Abstract
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 16 devices, taken in the $20\text{--}80$ mK temperature range, to the spin-diffusion model. This allows us to extract the spin-diffusion constant and its temperature dependence, suggesting that the spin system is close to a spin-glass phase transition.
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