Nuclear relaxation rates in the herbertsmithite kagome antiferromagnets ZnCu3(OH)6Cl2

Local spectral functions and nuclear magnetic relaxation (NMR) rates, 1/T1, for the spin-half Heisenberg antiferromagnet on the Kagome lattice are calculated using the Moriyas Gaussian approximation, as well as through an extrapolation of multiple frequency moments. The temperature dependence of the calculated rates is compared with the oxygen 1/T1 NMR data in Herbertsmithite. We find that the Gaussian approximation for 1/T1 shows behavior qualitatively similar to experiments with a sharp drop in rates at low temperatures, consistent with a spin-gapped behavior. However, this approximation significantly underestimates the magnitude of 1/T1 even at room temperature. Rates obtained from extrapolation of multiple frequency moments give very good agreement with the room temperature NMR data with J=195±20 K and hyperfine couplings determined independently from other measurements. The use of multiple frequency moments also leads to additional low-frequency weight in the local structure factors. The convergence of our calculations with higher-frequency moments breaks down at low temperatures, suggesting the existence of longer-range dynamic correlations in the system despite the very short range static correlations.