Geometry and temperature dependence of low frequency flux noise in dc SQUIDs

Measurements of low frequency magnetic flux noise in dc SQUIDs demonstrate a spectral density $S_\Phi(f)=A^2/f^\alpha$ in which the magnitude $A$ scales only weakly with the washer geometry and typically $0.5<\alpha<1$. An analytical model assuming non-interacting spins localized to the surface of the SQUID loop predicts that $A^2\propto R/W$ for $R/W\gg1$. Here, $R$ and $W$ are the outer radius and linewidth, respectively. Our numerical calculations extend the analytical results to arbitrary washer geometries. We compare both models to flux noise measurements on several dc SQUIDs fabricated simultaneously on a single chip using a Nb trilayer process. Multiple SQUIDs were measured within a single cool-down. The SQUID geometries were divided into two categories: fixed $W$=500~nm with $3