  We have examined the magnetic properties of polycrystalline, superconducting
YBa_2(Cu_0.96Ni_0.04)_3O_y (y ~ 7, T_sc ~ 75 K) using two local probe
techniques: 170Yb Moessbauer down to 0.1 K and muon spin relaxation (muSR) down
to 1.5 K. At 0.1 K, the 170Yb measurements show the Cu(2) over essentially all
the sample volume carry magnetically correlated moments which are static on the
time-scale of 10^{-9} s. The moments show a distribution in size. The
correlations are probably short range. As the temperature increases, the
correlated moments are observed to fluctuate with measurable rates (in the GHz
range) which increase as the temperature increases and which show a wide
distribution. The muSR measurements also evidence that the fluctuation rates
increase with increasing temperature and there is a distribution. The evidenced
fluctuating, correlated Cu(2) moments coexist at an atomic level with
superconductivity.
