We present a systematic ^{115}In NQR study on the heavy fermion compounds CeRh_{1-x}Ir_xIn_5 (x=0.25, 0.35, 0.45, 0.5, 0.55 and 0.75). The results provide strong evidence for the microscopic coexistence of antiferromagnetic (AF) order and superconductivity (SC) in the range of 0.35 leq x leq 0.55. Specifically, for x=0.5, T_N is observed at 3 K with a subsequent onset of superconductivity at T_c=0.9 K. T_c reaches a maximum (0.94 K) at x=0.45 where T_N is found to be the highest (4.0 K). Detailed analysis of the measured spectra indicate that the same electrons participate in both SC and AF order. The nuclear spin-lattice relaxation rate 1/T_1 shows a broad peak at T_N and follows a T^3 variation below T_c, the latter property indicating unconventional SC as in CeIrIn_5 (T_c=0.4 K). We further find that, in the coexistence region, the T^3 dependence of 1/T_1 is replaced by a T-linear variation below Tsim 0.4 K, with the value frac{(T_1)_{T_c}}{(T_1)_{low-T}} increasing with decreasing x, likely due to low-lying magnetic excitations associated with the coexisting magnetism.
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