1/f flux noise in low-Tc SQUIDs due to superparamagnetic phase transitions in defect clusters

It is shown here that 1/f(alpha) flux noise in conventional low-T-c SQUIDs is a result of low temperature superparamagnetic phase transitions in small clusters of strongly correlated color center defects. The spins in each cluster interact via long-range ferromagnetic interactions. Due to its small size, the cluster behaves like a random-telegraphic macrospin when transitioning to the superparamagnetic phase. This results in 1/f(alpha) noise when ensemble averaged over a random distribution of clusters. This model is self-consistent and explains all related experimental results which includes alpha similar to 0.8 independent of system size. The experimental flux-inductance-noise spectrum is explained through three-point correlation calculations and time-reversal symmetry-breaking arguments. Also, unlike the flux noise, it is shown why the second-spectrum inductance noise is inherently temperature dependent due to the fluctuation-dissipation theorem. A correlation-function calculation methodology using Ising-Glauber dynamics was key for obtaining these results.