  We discuss the fundamental noise limitations of a ferromagnetic torque sensor
based on a levitated magnet in the tipping regime. We evaluate the optimal
magnetic field resolution taking into account the thermomechanical noise and
the mechanical detection noise at the standard quantum limit (SQL). We find
that the Energy Resolution Limit (ERL), pointed out in recent literature as a
relevant benchmark for most classes of magnetometers, can be surpassed by many
orders of magnitude. Moreover, similarly to the case of a ferromagnetic
gyroscope, it is also possible to surpass the standard quantum limit for
magnetometry with independent spins, arising from spin-projection noise. Our
finding indicates that magnetomechanical systems optimized for magnetometry can
achieve a magnetic field resolution per unit volume several orders of magnitude
better than any conventional magnetometer. We discuss possible implications,
focusing on fundamental physics problems such as the search for exotic
interactions beyond the standard model.
