Magnon damping in the zigzag phase of the Kitaev-Heisenberg-$\Gamma$ model on a honeycomb lattice

TL;DR

This paper investigates magnon behavior, including damping and dispersion, in a complex honeycomb lattice model relevant to iridium and ruthenium oxides, using an innovative analytical spin-wave approach.

Contribution

It introduces an unconventional spin-wave expansion method that allows analytical solutions for magnon properties in the Kitaev-Heisenberg-$\Gamma$ model, especially in the zigzag phase.

Findings

Magnon damping is significant and affects neutron-scattering spectra.

Analytical expressions for magnon energies and eigenstates are derived.

Non-linear magnon coupling plays a crucial role in spectral features.

Abstract

We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $\Gamma$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $\alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $\alpha$-RuCl$_3$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is $\Gamma = K>0$, where $K$ is the Kitaev coupling. Within our approach we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of non-linear magnon coupling in interpreting broad features in the neutron-scattering spectra.