  There is currently fundamental and technological interest in measuring and
manipulating nanoscale magnets, particularly in the quantum coherent regime. To
observe the dynamics of such systems one requires a magnetometer with not only
exceptional sensitivity but also high gain, wide bandwidth and low backaction.
We demonstrate a dispersive magnetometer consisting of a two-junction SQUID in
parallel with an integrated, lumped-element capacitor. Input flux signals are
encoded as a phase modulation of the microwave drive tone applied to the
magnetometer, resulting in a single quadrature voltage signal. For strong drive
power, the nonlinearity of the resonator results in quantum limited, phase
sensitive parametric amplification of this signal, which improves flux
sensitvity at the expense of bandwidth. \ Depending on the drive parameters,
the device performance ranges from an effective flux noise of
0.29\textbf{}$\mu\Phi_{0}$Hz$^{-\frac{1}{2}}$ and 20 MHz of signal bandwidth to
a noise of 0.14 $\mu\Phi_{0}$Hz$^{-\frac{1}{2}}$ and a bandwidth of 0.6 MHz.
These results are in excellent agreement with our theoretical model.
