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Physical Review Letters

Complex Inductance, Excess Noise, and Surface Magnetism in dc SQUIDs

S. Sendelbach, David J. Hover, Michael Mück, Robert McDermott

Published Sep 9, 2009• 57 citations
Publisher

Abstract

We have characterized the complex inductance of dc SQUIDs cooled to millikelvin temperatures. The SQUID inductance displays a rich, history-dependent structure as a function of temperature, with fluctuations of order 1 fH. At a fixed temperature, the SQUID inductance fluctuates with a 1/f power spectrum; the inductance noise is highly correlated with the conventional 1/f flux noise. The data are interpreted in terms of the reconfiguration of clusters of surface spins, with correlated fluctuations of effective magnetic moments and relaxation times.

DOI
10.1103/physrevlett.103.117001

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We have characterized the complex inductance of dc SQUIDs cooled to millikelvin temperatures. The SQUID inductance displays a rich, history-dependent structure as a function of temperature, with fluctuations of order 1 fH. At a fixed temperature, the SQUID inductance fluctuates with a 1/f power spectrum; the inductance noise is highly correlated with the conventional 1/f flux noise. The data are interpreted in terms of the reconfiguration of clusters of surface spins, with correlated fluctuations of effective magnetic moments and relaxation times.
We have characterized the temperature dependence of the flux threading dc SQUIDs cooled to millikelvin temperatures. The flux increases as 1/T as temperature is lowered; moreover, the flux change is proportional to the density of trapped vortices. The data are compatible with the thermal polarization of surface spins in the trapped fields of the vortices. In the absence of trapped flux, we observe evidence of spin-glass freezing at low temperature. These results suggest an explanation for the universal 1/f flux noise in SQUIDs and superconducting qubits.
The spectral density S(Φ)(f) = A(2)/(f/1 Hz)(α) of magnetic flux noise in ten dc superconducting quantum interference devices (SQUIDs) with systematically varied geometries shows that α 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.
We have fabricated Y1Ba2Cu3O7−x step-edge junction dc superconducting quantum interference devices (SQUIDs) and characterized their noise performance. The current-voltage characteristics of our SQUIDs are of resistively shunted junction type with critical current densities jc of about 104 A/cm2 and maximum flux to voltage transfer functions δV/δΦ of 20 μV/Φ0 at 77 K. We compare model predictions for 1/f noise in dc SQUIDs with experimental data and show that the frequency dependent noise in our devices results from critical current fluctuations of the Josephson junctions. A bias current reversing technique is effective in suppressing this noise contribution. A flux noise Φn of 80 μΦ0/Hz1/2 at 1 Hz and 77 K was measured on a dc SQUID with an inductance Ls of 60 pH.
We examine the behavior of low frequency flux noise measured in ten Nb-NbOx-Pbln dc SQUIDs in the temperature range 1 K to 20 mK. As previously reported, the flux noise power spectrum SΦ(f) typically scales with frequency as A/fα. Remark ably, the excess noise power A at 1 Hz increases as the temperature is decreased below about 0.7 K, saturating to a value around (10 μΦα)2/Hz below about 0.2 K. Here we report on the dependence of both the magnitude A and the slope a on the size and linewidth of the SQUID loops. In particular, at the lowest temperatures we find that a declines to values as low as 0.5 in the smallest devices, while a is in the range 0.9-1 for the largest devices.
The excess low-frequency flux noise in dc superconducting quantum interference devices (SQUIDs) operated at ultra-low temperatures was studied. A large number of single SQUIDs as well as SQUID arrays from 16 wafers fabricated over a period of six years were characterized at 4.2 K and1/fon the SQUID design or fabrication parameters. In contrast, below 4.2 K the low-frequency noise changed moderately or increased strongly depending on whether the bottom Nb or the insulation layer were fabricated in our newer sputter system instead of the older one. The corresponding excess noise levels ε1/fat1/f∝ f-αwith α typically around 0.6 for good devices. For devices with strong low-frequency excess noise, α increases up to about 0.9. The best energy resolution ε achieved so far with a 50 pH test SQUID operated at 16 mK is 0.62 h at 100 kHz, increasing to 1.64 h at 1 kHz and 14 h at 10 Hz.
The noise characteristics at low frequencies are studied for various planar dc SQUIDs made of junctions with different barrier materials of a-Si, aluminum oxide, and niobium oxide. It is found that fluctuations of the parameters of individual junctions contribute to the flux noise of the SQUIDs in a magnitude of the same order with the apparent flux noise. The magnitude of the flux noise due to the parameter fluctuations depends on the barrier material and on the inductance parameter βL . We have observed a telegraph noise in the voltage time trace and a Lorentzian in the voltage power spectrum for a current-biased SQUID. As a source of the parameter fluctuations, capture and emission of electrons at the trapping sites in the barrier are indicated.