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The temperature (T) dependence of the muon and $^{63}$Cu nuclear spin-latticerelaxation rates $1/T_1$ in YbCu4.4Au0.6 is reported over nearly four decades.It is shown that for $T\to 0$ $1/T_1$ diverges following the behaviourpredicted by the self-consistent renormalization (SCR) theory developed byMoriya for a ferromagnetic quantum critical point. On the other hand, thestatic uniform susceptibility $\chi_s$ is observed to diverge as $T^{-2/3}$ and$1/T_1T\propto \chi_s^2$, a behaviour which is not accounted for by SCR theory.The application of a magnetic field $H$ is observed to induce a crossover to aFermi liquid behaviour and for $T\to 0$ $1/T_1$ is found to obey the scalinglaw $1/T_1(H)= 1/T_1(0)[1+(\mu_BH/k_BT)^2]^{-1}$.

Magnetic field induced non-Fermi liquid to Fermi liquid crossover at the quantum critical point of YbCu$_{5-x}$Au$_{x}$