Dynamical spin correlations of the kagome antiferromagnet

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 $S(\mathbf{q},\ensuremath{\omega})$ 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 ${120}^{\ensuremath{\circ}}$ AFM order parameter dominate the dynamical response. This leads to a nontrivial frequency dependence of $S(\mathbf{q},\ensuremath{\omega})$ 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 ${\mathrm{YCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{3}$, where its substantial ${D}^{z}\ensuremath{\approx}0.25J$ interaction is found to strongly affect its spin dynamics.

Topics & Concepts