Theory for the multiloop dc superconducting quantum interference device magnetometer and experimental verification

A theoretical analysis of the multiloop dc superconducting quantum interference device (SQUID) magnetometer fabricated from low-Tc (transition temperature) or high-Tc materials is presented. Using simple analytic formulas, the essential parameters of a multiloop magnetometer can be estimated: the effective area A, the effective SQUID inductance L, the transfer function VΦ, and the flux density noise √SB. The theoretical predictions are compared with experimental results of seven different low-Tc versions and good agreement is found. Based on the analytical description, a high-Tc magnetometer design with a 7 mm pickup coil and 16 parallel loops giving a sufficiently small SQUID inductance L≂145 pH is presented. At T=77 K a voltage swing 2δV≂8 μV and a white noise √SB≂8 fT/√Hz are predicted assuming a critical current I0=20 μA and a normal resistance R=2 Ω per junction and a damping resistance Rd=R across the SQUID inductance.