Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Observation of gyroscopic coupling in a non-spinning levitated ferromagnet

T0 review · 2 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A non-spinning levitated ferromagnet shows gyroscopic spin-rotation coupling between its librational modes, yielding a gyromagnetic g-factor of about 1.1–1.2.

desk verdict First convincing observation of gyroscopic coupling in a non-spinning levitated magnet, with calibration-free extraction of the Einstein-de Haas frequency; the unmeasured γ is a caveat but not fatal. read the letter →

arxiv 2504.13744 v1 pith:RV5OTYTR submitted 2025-04-18 quant-ph

F. Ahrens , A. Vinante This is my paper · ORCID
classification quant-ph
keywords Einstein-deHaaseffectspin-rotationcouplinggyroscopiclevitatedferromagnetlibrationalmodessuperconductingtrapgyromagneticratioSQUIDcross-correlation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports experimental signatures that a permanent ferromagnet carries real mechanical angular momentum from its electron spins even when the object is not rotating, so its rocking motion is coupled like a gyroscope's. The authors levitate a hard ferromagnetic microsphere in a superconducting trap, watch two orthogonal librational modes, and find an out-of-phase cross-correlation between two SQUID channels that matches the predicted spin-rotation coupling. From that coupling they extract the Einstein-de Haas frequency and a gyromagnetic g-factor of about 1.1–1.2, close to the 1.28 expected for Nd2Fe14B. The result matters because a non-spinning ferromagnet in this regime behaves like a giant atomic spin, opening a route to precession-based magnetometry and quantum-spin-stabilized levitation.

What carries the argument

The central object is the spin-rotation coupling term in the linearized Euler equations for a hard ferromagnet. With total angular momentum J = IΩ + S and the intrinsic spin S rigidly attached to the crystal easy axis, the librational modes obey üα + ωα²α + ωI β̇ = 0 and üβ + ωβ²β − ωI α̇ = 0. Because the coupling is kinetic, involving first derivatives, a mode excited along one axis drives the other axis in quadrature, creating elliptical motion with a π/2 phase shift. The two-SQUID cross-correlation technique extracts the sine (out-of-phase) part of this motion, and the product rα rβ cancels the unknown coil coupling constants, giving a calibration-free measurement of ωI.

What would settle it

Directly measure the rotation angle γ around the spin axis while repeating the cross-correlation measurement; if γ̇ is comparable to or larger than ωI, the out-of-phase component would persist even with the intrinsic spin contribution removed, falsifying the gyroscopic interpretation. Alternatively, reverse the particle's magnetization and check that the sign of the out-of-phase correlation reverses as predicted for intrinsic spin coupling.

Watch

Extended reading notes

Core claim

The central claim is that gyroscopic effects appear in the rigid-body dynamics of a non-spinning permanent hard ferromagnet: the intrinsic angular momentum S locked to the crystal lattice couples the two librational modes through the Einstein-de Haas frequency ωI = S/I, producing elliptical trajectories in the α-β plane with a π/2 phase shift between the two axes. The authors show that the ratio of out-of-phase to in-phase cross-correlation components in two imperfectly selective SQUID channels, combined for the quasi-α and quasi-β modes, gives a calibration-free expression for ωI. Applying this to four configurations with three particles yields Einstein-de Haas frequencies from 0.33 to 0.88 Hz and g-factors of about 1.10–1.19, consistent with the expected ~1.28 for the rare-earth alloy. The paper argues this is the first direct observation of gyroscopic spin-rotation coupling in the dynamics of a macroscopic non-spinning permanent magnet.

Load-bearing premise

The load-bearing premise is that the magnet does not rotate appreciably around its own magnetization axis: the authors estimate this rotation is thermal and about a hundred times smaller than the Einstein-de Haas frequency, but they do not measure it directly.

