We report systematic 57Fe-NMR and 75As-NMR/NQR studies on an underdoped sample (T_c=20 K), an optimally doped sample (T_c=28 K), and an overdoped sample (T_c=22 K) of oxygen-deficient iron (Fe)-based oxypnictide superconductor LaFeAsO_{1-y}$. A microscopic phase separation between superconducting domains and magnetic domains is shown to take place in the underdoped sample, indicating a local inhomogeneity in association with the density distribution of oxygen deficiencies. As a result, 1/T_1T in the normal state of the superconducting domain decreases significantly upon cooling at both the Fe and As sites regardless of the electron-doping level in LaFeAsO_{1-y}. On the basis of this result, we claim that $1/T_1T$ is not always enhanced by antiferromagnetic fluctuations close to an antiferromagnetic phase in the underdoped superconducting sample. This contrasts with the behavior in hole-doped Ba_{0.6}K_{0.4}Fe2As2(T_c= 38 K), which exhibits a significant increase in $1/T_1T$ upon cooling. We remark that the crucial difference between the normal-state properties of LaFeAsO_{1-y} and Ba_{0.6}K_{0.4}Fe2As2 originates from the fact that the relevant Fermi surface topologies are differently modified depending on whether electrons or holes are doped into the FeAs layers.
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