  We report a comprehensive Cu and La NQR study down to 350mK in the stripe
phase of the hole-doped high temperature superconductors with hole
concentration approximately 1/8. We observe the hyperfine broadened NQR
lineshape only below 8-20K for x=1/8, indicating that the ordered moments
continue to fluctuate slowly even below the temperature range where they appear
static in other measurements. Detailed numerical simulations of the Zeeman
perturbed Cu NQR lineshape establish that widely accepted models of periodic
modulation of spin density waves with maximum moment approxiamtely 0.3mu_B can
not account for the NQR lineshape. These results suggest that significant
disorder exists at NQR time scales. By fitting a single model to several sets
of experimental data, we deduce the spatial distribution of the spin
fluctuation frequency scale and its temperature dependence. Our results
indicate that as soon as charge dynamics slow down, the spin fluctuationsbegin
to slow dramatically with spin stiffness approximately 200K. However, the
motional narrowing feature observed in the Zeeman perturbed NQR measurements
suggest that the slowing of the spin fluctuations levels off at frequencies
somewhat below the NQR frequency. By extending the analysis to other hole
concentrations, we find a qualitative difference above and below x=1/8.

Superconductivity