Editorial extensions

If this is right

  • The measured intrinsic angular momentum confirms that electron spin contributes mechanically to a macroscopic rigid body's dynamics, extending the Einstein-de Haas equivalence to the quasi-static librational regime.
  • The calibration-free extraction gives an absolute estimate of S/I without knowing the SQUID coupling coefficients, so the same protocol can be transferred to other levitated ferromagnet platforms.
  • The inferred g-factors support identifying the commercial alloy's magnetism with Nd2Fe14B-like rare-earth spin-plus-orbital angular momentum, and deviations from 1.28 become a quantitative test of composition.
  • If scaled to nanomagnets with radius below about 500 nm, the full gyroscopic regime ωI ≫ ωα, ωβ becomes accessible, making Larmor-precession magnetometry and quantum-spin-stabilized levitation experimentally reachable.
  • A partial gyroscopic regime with ωβ ≫ ωI ≫ ωα may be achievable in the existing trap by compensating stray fields, allowing a modified Larmor precession to be observed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The main unmeasured loophole is rotation around the magnetization axis: because a classical γ̇ would produce exactly the same out-of-phase coupling, a direct measurement of γ̇, rather than a thermal estimate, would close the last alternative explanation.
  • The systematic ~10% shortfall of the measured g-factor relative to the Nd2Fe14B prediction could encode information about the alloy's Co and Pr substitution, or about small shape anisotropy, and could be tested by independent magnetization measurements on the same particles.
  • The same calibration-free rα rβ product could serve as a metrological tool: once ωI is calibrated, the cross-correlation phase would report changes in magnetization, moment of inertia, or surface mass, suggesting applications to adsorption and temperature sensing.
  • Pushing the trap toward the partial gyroscopic regime should make the out-of-phase component grow relative to the in-phase component, providing a clear experimental test of the model's scaling with ωI.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper reports an experiment in which a hard ferromagnetic microsphere is levitated in a superconducting trap and undergoes small librational oscillations around two transverse axes, α and β. The authors measure the cross-correlation between two SQUID readout channels and observe an out-of-phase component, which they interpret as evidence of gyroscopic spin-rotation coupling between the librational modes. For a non-spinning magnet, this coupling is attributed to the intrinsic spin angular momentum of the electron system, i.e., the Einstein-de Haas effect. From the measured coupling they extract the Einstein-de Haas frequency fI and a gyromagnetic g-factor, obtaining fI in the range 0.33-0.88 Hz and g ≈ 1.10-1.19, compared with a model expectation of geff ≈ 1.28 for Nd2Fe14B. The analysis is based on a calibration-free relation that is independent of the coil coupling coefficients, and the results are shown for four configurations including three particle radii and two cooldowns of one particle.

Significance. If the interpretation holds, this is the first direct observation of gyroscopic spin-rotation coupling in the mechanical librations of a non-spinning macroscopic ferromagnet, a regime that connects to proposals for ultrasensitive magnetometry and quantum-spin-stabilized levitation. The extraction of ωI via Eq. (9) is genuinely parameter-free with respect to the detection cross-couplings, which is a strong methodological strength. The nonzero out-of-phase component in the cross-correlation is a specific, falsifiable signature, and the consistency of the inferred fI across sizes and cooldowns supports the internal validity of the measurement. The paper is clearly written and the experimental controls (including the measured differential phase delay between channels and the zero out-of-phase autocorrelation) are appropriate. The main weakness is that the interpretation as an intrinsic, non-spinning Einstein-de Haas signal rests on an unmeasured mechanical rotation degree of freedom about the easy axis.

