The longitudinal in-plane magnetoresistance (LMR) has been measured in different Ba(Fe_(1-x)Co_x)2As2 single crystals and in LiFeAs. For all these compounds, we find a negative LMR in the paramagnetic phase whose magnitude increases as H^2. We show that this negative LMR can be readily explained in terms of suppression of the spin fluctuations by the magnetic field. In the Co-doped samples, the absolute value of the LMR coefficient is found to decrease with doping content in the paramagnetic phase. The analysis of its T dependence in an itinerant nearly antiferromagnetic Fermi liquid model evidences that the LMR displays a qualitative change of T variation with increasing Co content. The latter occurs at optimal doping for which the antiferromagnetic ground state is suppressed. The same type of analysis for the negative LMR measured in LiFeAs suggests that this compound is on the verge of magnetism.
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