  We consider the polarization function P^{exp}_Z(t) measured by the muon-spin
relaxation (muSR) technique for the SrCr8Ga4O19 and ZnCu3(OH)6Cl2 spin-liquid
systems. We show the functional form of P^{exp}_Z(t) to imply that, in the
temperature range of order 0.1 K, the spectral-weight function F(\omega) of the
magnetic correlations scales with 1/|\omega|^{1 -x} (0 < x < 1) in the energy
range of one microelectronvolt, i.e. \hbar \omega ~ 1 \mu eV. We derive the
parameters involved in F(\omega) from fits to available experimental data.
Inelastic neutron scattering data probing F(\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 muSR
measurements are proposed and theoretical developments are suggested to
pinpoint the mechanisms at play.