major comments (2)
  1. [Supplemental Information, Eq. (S3)] The paper's central quantitative conclusion relies on the assumption ˙γ = 0, i.e., no mechanical rotation about the spin axis. Equation (S3) shows explicitly that a constant ˙γ enters the equations of motion in exactly the same additive way as ωI, so the quantity extracted from Eq. (9) is actually (ωI + ˙γ)^2, not ωI^2 alone. The thermal estimate ˙γrms = sqrt(kBT/I) < 0.01ωI quoted in the main text bounds the standard deviation of a zero-mean stochastic process; it does not exclude a nonzero mean or a slowly decaying residual spin imparted during magnetization or loading. This is quantitatively relevant because the inferred g-factors in Table I are systematically 10-15% below the geff = 1.28 model value, so a residual counter-rotation of about -0.1ωI would fully account for the observed discrepancy without any error in the intrinsic-spin interpretation. Since the claim of observing the Einstein-de Haas effect is specifically about a non-spinning magnet, this degeneracy is load-bearing. Please add a direct or indirect constraint on ˙γ, for example by reporting the waiting time after loading relative to the rotational damping time, measuring fI as a function of time after loading, or comparing the extracted coupling at different gas pressures; these would clarify whether the system is in rotational equilibrium around the easy axis.
  2. [Main text, Table I and Eq. (9)] The consistency of fI across the four configurations is presented as evidence for the intrinsic-spin interpretation, but this argument has limited discriminating power against a constant relative mechanical rotation of the form ˙γ = c ωI: such an offset would leave the R-dependence of fI and the run-to-run scatter essentially unchanged, while shifting all inferred g-values coherently. The two-cooldown measurement on the same particle (Table I, rows 3 and 4) is the closest available control, since any spin imparted during the initial loading would presumably have decayed before the second cooldown; however, the paper does not state the time elapsed between loading and each measurement, nor between the two cooldowns. Please state these times and the estimated rotational damping time, and discuss explicitly what the reproducibility in Table I does and does not constrain about a possible residual ˙γ.
minor comments (5)
  1. [Introduction, paragraph 2] The word 'cylidrically' should be 'cylindrically'.
  2. [Main text, data availability statement] The statement that the data 'will be available in the future' is vague; please specify where and when the data will be deposited, or state that they are available from the authors upon request.
  3. [Main text, after Eq. (12)] The sentence 'A value of only slightly higher 1.36 is obtained by replacing Nd with Pr' is grammatically awkward; please rephrase, e.g., 'Replacing Nd by Pr gives a value of 1.36, only slightly higher.'
  4. [Supplemental Information, Eq. (S11)] The envelope 1 - A1|τ| in the correlation fit is stated to be an artifact of the finite integration window; since the expected value is A1 = 1/T, it would be useful to state explicitly that A1 is left free as a consistency check and to confirm that the fitted A1 is consistent with 1/T within the statistical uncertainty.
  5. [References] Reference [17] is a placeholder ('see Supplemental Information at URL'); in the published version the actual DOI or URL should be provided.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the out-of-phase cross-correlation is an independently measured observable, and the inferred g-factor is benchmarked against external material-property values.

full rationale

The derivation chain is self-contained rather than circular. Equations (2)-(5) provide a parameter-free dynamical prediction: if a non-spinning ferromagnet has intrinsic angular momentum S, its two librational modes acquire elliptical trajectories with π/2-phase-shifted components. Equations (4) and (5) define the small geometric factors gα and gβ, and Eq. (9) is a derived relation connecting the measured product rαrβ to the Einstein-de Haas frequency ωI while explicitly canceling the coil coupling constants A, B, C, D under the stated selectivity assumptions. The out-of-phase components s12 and s21 are extracted from fits to measured cross-correlations; they are not constructed from ωI and could in principle be zero. The paper then solves Eq. (9) for ωI and combines this calibration-free value with R and M inferred independently from the z and β mode frequencies, finally comparing the resulting g-factor with an external literature estimate for Nd2Fe14B, Eq. (12). The main caveat, an unmeasured classical rotation γdot about the spin axis, is explicitly acknowledged in the Supplemental Information: Eq. (S3) shows that γdot enters exactly as an additive shift to ωI. However, the paper neither fits γdot to the observed signal nor defines the prediction in terms of it; instead it provides a thermal upper bound γdot_rms < 0.01ωI. That is a robustness/correctness risk, not a circularity. Self-citations to the image-method model are not load-bearing in a circular sense, because that model is externally checkable and R is cross-checked against optical inspection. No step reduces the claimed observation to its own inputs.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard rigid-body dynamics and the hard-ferromagnet spin-lattice locking assumption, both well established. The main auxiliary assumptions are the image-method trap model and the thermal equilibrium of the gamma degree of freedom; the latter is explicitly argued but not directly measured.

