Systematic P-NMR studies on LaFe(As_1-xP_x)(O_1-yF_y) with y=0.05 and 0.1 have revealed that the antiferromagnetic spin fluctuations (AFMSFs) at low energies are markedly enhanced around x=0.6 and 0.4, respectively, and as a result, Tc exhibits respective peaks at 24 K and 27 K against the P-substitution for As. This result demonstrates that the AFMSFs are responsible for the increase in Tc for LaFe(As_1-xP_x)(O_1-yF_y) as a primary mediator of the Cooper pairing. From a systematic comparison

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... AFMSFs with a series of (La_1-zY_z)FeAsO_δ compounds in which Tc reaches 50 K for z=0.95, we remark that a moderate development of AFMSFs causes the Tc to increase up to 50 K under the condition that the local lattice parameters of FeAs tetrahedron approaches those of the regular tetrahedron. We propose that the T_c of Fe-pnictides exceeding 50 K is maximized under an intimate collaboration of the AFMSFs and other factors originating from the optimization of the local structure.