(a) False color SEM micrograph of the dispersive SQUID magnetometer. The SQUID loop is shown in the inset. The fast flux line can be used to apply an external flux Φ. (b) Schematic of the device. The flux bias circuit is shown on the left, and the crosses represent the Josephson junctions. An incoming microwave excitation signal (red arrow) is reflected (blue arrow) with a flux-dependent phase ϕ. (c) The Josephson inductance of a Josephson junction is given by the slope of the sinusoidal ϕ-I relation and depends on the phase ϕ across the junction. (d) Resonance curves for the oscillating current of the tank circuit and the phase ϕ of the reflected microwave signal. A small change of the flux Φ shifts the resonance frequency and is thus equivalent to a change of the excitation frequency. At large amplitude (blue), the nonlinearity of the inductance [see panel (c)] leads to a downshift of the resonance frequency as the resonance is approached, and thus a bending of the resonance curve towards the left. The resulting steeper dependence of ϕ (red circle) on the applied flux leads to improved sensitivity.