Levitated Sensor for Magnetometry in Ambient Environment

Changhao Xu; Dmitry Budker; Guofeng Qu; Wei Ji

REVIEW 2 major objections 6 minor 4 cited by

Levitated Sensor for Magnetometry in Ambient Environment

T0 review · 2 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A room-temperature, magnetically levitated micro-magnet achieves a magnetic-field sensitivity of $32\pm 3\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at its torsional resonance.

desk verdict Promising room-temperature levitated magnetometer with a real sensitivity record, but the absolute scale depends on an uncalibrated calibration coil; referee it and ask for the missing calibration details. read the letter →

arxiv 2504.21524 v1 pith:AZRWKZRW submitted 2025-04-30 physics.ins-det

Wei Ji , Changhao Xu , Guofeng Qu , Dmitry Budker This is my paper · ORCID

classification physics.ins-det

keywords levitatedmagnetometerfemtoteslasensitivitydiamagneticlevitationtorsionalresonatorJohnsonnoiseopticalleverroom-temperaturemagnetometryambientenvironment

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 claims that a tiny ferromagnetic disk, levitated at room temperature by magnetic forces and stabilized by a diamagnetic graphite layer, can detect magnetic fields at $32\pm 3\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$ on its torsional resonance. The point of the claim is that femtotesla-class magnetometry, usually the territory of cryogenic SQUIDs or heated atomic-vapor cells, can work in an ambient, Earth-field-compatible setup. The authors show that the dominant noise is Johnson magnetic noise from surrounding conductors, and that grinding pyrolytic graphite into epoxy-isolated particles cuts that noise roughly fourfold. If the result stands, it gives biology, chemistry, and fundamental physics a magnetometer that can sit close to a sample without cryogens or magnetic-field suppression.

What carries the argument

The load-bearing object is a torsional oscillator: a magnetized disk levitated in a potential well formed by gravity, the field of a lifting magnet, and the repulsion of a diamagnetic pyrolytic graphite plate. A magnetic field along the $x$-axis exerts a torque that tilts the disk, and a $3.4\,\mathrm{m}$ optical lever magnifies the rotation on a quadrant photodiode. The resonant torsional mode at $f_0=\sqrt{MB/I}/2\pi$ concentrates the response, while the ferromagnet's strong spin-lattice coupling rapidly averages spin-projection noise; the graphite is ground to powder and epoxy-bonded so eddy currents and the associated Johnson noise are confined to small loops.

What would settle it

Drive the calibration coils with the same current while measuring the field at the sensor location with an independently calibrated magnetometer, then recompute the response curve using the measured amplitude; if it is not 10 pT, the quoted $32\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$ changes by the same factor.

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Extended reading notes

Core claim

The central result is that a levitated $0.2\,\mathrm{mm}^3$ ferromagnetic magnet, read out by an optical lever, reaches a magnetic field sensitivity of $32\pm 3\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$ at a torsional resonance near $305\,\mathrm{Hz}$ while operating at room temperature, at $0.025\,\mathrm{mbar}$ pressure, and in magnetic fields up to the millitesla range. The sensitivity comes from combining high spin density and spin-lattice coupling in the ferromagnet, which suppresses spin-projection noise, with a low-dissipation levitation trap made of a lifting magnet and an epoxy-glued pyrolytic graphite stabilizer. The paper reports that the measured performance is several orders of magnitude better than the earlier reflection-based superconducting levitated magnetometer and comparable to similarly sized SERF and SQUID devices, but without their cryogenic or low-field constraints.

Load-bearing premise

If the field coils actually produce a field stronger or weaker than the stated 10 pT, the quoted sensitivity is off by the same factor, and the paper does not report how that 10 pT value was verified at the sensor magnet.