free parameters (1)
  • Radius R and magnetization M (per particle, fitted in-situ) = R = 31.2, 23.6, 19.0, 18.8 μm; M = 591, 675, 574, 581 kA/m
    Inferred by solving Eqs. (S7)-(S8) from measured f_z and f_beta. These values are used to compute the magnetic moment and moment of inertia, and hence the g-factor. They do not enter the raw detection of omega_I, but they affect the reported g-factor.
assumptions (5)
  • domain assumption The intrinsic spin angular momentum S is rigidly attached to the magnet lattice (S = S n) for a hard ferromagnet.
    Assumed in Eqs. (2) and used to derive the coupled libration equations (3). Supported by the separation between GHz internal magnetization dynamics and kHz mechanical motion, as argued in the main text.
  • domain assumption The rotation angle gamma around the spin axis is zero or thermally distributed with rms sqrt(kBT/I).
    Used to rule out classical rotation as the source of the out-of-phase coupling. Relies on the particle not having residual spin from the magnetization or loading procedure; this is estimated but not directly measured.
  • domain assumption The image-method potential of Eq. (S6) for a spherical cavity correctly describes the trap and determines R and M from f_z and f_beta.
    Used in the Supplemental Information to extract R and M from the measured mode frequencies. Relies on the assumed geometry, density, and gravitational acceleration.
  • domain assumption The particle is perfectly spherical and isotropic in moment of inertia.
    Assumed in the main derivation. The Supplemental Information shows that deviations of about 1 percent produce only in-phase coupling and do not affect the out-of-phase component.
  • standard math Standard equations of rigid-body dynamics, including conservation of total angular momentum J = L + S, apply.
    Eq. (2) restates angular momentum conservation and the spin-locking condition for a rigid rotor. This is a standard physical principle invoked throughout.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Observation of gyroscopic coupling in a non-spinning levitated ferromagnet." pith.science (2026). https://pith.science/paper/RV5OTYTR

@misc{pith2026250413744,
  author       = {Pith},
  title        = {Pith review of: Observation of gyroscopic coupling in a non-spinning levitated ferromagnet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RV5OTYTR}},
  note         = {Machine review of arXiv:2504.13744}
}
abstract

A non-spinning permanent ferromagnet is predicted to behave as a gyroscope at sufficiently low frequencies, which can be seen as a manifestation of the Einstein-de Haas effect. This yet unexplored regime has been recently proposed for ultrasensitive precession-based magnetometry and for atomic-like quantum stabilization of a levitated nanomagnet in a static field. Here, we observe signatures of gyroscopic effects in the rotational dynamics of a non-spinning permanent ferromagnet levitated in a superconducting trap. Specifically, we detect spin-rotation coupling between different librational modes, in good agreement with theoretical predictions. From our measurements, we can infer both the intrinsic angular momentum of the levitated magnet and its gyromagnetic $g$-factor.

Figures

Figures reproduced from arXiv: 2504.13744 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Model and conventions adopted. A ferromagnet with [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Representative samples of raw and cross-correlation data. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Levitated Milligram-scale Ferromagnetic Magnetometer at Room Temperature

    quant-ph 2026-08 conditional novelty 6.0 of 10

    A room-temperature diamagnetically levitated 60-mg ferromagnet achieves 23 fT/√Hz magnetic sensitivity near 153 Hz, validated by two independent calibrations and limited by vibration noise.

Reference graph

Works this paper leans on

21 extracted references · 20 canonical work pages · cited by 1 Pith paper

  1. [1]

    Einstein and W

    A. Einstein and W. de Haas, Experimental proof of the exis- tence of Amp `ere’s molecular currents, Koninklijke Akademie van Wetenschappen te Amsterdam Proceedings18, 696 (1915)

    work page 1915

  2. [2]

    Barnett, Magnetization by rotation, Physical Review 6, 239 (1915)

    S. Barnett, Magnetization by rotation, Physical Review 6, 239 (1915)

    work page 1915

  3. [3]

    Dornes and et al., The ultrafast Einstein–de Haas effect, Na- ture 565, 209 (2019)

    C. Dornes and et al., The ultrafast Einstein–de Haas effect, Na- ture 565, 209 (2019)

    work page 2019

  4. [4]

    D. F. Jackson Kimball, A. O. Sushkov, and D. Budker, Precess- ing Ferromagnetic Needle Magnetometer, Physical Review Let- ters 116, 190801 (2016)

    work page 2016

  5. [5]

    Rusconi, V

    C. Rusconi, V . P ¨ochhacker, K. Kustura, J. Cirac, and O. Romero-Isart, Quantum spin stabilized magnetic levitation, Physical Review Letters 119, 167202 (2017)

    work page 2017

  6. [6]

    Rusconi, V

    C. Rusconi, V . P ¨ochhacker, K. Kustura, J. I. Cirac, and O. Romero-Isart, Linear stability analysis of a levitated nano- magnet in a static magnetic field: Quantum spin stabilized mag- netic levitation, Physical Review B 96, 134419 (2017)

    work page 2017

  7. [7]

