Magnetic Flux Noise in dc SQUIDs: Temperature and Geometry Dependence

The spectral density $S_{\Phi }(f)=A^2/(f/1\mathrm{Hz}{)}^{\alpha }$ of magnetic flux noise in ten dc superconducting quantum interference devices (SQUIDs) with systematically varied geometries shows that $\alpha$ increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean-square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID. These results are incompatible with a model based on the random reversal of independent, surface spins.

Figure 1

Configuration of measurement system to measure flux noise in three SQUIDs. The bias current $I_b$ enables the measurement of the middle SQUID. The static voltage across the SQUID is canceled by the current $I_r$ applied to $R_c$.

Figure 2

Power spectra $S_{\Phi }(f)$. (a) As-acquired flux noise spectral densities for SQUID II.3 at 11 temperatures. Inset shows data at 0.1 K with corresponding fit to $A^2/(f/1\mathrm{Hz}{)}^{\alpha }+C^2$ (dashed line). Fits of $S_{\Phi }(f)$ for (b) SQUID I.1 at 10 temperatures and (c) SQUID II.3 at 11 temperatures.

Figure 3

Temperature dependence of $1/f$ flux noise for 10 SQUIDs. (a), (b) Fit coefficients $A^2$ for SQUIDs I and II vs $T$. (c), (d) Fit coefficients $\alpha$ for SQUIDs I and II vs $T$. Confidence in fits is $\pm 10\%$ in (a), (b); $\pm 0.03$ ($T\le 1.1\mathrm{K}$) and $\pm 0.05$ ($T>1.1\mathrm{K}$) in (c); and $\pm 0.03$ ($T\le 1.1\mathrm{K}$) and $\pm 0.07$ ($T>1.1\mathrm{K}$) in (d).

Figure 4

Mean-square flux noise, inferred from measured power spectra using Eq. (2), vs $T$. (a) Chip I and (b) Chip II. Horizontal dashed lines represent the predictions of Eqs. (1, 2) for the values of $R$ and $W$ listed in Table .

Figure 5

Scaling of noise power with $R$ for SQUIDs I for ten temperatures from 0.1 K to 4.0 K. (a) $S_{\Phi }(54\mathrm{Hz})$ vs $R$. Dashed line indicates scaling with $R$, with arbitrary magnitude. (b) $⟨{\Phi }^2⟩$ vs $R$. Dashed line represents prediction of Eq. (1).