We report the phase diagram of the doping series U_2Pt_xRh_(1-x)C_2, studied through measurements of resistivity, specific heat and magnetic susceptibility. The Neel temperature of U_2RhC_2 of ~ 22 K is suppressed with increasing Pt content, reaching zero temperature close to x=0.7, where we observed signatures of increased quantum fluctuations. In addition, evidence is presented that the antiferromagnetic state undergoes a spin-reorientation transition upon application of an applied magnetic field. This transition shows non-monotonic behaviour as a function of x, peaking at around x=0.3. Superconductivity is observed for x>=0.9, with T_c increasing with increasing x. The reduction in T_c and increase in residual resistivity with decreasing Pt content is inconsistent with the extension of the Abrikosov-Gorkov theory to unconventional superconductivity.
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