  Noise properties of an idealized atomic magnetometer that utilizes spin
squeezing induced by a continuous quantum nondemolition measurement are
considered. Such a magnetometer measures spin precession of $N$ atomic spins by
detecting optical rotation of far-detuned light. Fundamental noise sources
include the quantum projection noise and the photon shot-noise. For measurement
times much shorter than the spin-relaxation time observed in the absence of
light ($\tau_{\rm rel}$) divided by $\sqrt{N}$, the optimal sensitivity of the
magnetometer scales as $N^{-3/4}$, so an advantage over the usual sensitivity
scaling as $N^{-1/2}$ can be achieved. However, at longer measurement times,
the optimized sensitivity scales as $N^{-1/2}$, as for a usual shot-noise
limited magnetometer. If strongly squeezed probe light is used, the Heisenberg
uncertainty limit may, in principle, be reached for very short measurement
times. However, if the measurement time exceeds $\tau_{\rm rel}/N$, the
$N^{-1/2}$ scaling is again restored.
