We operate a nitrogen vacancy (NV-) diamond magnetometer at ambient temperatures and study the dependence of its bandwidth on experimental parameters including optical and microwave excitation powers. We introduce an analytical theory that yields an explicit formula for the response of an ensemble of NV- spins to an oscillating magnetic field, such as in NMR applications. We measure a detection bandwidth of 1.6 MHz and a sensitivity of 4.6 nT/Hz^(1/2), unprecedented in a detector with this active volume and close to the photon shot noise limit of our experiment.
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