Editorial extensions

If this is right

A room-temperature sensor runs in Earth's field and in millitesla-range backgrounds, avoiding the shielded low-field environments needed by SERF magnetometers and the cryogens needed by SQUIDs.
The resonance frequency is tunable from about 260 Hz to 318 Hz by changing the bias field along $z$, so the same device can be used for frequency-modulated detection or closed-loop operation.
Because the sensing element is a bare magnet with no cell or window, a signal source can be placed within a millimeter of it, strengthening biomagnetic measurements and short-range searches for spin-dependent forces such as axion-mediated interactions.
The authors estimate that replacing the graphite stabilizer with lower-noise materials, adding high-reflectivity coatings, and using better photodiodes could push sensitivity toward $0.1\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$, where vibration noise would dominate.

Reading between the lines

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

The headline sensitivity is a resonant, narrow-band number: the same sensor shows noise near $1\,\mathrm{nT}/\sqrt{\mathrm{Hz}}$ below 15 Hz and hundreds of $\mathrm{pT}/\sqrt{\mathrm{Hz}}$ between 80 and 200 Hz, so the practical advantage is for signals that can be modulated onto the torsional resonance.
The stated 10 pT calibration amplitude carries no uncertainty and no independent verification at the sensor location; if the true field differs, the quoted sensitivity shifts by the same factor, and a cross-calibration with a commercial atomic magnetometer would settle it.
The trick of granularizing a conductor to shrink eddy-current loops is a general noise-suppression principle that could also be applied to magnetic shields and other conductive structures near any precision magnetometer.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Ji et al. report a diamagnetically stabilized levitated magnet (LeMaMa) that hits 32 fT/√Hz at a ~305 Hz torsional resonance under room temperature and a ~1.9 mT bias field. That is a genuine record for levitated magnetometry at ambient conditions, about four orders of magnitude better than the cryogenic levitated-mirror magnetometer of Jiang 2020. The new combination is real: diamagnetic stabilization with an epoxy-glued pyrolytic graphite plate (EGPG) to cut eddy-current dissipation and Johnson noise, plus optical lever readout of the magnet's rotation. The authors also demonstrate tuning the resonance from 260 to 318 Hz by varying the bias field, and they give a careful noise budget with air-collision, vibrational, and detection noise contributions.

The paper does a lot right. The noise decomposition is physically sensible, and the claim that Johnson noise from the conductive plate drops from 110 to 30 fT/√Hz when the graphite is powdered is exactly the kind of testable design improvement that makes the result credible. The statistical uncertainty on the sensitivity is honestly reported as the spread over five 100-s datasets.

The soft spot is the one the reader flagged: the absolute sensitivity scale is set by a 10 pT calibration field whose amplitude is asserted without stated uncertainty or in-situ verification. The response curve in Fig. 2 and the conversion of voltage noise to magnetic noise both scale linearly with that amplitude. If the field at the magnet differs from 10 pT—due to coil constant error, eddy-current screening by the shield, or field inhomogeneity—the 32 fT/√Hz changes proportionally. The ±3 fT/√Hz is statistical only. The authors mention validating the Johnson-noise estimate with a commercial atomic magnetometer, but never connect that to the drive-field calibration, which is a missed opportunity to close the loop. This is not a reason to reject; it is a missing measurement that the authors can supply. But until they do, the comparison to SQUIDs and SERF magnetometers is not fully traceable.

Two smaller points. The supplementary text is referenced several times for the noise decomposition, but it is not included in the preprint, so the referee cannot check those details. And the 'ambient environment' framing should be qualified: the sensor sits in a vacuum chamber inside a four-layer magnetic shield, and it is a resonant detector, not a broadband one. The authors are honest about the resonant character, and the tuning demonstration helps, but the abstract's comparison to SQUID/SERF needs that caveat.

Bottom line: this is a clever, well-executed experiment with a plausible result. The calibration gap is the main obstacle, and it is addressable. I would send it to peer review with a request for calibration details and uncertainty, and ideally a data release of the noise spectra and response curves.

