1/f Flux Noise in low-T$_c$ SQUIDs due to Superparamagnetic Phase Transitions in Defect Clusters

TL;DR

This paper explains the 1/f flux noise in low-Tc SQUIDs as arising from superparamagnetic phase transitions in defect clusters, providing a comprehensive model that matches experimental observations.

Contribution

It introduces a self-consistent model linking flux noise to superparamagnetic transitions in defect clusters, explaining experimental data and noise characteristics.

Findings

Flux noise arises from superparamagnetic phase transitions in defect clusters.

The model explains the frequency exponent α ≈ 0.8 independent of system size.

Temperature dependence of inductance noise is explained via fluctuation-dissipation theorem.

Abstract

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' macro-spin 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 $\alpha\sim 0.8$ 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.