  LuCuGaO4 has magnetic Cu2+ and diamagnetic Ga3+ ions distributed on a
triangular bilayer and is suggested to undergo a spin-glass transition with T_g
approximately 0.4 K. Using muSR and neutron scattering measurements, we show
that at low temperature the spins form a short-range correlated state with spin
fluctuations detectable over a wide range of timescales: at 0.05 K magnetic
fluctuations can be detected in both the muSR time window and also extending
beyond 7 meV in the inelastic neutron scattering response, indicating magnetic
fluctuations spanning timescales between 1E-5 and 1E-10 seconds. The dynamical
susceptibility scales according to the form \chi''(\omega)T^\alpha, with
\alpha=1, throughout the measured temperature range (0.05 - 50 K). These
effects are associated with quantum fluctuations and some degree of structural
disorder in ostensibly quite different materials, including certain heavy
fermion alloys, kagome spin liquids, quantum spin glasses, and valence bond
glasses. We therefore suggest LuCuGaO4 is an interesting model compound for the
further examination of disorder and quantum magnetism.
