically ordered phases of the Kitaev–Heisenberg-\(\Gamma \) model, including dispersion correction and spontaneous decay rates. This model shows a rich phase diagram and is believed to describe most of the Kitaev spin liquid candidate materials. Experimentally observed spin excitation spectra in magnetically ordered Kitaev materials usually show features beyond linear spin wave theory(LSWT), which are often interpreted as signatures of proximate spin liquid states. However, magnon interactions in this frustrated model are known to produce important corrections to LSWT, including the pseudo-Goldstone mode gaps in the low energy spin excitations. In this work we employ Hartree-Fock mean-field theory augmented by perturbative corrections of magnon interactions to calculate the entire magnon dispersion and the spontaneous magnon decay in the Kitaev–Heisenberg-\(\Gamma \) model. Our results reveal that the interaction-corrected magnon dispersion in the zigzag state differs significantly from LSWT. This discrepancy underscores the necessity of accounting for magnon interactions when computing spin excitation spectra under these frustrated spin models and comparing them to experimental observations.