Model for 1/f Flux noise in Superconducting Aluminum Devices: Impact of External Magnetic Fields

Superconducting quantum interference devices (SQUIDs) and related circuits made of aluminum are known to display $1\mathrm{/}\omega$ flux noise, where $\omega$ is frequency. A recent experiment showed that the application of an external magnetic field in the $10-100$~G range changed the noise to a single Lorentzian peaked at $\omega =0$. Here it is shown that a model based on independent impurity spin flips with coexisting cross and direct mechanisms of spin relaxation may explain these experiments. The model shows that application of an external magnetic field can be used to reduce the impact of flux noise in qubits.