^{31}P and ^{75}As NMR measurements were performed in superconducting BaFe_2(As_{0.67}P_{0.33})_2 with T_c = 30 K. The nuclear-spin-lattice relaxation rate T_1^{-1} and the Knight shift in the normal state indicate the development of antiferromagnetic fluctuations, and T_1^{-1} in the superconducting (SC) state decreases without a coherence peak just below T_c, as observed in (Ba_{1-x}K_{x})Fe_2As_2. In contrast to other iron arsenide superconductors, the T_1^{-1} propto T behavior is observed below 4K, indicating the presence of a residual density of states at zero energy. Our results suggest that strikingly different SC gaps appear in BaFe_2(As_{1-x}P_{x})_2 despite a comparable T_c value, an analogous phase diagram, and similar Fermi surfaces to (Ba_{1-x}K_{x})Fe_2As_2.
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