Optimization of SQUID magnetometers and gradiometers for magnetic-field-fluctuation thermometers

We report on the design and optimization of SQUID magnetometers and gradiometers intended for use in compact Magnetic-Field-Fluctuation Thermometers (MFFTs). The MFFT is a novel implementation of a noise thermometer, in which the thermally driven Johnson noise currents are detected by measuring the corresponding fluctuations of the magnetic field. This inductive readout can be realized by means of a classical wire-wound pick-up coil connected to a SQUID current sensor or by using single-chip SQUID magnetometers or gradiometers. In either case the pick-up coil should be as close as possible to the surface of the metallic temperature sensor in order to maximize amplitude and bandwidth of the spectral density of the flux noise. However, the spectral density depends on the geometries of pick-up coil and temperature sensor as well. Here we discuss the particular case of planar magnetometers and gradiometers. By solving the forward problem for an infinite slab we are able to calculate the spectral density of the flux noise in pick-up coils of arbitrary shape. The model is then applied to identify the optimal gradiometer configuration to be used in the MFFT. Finally, we compare calculations of this simple model with experimental data obtained in real setups. A MFFT containing such an optimized SQUID gradiometer was successfully operated down to 7 mK even without a superconducting magnetic shielding