Magnon chiral damping beyond the Dzyaloshinskii-Moriya interaction

Magnon chiral damping denotes damping that is asymmetric with respect to the magnon wave vector. Such nonreciprocity has been attributed to antisymmetric Dzyaloshinskii-Moriya spin interactions. Here, we provide an alternative theoretical explanation of magnon chiral damping using linear spin-wave theory and antisymmetric Gilbert damping introduced within the Landau-Lifshitz-Gilbert equation of motion. First, employing a minimal model of a single sublattice ferromagnet on a rectangular lattice, we show that the effective magnon damping is independent of the system's energy, including contributions from Dzyaloshinskii-Moriya interactions. Considering scalar nonlocal Gilbert damping, the effective damping parameter α eff becomes wave-vector dependent. In the long-wavelength limit, α eff acquires a quadratic dependence on. Furthermore, the antisymmetric component of the Gilbert damping tensor gives rise to asymmetric (nonreciprocal) magnon damping. We find the asymmetry to be linear in in the long-wavelength limit, consistent with recent experiments. Extending the analysis to a two-sublattice system, we consider cross-sublattice Gilbert damping. In the presence of only scalar Gilbert damping, broken reciprocity in magnon relaxation arises from Dzyaloshinskii-Moriya interactions. In contrast, the cross-sublattice antisymmetric component of the Gilbert damping tensor can generate nonreciprocal magnon damping even if the Dzyaloshinskii-Moriya interaction is parametrically set to zero, providing an alternative mechanism for asymmetric spin-wave relaxation. Notably, the nonreciprocity induced by antisymmetric Gilbert damping is roughly an order of magnitude larger than that arising from Dzyaloshinskii-Moriya interactions.