  We present measurements of the dynamics of a polarized magnetic environment
coupled to the flux degree of freedom of rf-SQUID flux qubits. The qubits are
used as both sources of polarizing field and detectors of the environmental
polarization. We probe dynamics at timescales from 5 $\mu$s to 5 ms and at
temperatures between 12.5 and 22 mK. The measured polarization versus
temperature provides strong evidence for a phase transition at a temperature of
$5.7\pm 0.3$ mK. Furthermore, the environmental polarization grows initially as
$\sqrt{t}$, consistent with spin diffusion dynamics. However, spin diffusion
model deviates from data at long timescales, suggesting that a different
phenomenon is responsible for the low-frequency behavior. A simple $1/f$ model
can fit the data at all time scales but it requires empirical low- and
high-frequency cutoffs. We argue that these results are consistent with an
environment comprised of random clusters of spins, with fast spin diffusion
dynamics within the clusters and slow fluctuations of the total moments of the
clusters.
