We report the transverse relaxation rates 1/T2's of the Cu63 nuclear spin-echo envelope for double-layer high-Tc cuprate superconductors HgBa2CaCu2O6+δ from underdoped to overdoped. The relaxation rate 1/T2L of the exponential function (Lorentzian component) shows a peak at 220-240 K in the underdoped (Tc=103 K) and the optimally doped (Tc=127 K) samples but no peak in the overdoped (Tc=93 K) sample. The enhancement in 1/T2L suggests a development of the zero frequency components of local field fluctuations. Ultraslow fluctuations are hidden in the pseudogap states.
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