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.
Figures
17 panels with data across 6 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.
Fig. 1
panel (b): Simulated spin angular momentum $S_z$, lattice angular momentum $L_z$ and their sum $J_z$ (units of $\hbar/2$) against $\omega_L t$ for the $N = 50$ chain, with the time average $\langle L_z\rangle$ and $\omega_L I$ as horizontal lines. The print labels the axis only as $\times10^{-4}$ ($\hbar/2$); values here are in $\hbar/2$. data.csv
panel (c-1): Positions $x/r_0$, $y/r_0$ of the $N = 50$ atoms of the chain at $\omega_L t = 0$, coloured by atom from one end (red) to the other (blue). data.csv
panel (c-2): Positions $x/r_0$, $y/r_0$ of the $N = 50$ atoms of the chain at $\omega_L t = \pi/4$, coloured by atom from one end (red) to the other (blue). data.csv
panel (c-3): Positions $x/r_0$, $y/r_0$ of the $N = 50$ atoms of the chain at $\omega_L t = \pi/2$, coloured by atom from one end (red) to the other (blue). data.csv
panel (c-4): Positions $x/r_0$, $y/r_0$ of the $N = 50$ atoms of the chain at $\omega_L t = \pi$, coloured by atom from one end (red) to the other (blue). data.csv
Fig. 2
The underlying data is not available. The figure is shown in the paper PDF.
Fig. 3
panel (b): Angle $\Omega$ ($^\circ$) between the initial and final needle configurations against the field's polar angle $\theta$ ($^\circ$): numerical results (markers) and the theoretical curve. The two 3D needle sketches above the printed plot are not hosted. data.csv
panel (d): Simulated $M_z$ against $\omega_L t$ for a needle in an oscillating magnetic field (numerical, solid) with a dashed guide line. The print cuts the oscillation at $M_z = 0.4$; the hosted trace keeps that cut, with gaps where it leaves the axes. data.csv
Fig. 4
panel (a): Effective Gilbert damping coefficient $\langle\eta\rangle$ from the simulations against the spin-lattice coupling strength $C_0$, markers joined by a line. data.csv
panel (b): Effective Gilbert damping coefficient $\langle\eta\rangle$ from the simulations against the spin-spin exchange strength $J_0$ (log scale), markers with error bars joined by a line. data.csv
panel (c): Effective Gilbert damping coefficient $\langle\eta\rangle$ from the simulations against the lattice vibration strength $V_0$, markers joined by a line. data.csv
panel (d): Effective Gilbert damping coefficient $\langle\eta\rangle$ from the simulations against the effective lattice temperature $T$ (mK, log scale), markers with error bars. data.csv
panel (c-inset): Inset of panel (c): $\langle\eta\rangle$ against $1/V_0$, open markers with a straight line. data.csv
Fig. 5
panel (a): Gilbert damping coefficient $\langle\eta\rangle$ from the simulations against the number of atoms $N$, grey square markers joined by a line. data.csv
panel (b-1): Positions $x/r_0$, $y/r_0$ of the $N = 10$ atoms of the chain at 1/8 of a precession period, coloured by atom from one end (red) to the other (blue). data.csv
panel (b-2): Positions $x/r_0$, $y/r_0$ of the $N = 100$ atoms of the chain at 1/8 of a precession period, coloured by atom from one end (red) to the other (blue). data.csv
Fig. 6
The underlying data is not available. The figure is shown in the paper PDF.
Fig. 7
The underlying data is not available. The figure is shown in the paper PDF.
Fig. 8
The underlying data is not available. The figure is shown in the paper PDF.
Fig. 9
The underlying data is not available. The figure is shown in the paper PDF.
Fig. 10
panel (b): Libration frequency and the frequency of the slow rotation of the libration plane, $f$ (MHz), against magnetic field $B$ (mT) for 50 atoms: open markers joined by lines. data.csv
Fig. 11
panel (a): Uncertainty of the nutational motion $\Delta M_z$ over the spins of the needle against $\omega_L t$, one simulated trace. data.csv
Cite
Xueqi Ni, Zhixing Zou, Ruvi Lecamwasam, Andrea Vinante, Dmitry Budker, Ping Koy Lam, Tao Wang, Jiangbin Gong. Microscopic theory of a precessing ferromagnet for ultrasensitive magnetometry. Phys. Rev. Research 7, 043120 (2025). https://doi.org/10.1103/1v1p-kpb2
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