  We have characterized the temperature dependence of the flux threading dc
SQUIDs cooled to millikelvin temperatures. The flux increases as 1/T as
temperature is lowered; moreover, the flux change is proportional to the
density of trapped vortices. The data is compatible with the thermal
polarization of surface spins in the trapped fields of the vortices. In the
absence of trapped flux, we observe evidence of spin-glass freezing at low
temperature. These results suggest an explanation for the "universal" 1/f flux
noise in SQUIDs and superconducting qubits.
