We report the doping dependence of the planar
63Cu Knight shift (
63K), the nuclear spin-lattice relaxation rate
63(1/T
1T) and the Gaussian spin-echo decay rate
63(1/T
G) for the high-T
c monolayer HgBa
2CuO
4+δ over a wide doping range [T
c=50, 72, 82, K (underdoping), 96, K (optimal doping) and 30, K (overdoping)], measured by the Cu NMR spin-echo technique. We found the following new facts; (1) both the static and the dynamical spin susceptibilities exhibit the pseudo spin-gap behavior over a wide q region around the staggered mode Q, (2) the dynamical pseudo spin-gap in 1/T
1T can mainly be ascribed to the static one in 1/T
G, and (3) a spin fluctuation amplitude probed by the empirical ratio T
1T/(T
G)
2 is a monotonic decreasing function of the doping level but not proportional to T
c. From comparison with La
2-xSr
xCuO
4, we discussed the role of the pseudo spin-gap in the high-T
c superconductivity.
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