    Fadeev, T

    P. Fadeev, T. Wang, Y . Band, D. Budker, P. W. Graham, A. O. Sushkov, and D. F. J. Kimball, Gravity probe spin: Prospects for measuring general-relativistic precession of intrinsic spin us- ing a ferromagnetic gyroscope, Physical Review D103, 044056 (2021)

    work page 2021

  8. [8]

    Fadeev, C

    P. Fadeev, C. Timberlake, T. Wang, A. Vinante, Y . B. Band, D. Budker, A. O. Sushkov, H. Ulbricht, and D. F. Jack- son Kimball, Ferromagnetic gyroscopes for tests of funda- mental physics, Quantum Science and Technology 6, 024006 (2021)

    work page 2021

Show all 21 references
  1. [9]

    X. Ni, Z. Zou, R. Lecamwasam, A. Vinante, D. Bud- ker, P. K. Lam, T. Wang, and J. Gong, Microscopic theory of a precessing ferromagnet for ultrasensitive magnetometry, arXiv:2503.00728 (2025)

    2025

  2. [10]

    Vinante, C

    A. Vinante, C. Timberlake, D. Budker, D. F. Jackson Kimball, A. O. Sushkov, and H. Ulbricht, Surpassing the energy resolu- tion limit with ferromagnetic torque sensors, Physical Review Letters 127, 070801 (2021)

    2021

  3. [11]

    Kalia, D

    S. Kalia, D. Budker, D. F. J. Kimball, W. Ji, Z. Liu, A. O. Sushkov, C. Timberlake, H. Ulbricht, A. Vinante, and T. Wang, Ultralight dark matter detection with levitated ferromagnets, Physical Review D 110, 115029 (2024)

    2024

  4. [12]

    Ahrens, W

    F. Ahrens, W. Ji, D. Budker, C. Timberlake, H. Ulbricht, and A. Vinante, Levitated ferromagnetic magnetometer with energy resolution well below ℏ, Physical Review Letters 134, 110801 (2025)

    2025

  5. [13]

    Bassani, Earnshaw (1805–1888) and passive magnetic levi- tation, Meccanica 41, 375 (2006)

    R. Bassani, Earnshaw (1805–1888) and passive magnetic levi- tation, Meccanica 41, 375 (2006)

    2006

  6. [14]

    Magnequench powder type MQP-S-11-9-20001, see URL: https://mqitechnology.com/product/mqp-s-11-9-20001/

  7. [15]

    Vinante, P

    A. Vinante, P. Falferi, G. Gasbarri, A. Setter, C. Timberlake, and H. Ulbricht, Ultralow mechanical damping with Meissner- levitated ferromagnetic microparticles, Physical Review Ap- plied 13, 064027 (2020)

    2020

  8. [16]

    Vinante, C

    A. Vinante, C. Timberlake, and H. Ulbricht, Levitated micro- magnets in superconducting traps: A new platform for tabletop fundamental physics experiments, Entropy 24, 1642 (2022)

    2022

  9. [17]

    See Supplemental Information at URL for further details on the characterization and modelling of the system

  10. [18]

    Buschow and F

    K. Buschow and F. de Boer, Physics of Magnetism and Magnetic Materials (Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow)

  11. [19]

    J. A. Zieli ´nska, F. van der Laan, A. Norrman, R. Reimann, M. Frimmer, and L. Novotny, Long-axis spinning of an opti- cally levitated particle: A levitated spinning top, Physical Re- view Letters 132, 253601 (2024)

    2024

  12. [20]

    Perdriat, C

    M. Perdriat, C. Pellet-Mary, T. Copie, and G. H ´etet, Planar magnetic paul traps for ferromagnetic particles, Physical Re- view Research 5, L032045 (2023)

    2023

  13. [21]

    Dania, D

    L. Dania, D. S. Bykov, F. Goschin, M. Teller, A. Kas- sid, and T. E. Northup, Ultrahigh quality factor of a levi- tated nanomechanical oscillator, Physical Review Letters 132, 133602 (2024). 6 SUPPLEMENTAL INFORMA TION Theoretical model and caveats Equations (3) in the main te...

    2024

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.