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.
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