Power-law dynamics in the spin-liquid kagome latticesSrCr8Ga4O19andZnCu3(OH)6Cl2

Abstract

We consider the polarization function ${P}_{Z}^{\mathrm{exp}}(t)$ measured by the muon-spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) technique for the ${\mathrm{SrCr}}_{8}{\mathrm{Ga}}_{4}{\mathrm{O}}_{19}$ and ${\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}$ spin-liquid systems. We show the functional form of ${P}_{Z}^{\mathrm{exp}}(t)$ to imply that, in the temperature range of order 0.1 K, the spectral-weight function $F(\ensuremath{\omega})$ of the magnetic correlations scales with $1/{|\ensuremath{\omega}|}^{1\ensuremath{-}x}$ ($0<x<1$) in the energy range of $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{eV}$. We derive the parameters involved in $F(\ensuremath{\omega})$ from fits to available experimental data. Inelastic neutron scattering data probing $F(\ensuremath{\omega})$ in the millielectronvolt energy range are consistent with a more conventional behavior. These differences could be due to a variety of spin-dynamics mechanisms, i.e., intrinsic to the kagome layer or related to the magnetic defects that have been evidenced in these compounds, acting at different energies. New $\ensuremath{\mu}\mathrm{SR}$ measurements are proposed and theoretical developments are suggested to pinpoint the mechanisms at play.