Monte Carlo Spin Simulations of Magnetic Noise -- The Search for Pivoting

Superconducting quantum interference devices (SQUIDs) show great promise as quantum bits (qubits) but continue to be hindered by flux noise. The flux noise power spectra of SQUIDs go as $1/f^\alpha$, where $\alpha$ is the temperature-dependent noise exponent. Experiments find $0.5 \lesssim \alpha \lesssim 1$. Furthermore, experiments find that the noise power spectra versus frequency at different temperatures pivot about or cross at a common point for each SQUID. To try to better understand the results and motivated by experimental evidence that magnetic moments on the surface of SQUIDS produce flux noise, we present the results of our Monte Carlo simulations of various spin systems on 2D lattices. We find that only spin glasses produce $\alpha \sim 1$ at low temperature. We find that aliasing of the noise power spectra at high frequencies can lead to spectral pivoting if it is in proximity to a knee at a slightly lower frequency. We show that the pivot frequency depends on the method of site selection and how often the magnetization is recorded. The spectral pivoting that occurs in our simulations is due to aliasing and does not explain the spectral pivoting of experiments.