We present a systematic In-115 NQR study on the heavy-fermion compounds CeRh1-xIrxIn5 (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 0.35less than or equal toxless than or equal to0.55. 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 CeIrIn5 (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 Tsimilar to0.4 K, with the value (T-1)(Tc)/(T-1)(low T) increasing with decreasing x, likely due to low-lying magnetic excitations associated with the coexisting magnetism.
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