1/f noise from a finite entropy bath: Comparison with flux noise in SQUIDs

The primary low-frequency noise in superconducting quantum interference devices (SQUIDs) at low temperature is flux noise with a power spectral density of the form S( f)α1/fαwithα≈ 1. Experiments show this noise is due to independent clusters of interacting spins at the metalinsulator interface of the Josephson junction. The temperature dependences of the amplitude and the spectral exponent α are such that the noise spectra S( f) of devices taken at different temperatures cross each other at a common crossing frequency fc, so that S(fc) is constant over a wide range of temperatures. Presented here are Monte Carlo simulations of a Heisenberg spin model modified with a type of dynamic constraint that depends on the configurational entropy of clusters of spins. The constraint arises from assuming that coupling between clusters of spins and the thermal reservoir is mediated by a local bath. Noise in the alignment of this model shows similarities to the temperaturedependent flux noise of SQUIDs, reproducing the relationship between α and the amplitude that leads to the existence of a crossing frequency fc of spectra at different temperatures.