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We report the transverse relaxation rates 1/’s of the Cu nuclear spin-echo envelope for double-layer high- cuprate superconductors HgBaCaCuO from underdoped to overdoped. The relaxation rate 1/ of the exponential function (Lorentzian component) shows a peak at 220240 K in the underdoped ( = 103 K) and the optimally doped ( = 127 K) samples but no peak in the overdoped ( = 93 K) sample. The enhancement in 1/ suggests development of the zero frequency components of local field fluctuations. Ultraslow fluctuations are hidden in the pseudogap states.

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