  The intrinsic flux noise observed in superconducting quantum interference
devices (SQUIDs) is thought to be due to the fluctuation of electron spin
impurities, but the frequency and temperature dependence observed in
experiments do not agree with the usual 1/f models. We present theoretical
calculations and experimental measurements of flux noise in rf-SQUID flux
qubits that show how these observations, and previous reported measurements,
can be interpreted in terms of a spin-diffusion constant that increases with
temperature. We fit measurements of flux noise in sixteen devices, taken in the
20-80 mK temperature range, to the spin-diffusion model. This allowed us to
extract the spin-diffusion constant and its temperature dependence, suggesting
that the spin system is close to a spin-glass phase transition.
