Here we present details of a calculation that allows us to extract a surface density of unpaired spins from flux vs. temperature experiments performed on field-cooled dc Superconducting QUantum Interference Devices (dc SQUIDs).
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. Th
e 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.
