  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.
