Nuclear relaxation rates in the Herbertsmithite Kagome antiferromagnets ZnCu3(OH)6Cl2

TL;DR

This study calculates nuclear relaxation rates in Herbertsmithite Kagome antiferromagnets using Gaussian approximation and frequency moments, revealing insights into spin dynamics and correlations at various temperatures.

Contribution

It introduces a combined approach of Gaussian approximation and frequency moment extrapolation to analyze NMR relaxation rates in Kagome antiferromagnets, aligning well with experimental data.

Findings

Gaussian approximation captures low-temperature drop in relaxation rates

Frequency moment extrapolation matches room temperature NMR data

Long-range dynamic correlations emerge at low temperatures

Abstract

Local spectral functions and Nuclear Magnetic Relaxation (NMR) rates, 1/T1, for the spin-half Heisenberg antiferromagnet on the Kagome Lattice are calculated using 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.