Referee Report

2 major / 6 minor

Summary. The paper reports a room-temperature magnetometer based on a diamagnetically stabilized, magnetically levitated permanent-magnet disk (LeMaMa). A lifting magnet provides the magnetic force, an epoxy-glued pyrolytic graphite (EGPG) plate provides diamagnetic stabilization, and torsional oscillations of the disk are read out by an optical lever onto a quadrant photodiode. Applying a 10 pT alternating field from in-shield coils, the authors measure a response curve with resonance at f0 ≈ 304.84 Hz and Q ≈ 1.2 × 10^4, convert the voltage noise spectrum to a magnetic noise spectrum, and report a sensitivity of 32 ± 3 fT/√Hz at resonance (five 100-s datasets). They present a noise budget identifying Johnson noise from conducting surroundings (~30 fT/√Hz), air collisions (≤20), vibration (~10), and detection noise (~2), claim validation of the Johnson-noise estimate with a commercial atomic magnetometer, and demonstrate resonance tuning between 260 and 318 Hz by varying the bias field (1.42–2.12 mT). On this basis they argue the sensor is competitive with SQUID and SERF magnetometers while operating at room temperature and in mT-range fields, and discuss applications in bio-magnetometry and searches for exotic spin-dependent forces.

Significance. If the headline number survives scrutiny, this is a notable experimental advance: a room-temperature, optically read levitated magnet reaching 32 fT/√Hz at ~305 Hz is roughly four orders of magnitude better than the previous levitated reflection magnetometer (370 pT/√Hz, Ref. 27) and sits in the same range as SQUID and SERF devices, with the distinctive feature of operation in a mT-level bias field. Credit where due: the sensitivity is measured, not reverse-engineered—the response curve is fitted to a driven harmonic-oscillator model and the noise is converted by that same curve; the spin-correlation benefit is taken from prior theory (Refs. 24, 25) and is not fitted to the data; the noise decomposition is explicit; the frequency tunability (260–318 Hz) is directly demonstrated; and the projected 0.1 fT/√Hz limit gives a concrete falsifiable target. The principal barrier to accepting the quantitative claim is traceability of the absolute field scale, which rests on a single stated 10 pT drive amplitude without calibration uncertainty. The paper is well suited to this journal and will interest the levitodynamics and quantum-sensing communities.

major comments (2)

[Experimental Setup; Fig. 2] The absolute scale of the headline sensitivity is anchored entirely by the 10 pT amplitude of the drive field, and that amplitude is never calibrated. In the 'Experimental Setup' section the text states 'we apply an alternating magnetic field along the x-axis with an amplitude of 10 pT using a set of field coils placed inside the magnetic shielding', but no coil geometry, current-to-field constant, in-situ verification, or uncertainty is provided. Since the voltage-noise spectrum is converted to a magnetic-noise spectrum by dividing by the fitted response curve A/sqrt((f^2 - f0^2)^2 + gamma^2 f^2) whose amplitude A is set by this 10 pT drive, any fractional error in the field actually seen by the 410-um-radius sensor magnet (eddy-current screening by the shield or the EGPG, field inhomogeneity across the magnet, current-setting error) propagates linearly into the quoted 32 ± 3 fT/√Hz and therefore into the comparison with SQUID and SERF sensors. A second internal ambiguity is that the drive is quoted as an 'amplitude' while the recorded output is described as 'root-mean-square (RMS)'; the peak-versus-RMS convention must be stated explicitly and used consistently in the noise conversion, because a √2 discrepancy is comparable to the reported statistical uncertainty. Please supply a calibration procedure with a quantified uncertainty, ideally cross-checked against the commercial atomic magnetometer already used for the Johnson-noise validation, or report the sensitivity with the associated systematic scale error.
[System sensitivity studies] The quoted error of ±3 fT/√Hz is only the statistical spread over five 100-s datasets, so the error budget of the headline number is incomplete. Systematic contributions that should be propagated include the drive-field calibration discussed above, the fitted response amplitude A, the photodiode voltage calibration, and the stated dimensional tolerances (±2 um on radius and thickness), the last of which enter the resonance model f0 = sqrt(MB/I)/2π through the moment of inertia. I do not see circularity here: the sensitivity is measured, and the noise decomposition in the 'System sensitivity studies' section is explanatory rather than used to force the result. However, two supporting claims need hardened evidence: the statement that the Johnson-noise estimate is 'validated by measurements using a commercial atomic magnetometer' and the Monte-Carlo air-collision estimate of 'below 20 fT/√Hz' are described only verbally, with the details deferred to a 'Supplementary Text' that is not included in the posted preprint; these data must be part of the submitted manuscript so that the claimed noise floor near resonance can be checked.

