We report a systematic investigation of Ba[Fe(1-x)Co(x)]2As2 based on transport and 75-As NMR measurements, and establish the electronic phase diagram. We demonstrate that doping progressively suppresses the uniform spin susceptibility and low frequency spin fluctuations. The optimum superconducting phase emerges at x_c~0.08 when the tendency toward spin ordering completely diminishes. Our findings point toward the presence of a quantum critical point near x_c between the SDW (spin density wave) and superconducting phases.
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