Dynamical spin correlations of the kagome antiferromagnet

Temperature-dependent dynamical spin correlations, which can be readily accessed via a variety of experimental techniques, hold the potential of offering a unique fingerprint of quantum spin liquids and other intriguing dynamical states. In this work we present an in-depth study of the temperature-dependent dynamical spin structure factor S(q, omega) of the antiferromagnetic (AFM) Heisenberg spin-1/2 model on the kagome lattice with additional Dzyaloshinskii-Moriya (DM) interactions. Using the finite-temperature Lanczos method on lattices with up to N = 30 sites we find that even without DM interactions, chiral low-energy spin fluctuations of the 120 degrees AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of S(q, omega) and the appearance of a pronounced low-frequency mode at the M point of the extended Brillouin zone. Adding an out-of-plane DM interactions D-z gives rise to an anisotropic dynamical response, a softening of in-plane spin fluctuations, and, ultimately, the onset of a coplanar AFM ground-state order at D-z > 0.1J. Our results are in very good agreement with existing inelastic neutron scattering and temperature-dependent NMR spin-lattice relaxation rate (1/T-1) data on the paradigmatic kagome AFM compound herbertsmithite, where the effect of its small D-z on the dynamical spin correlations is shown to be rather small, as well as with 1/T-1 data on the novel kagome AFM compound YCu3(OH)(6)Cl-3 , where its substantial D-z approximate to 0.25J interaction is found to strongly affect its spin dynamics.