Microscopic theory of a precessing ferromagnet for ultrasensitive magnetometry

Levitated systems have great potential in quantum sensing and exploring fundamental physics at the macroscopic scale. Of particular interest are recent works suggesting that a levitated ferromagnet can beat the standard quantum limit of magnetometry, a benchmark for quantum sensors. In this work, we show how a microscopic theory capturing atomic-scale spin-lattice interactions can be used to fully explain the emergence of collective precession dynamics of a levitated ferromagnet and the origin of its enhanced magnetometric sensitivity beyond that of independent spins. Our theory further takes us to two innovative experimental designs of immediate interest: measurement of the celebrated Berry phase with a precessing ferromagnetic needle and the use of its nutation motion to sense a low-frequency oscillating magnetic field. With a microscopic theory established for levitated ferromagnetic needles, future studies of macroscopic quantum effects and the associated quantum-classical transition also become possible.