  A quantum limit on the measurement of magnetic field has been recently
pointed out, stating that the so-called Energy Resolution $E_\mathrm{R}$ is
bounded to $E_\mathrm{R} \gtrsim \hbar$. This limit holds indeed true for the
vast majority of existing quantum magnetometers, including SQUIDs, solid state
spins and optically pumped atomic magnetometers. However, it can be surpassed
by highly correlated spin systems, as recently demonstrated with a
single-domain spinor Bose-Einstein Condensate. Here we show that similar and
potentially much better resolution can be achieved with a hard ferromagnet
levitated above a superconductor at cryogenic temperature. We demonstrate
$E_\mathrm{R}=\left( 0.064 \pm 0.010 \right) \, \hbar$ and anticipate that
$E_\mathrm{R}<10^{-3} \, \hbar$ is within reach with near-future improvements.
This finding opens the way to new applications in condensed matter, biophysics
and fundamental science. In particular, we propose an experiment to search for
axionlike dark matter and project a sensitivity orders of magnitude better than
in previous searches.
