Magnetism in SQUIDs at Millikelvin Temperatures

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.

Figure 1

(a) Schematic of two-stage SQUID amplifier. The first-stage Al SQUID is biased with a voltage, and the current through this device is read out with a Nb SQUID operated in a flux-locked loop. Both devices are operated inside a superconducting aluminum shield (dashed box). (b) Layout of the thin-film SQUIDs. The Al SQUID has inner and outer dimensions 60 and $300\mu \mathrm{m}$; the Nb SQUID has inner and outer dimensions $200\mu \mathrm{m}$ and 1 mm. (c) Power spectral density of flux noise of the two-SQUID amplifier measured at 100 mK.

Figure 2

Temperature dependence of the flux threading the SQUIDs of the amplifier described in Fig. 1. (a) $I\mathrm{\text{−}}\Phi$ characteristic of the Al first-stage SQUID measured at three temperatures; flux ${\Phi }_1$ through the Al first-stage SQUID is plotted on the horizontal axis, and current $I$ through the Al first-stage SQUID is expressed as a flux ${\Phi }_2$ coupled to the Nb second-stage SQUID and plotted on the vertical axis. (b) Quasistatic flux threading the SQUIDs vs temperature.

Figure 3

(a) Temperature dependence of the flux threading a 350 pH $\mathrm{Nb}/\mathrm{Al}$ $\mathrm{oxide}/\mathrm{Nb}$ SQUID, for different fields $B_{\mathrm{fc}}$ applied as the device was cooled through the superconducting transition (from bottom to top, $B_{\mathrm{fc}}=-500$, $-20$, 0, 20, 50, 100, 200, $500\mu \mathrm{T}$). (b) Temperature-induced flux change $\Delta \Phi =\Phi (100\mathrm{mK})–\Phi (500\mathrm{mK})$ on cooling from 500 to 100 mK vs cooling field $B_{\mathrm{fc}}$. A linear fit to the data yields a slope $\Delta \Phi /B_{\mathrm{fc}}=1.3{\Phi }_0/\mathrm{mT}$.

Figure 4

Temperature dependence of the flux threading narrow ($2\mu \mathrm{m}$) linewidth $\mathrm{Nb}/\mathrm{Al}$ $\mathrm{oxide}/\mathrm{Nb}$ SQUIDs with inductances 160 and 870 pH. SQUID loop geometry is shown in the inset.