  We report the divergence of the nonlinear component of the bulk
susceptibility in NaxCoO2 (0.3<x<0.62) as T goes to 0 K. These experiments
provide an striking evidence of the existence of a ferromagnetic phase
transition at zero Kelvin (quantum phase transition). The possible role of
magnetic fluctuations in the superconductivity is discussed to the light of the
observed (H,T) scaling of the magnetization, which implies a local character of
the fluctuations.
