Dynamical spin correlations of the kagome antiferromagnet

TL;DR

This study investigates the temperature-dependent dynamical spin correlations in the kagome antiferromagnet, revealing how Dzyaloshinskii--Moriya interactions influence spin dynamics and ground states, with implications for experimental observations.

Contribution

The paper provides a detailed analysis of dynamical spin structure factors in the kagome antiferromagnet, highlighting the effects of Dzyaloshinskii--Moriya interactions using finite-temperature Lanczos calculations.

Findings

Chiral low-energy spin fluctuations dominate without DM interactions.

Out-of-plane DM interactions induce anisotropic response and ground-state order.

Results agree with neutron scattering and NMR data on herbertsmithite and YCu₃(OH)₆Cl₃.

Abstract

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 $S({\bf q}, \omega)$ 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 $120^\circ$ AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of $S({\bf q}, \omega)$ 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 $D^z > 0.1 J$. 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 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 YCu$_3$(OH)$_6$Cl$_3$, where its substantial $D^z \approx 0.25 J$ interaction is found to strongly affect the spin dynamics.