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We present a comprehensive $1/S$ study of the field-induced dynamicalproperties of the nearest-neighbor $XXZ$ antiferromagnet on a honeycomb latticeusing the formalism of the nonlinear spin-wave theory developed for this model.The external magnetic field controls spin frustration in the system and inducesnon-collinearity of the spin structure, which is essential for the two-magnondecay processes. Our results include an intriguing field-evolution of theregions of the Brillouin zone wherein decays of spin excitations are prominent,a detailed classification of the decay channels involving magnons from bothexcitation branches, and a thorough analysis of the singularities in the magnonspectra due to coupling to the two magnon continuum, all of which areillustrated for several field and anisotropy values. We highlight a number offeatures related to either the non-Bravais nature of the lattice, or theexistence of the Dirac-like points in the spectrum. In addition, the asymptoticbehavior of the decay rates near high-symmetry points is analyzed in detail.The inelastic neutron-scattering spin-spin structure factor is obtained in theleading $1/S$ order and is shown to exhibit qualitatively distinct fingerprintsof the decay-induced magnon dynamics such as quasiparticle peaks broadened bydecays and strong spectral weight redistribution.

Field-induced dynamical properties of the $XXZ$ model on a honeycomb lattice