A levitated magnet shows gyroscopic coupling without spinning

A gyroscope without a spinning body

A permanent magnet’s magnetization is associated with intrinsic angular momentum, arising from its constituent particles’ quantum spin and, potentially, atomic orbital angular momentum. Quantum spin is not a miniature object literally turning, but it nevertheless contributes genuine mechanical angular momentum.

Theory predicts that this internal angular momentum can make a non-spinning magnet behave like a gyroscope when its orientation changes sufficiently slowly under weak torque. The authors trace the experimental idea to Maxwell in 1861.

The present experiment does not reach that fully gyroscopic regime. Instead, the magnet mainly rocks back and forth, a motion called libration. The researchers look for a smaller gyroscopic contribution that connects two otherwise distinct rocking motions.

Watching two directions at once

The team levitated rare-earth-alloy magnetic microspheres in a superconducting lead trap at 4.18 kelvin. Superconducting screening currents provide the levitating interaction through the Meissner effect. The inferred particle radii ranged from about 19 to 31 micrometres.

The magnet’s magnetic moment lay approximately horizontally. It could rock around two different axes, with typical frequencies near 100 and 400 hertz. The researchers modelled how angular momentum associated with the magnetization should couple these motions.

Without that coupling, each idealized mode would rock along a single angular direction. With coupling, a small motion appears in the other direction, displaced by a quarter-cycle. Combining the two angular coordinates produces a narrow ellipse rather than a line.

Two superconducting pickup coils, connected to independent superconducting quantum interference devices, or SQUIDs, monitored changes in magnetic flux as the magnet moved. One channel preferentially detected one rocking direction; the other favoured the second.

That separation was imperfect: each channel also picked up a few percent of the other motion. The analysis therefore had to distinguish genuine elliptical motion from ordinary detector crosstalk.

Extracting the weak coupling

The researchers excited each rocking mode separately above the noise level and calculated cross-correlations between the detector signals—measures of how closely the signals matched as one was shifted in time.

In their model, detector crosstalk contributes an in-phase component, while gyroscopic coupling produces an out-of-phase component. Fitting these components allowed the team to isolate the signature expected from elliptical motion.

Combining measurements from both modes eliminated the detector coupling constants from the expression used to infer the Einstein–de Haas frequency. This quantity measures intrinsic angular momentum divided by the particle’s moment of inertia. The procedure is calibration-free with respect to those detector couplings, although it still depends on the model and its assumptions.

Across three particles and four experimental configurations, the inferred Einstein–de Haas frequencies ranged from 0.33 to 0.88 hertz. One particle was measured during two different cooldowns.

The team separately inferred particle size and magnetization from measured mechanical frequencies using a model of the superconducting trap. Combining those estimates with the coupling measurements yielded gyromagnetic g-factors between 1.10 and 1.19. This factor relates magnetic moment to intrinsic angular momentum. The values were mutually consistent within their reported uncertainties and roughly 10 percent below the authors’ simplest material estimates.

Alternative explanations and remaining assumptions

Continuous bodily rotation around the magnetization direction could produce similar coupling. The detectors cannot observe that rotation directly. Assuming it is thermal, the authors estimate its root-mean-square angular speed to be less than one percent of the inferred Einstein–de Haas angular frequency, making it a negligible contribution under that assumption.

They also considered departures from a perfect sphere, gas damping and instrumental delays. Shape-related coupling alone would not produce the required out-of-phase motion in their model; the gas-related contribution was estimated to be negligible. They report suppressing differential instrumental delays.

Additional field-tuning measurements supported predominantly magnetic-dipole confinement of the lower-frequency rocking mode. However, the precise source of the residual magnetic field remained unresolved, and weak additional confinement could not be excluded.

A step toward a different regime

The result supports gyroscopic coupling within predominantly ordinary rocking dynamics. It does not demonstrate ultrasensitive gyroscopic magnetometry or spin-stabilized trapping in a static field; those remain proposed applications. For full gyroscopic dynamics in a superconducting trap, the authors identify a necessary condition requiring much smaller magnets, with radii below about 500 nanometres.

This briefing concerns arXiv preprint version 2504.13744v2, dated November 9, 2026. Its reported evidence should be read with the model assumptions and experimental limitations above, rather than as a demonstration of every predicted gyroscopic behaviour.