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 offering unique fingerprint quantum liquids and other intriguing states. In this work we present an in-depth study temperature-dependent structure factor $S({\bf q}, \omega)$ antiferromagnetic (AFM) Heisenberg spin-1/2 model on kagome lattice with additional Dzyaloshinskii--Moriya (DM) interactions. Using finite-temperature Lanczos method lattices up to $N = 30$ sites find that even without DM interactions, chiral low-energy fluctuations $120^\circ$ AFM order parameter dominate response. This leads nontrivial frequency dependence appearance pronounced low-frequency mode at M point extended Brillouin zone. Adding out-of-plane interactions $D^z$ gives rise anisotropic response, softening in-plane fluctuations, and, ultimately, onset coplanar ground-state $D^z > 0.1 J$. Our results are in very good agreement existing inelastic neutron scattering NMR spin-lattice relaxation rate ($1/T_1$) data paradigmatic herbertsmithite, where effect its small correlations is shown rather small, as well $1/T_1$ novel YCu$_3$(OH)$_6$Cl$_3$, substantial \approx 0.25 J$ interaction found strongly affect dynamics.