We explore the magnetic excitations of the spin-$\frac{1}{2}$ triangular antiferromagnet ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9$ in its ${120}^{\circ }$ ordered phase using single-crystal high-resolution inelastic neutron scattering. Sharp magnons with no decay are observed throughout reciprocal space, with a strongly renormalized dispersion and multiple soft modes compared to linear spin-wave theory. We propose an empirical parametrization that can quantitatively capture the complete dispersions in the three-dimensional Brillouin zone and explicitly show that the dispersion renormalizations have the direct consequence that $\mathrm{one}\to \mathrm{two}$ magnon decays are avoided throughout reciprocal space, whereas such decays would be allowed for the unrenormalized dispersions. At higher energies, we observe a very strong continuum of excitations with highly structured intensity modulations extending up at least $4\times$ the maximum one-magnon energy. The one-magnon intensities decrease much faster upon increasing energy than predicted by linear spin-wave theory and the higher-energy continuum contains much more intensity than can be accounted for by a two-magnon cross-section, suggesting a significant transfer of spectral weight from the high-energy magnons into the higher-energy continuum states. We attribute the strong dispersion renormalizations and substantial transfer of spectral weight to continuum states to the effect of quantum fluctuations and interactions beyond the spin-wave approximation, and we make connections to theoretical approaches that might capture such effects. Finally, through measurements in a strong applied magnetic field, we find evidence for magnetic domains with opposite senses for the spin rotation in the ${120}^{\circ }$ ordered ground state, as expected in the absence of Dzyaloshinskii-Moriya interactions, when the sense of spin rotation is selected via spontaneous symmetry breaking.

• Received 29 January 2020
• Accepted 15 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.064421