minor comments (6)

[System sensitivity studies; Fig. 3 caption] The translational-mode peak frequencies are given as 3, 5, and 15 Hz for the x, y, and z axes in the main text but as 3, 4, and 10 Hz in the Fig. 3 caption; please reconcile the two sets of numbers.
[System sensitivity studies; Fig. 3 caption] The color coding used for the noise components differs between the text ('solid purple line', 'green dashed line', 'black dotted line') and the Fig. 3 caption ('red line (rescaled from the actual noise background)', 'yellow line (determined by fitting)', 'black-dashed line'); unify the notation so the reader can match each component to its curve.
[System sensitivity studies] When the quoted near-resonance components are combined in quadrature (30 fT/√Hz Johnson, ~20 fT/√Hz air collision, ~10 fT/√Hz vibration, ~2 fT/√Hz detection), the total is about 37 fT/√Hz, which is above the measured 32 ± 3 fT/√Hz; please state whether the component estimates are intended as upper bounds or are expected to add with some correlation.
[Abstract and Discussion] The claim of operation 'under Earth's magnetic field' and 'in an ambient environment' is not directly demonstrated, because all measurements are taken inside a four-layer magnetic shield; since the DC bias from the lifting magnet (1.92 mT) already exceeds the Earth's field, the relevant question is whether the shield is needed only for AC interference, and the text should say so explicitly or report an unshielded test.
[References] Reference [34] is incomplete ('Measurement systems: application and design' with no authors, venue, or year), and the reference list mixes entries with and without DOIs; please normalize the bibliography.
[Fig. 2] The green response points in Fig. 2 are not described as single measurements or averages, and no error bars are shown; a short statement would let the reader judge the quality of the fit and the accuracy of the response amplitude A.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the headline 32 fT/√Hz is an empirically measured sensitivity referenced to an applied 10 pT field, not a quantity derived from its own fit.

full rationale

The central result is obtained by direct measurement: a 10 pT alternating field is applied and the voltage noise spectrum is divided by the measured response curve to obtain a magnetic-field noise spectral density. This is a calibration-transfer measurement, not a derivation in which the conclusion is an input. The noise decomposition is explanatory and does not feed back into the reported sensitivity. The ferromagnetic spin-correlation advantage is cited to Kimball et al. (2016) and Vinante et al. (2021); although one cited paper shares an author with the present work, the cited results are external prior publications with their own independent content and are not used as fitted parameters or as a uniqueness theorem, so they do not make the argument circular. The one legitimate concern—that the absolute scale of 32 fT/√Hz inherits the uncalibrated 10 pT drive amplitude—is an accuracy/traceability issue, not a circularity: a wrong coil constant would scale the result, but nothing in the paper defines the result in terms of itself. Therefore no circular step can be exhibited, and the score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claim is a measured sensitivity, not a fitted derivation. The response curve amplitude A is fitted to calibration data but serves as a calibration factor, not a free parameter of a model. No numbers are tuned to make the sensitivity claim hold.

assumptions (4)

domain assumption Diamagnetically stabilized levitation creates a stable potential minimum for the sensor magnet.
The stable levitation is the enabling condition, imported from Simon et al. (2001).
domain assumption Strong spin-lattice coupling in the ferromagnet suppresses spin-projection noise, improving sensitivity.
Basis for the sensitivity advantage, cited from Kimball et al. (2016) and Vinante et al. (2021).
domain assumption The measured response curve accurately converts voltage noise to equivalent magnetic noise.
Assumes linear response and that the 10 pT drive couples to the torsional mode exactly as external noise does.
domain assumption Johnson noise from conducting materials and gas collision noise are modeled correctly and validated in supplementary material.
Used to attribute the observed noise floor; details are in the supplementary text.

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Pith. "Pith review of Levitated Sensor for Magnetometry in Ambient Environment." pith.science (2026). https://pith.science/paper/AZRWKZRW

@misc{pith2026250421524,
  author       = {Pith},
  title        = {Pith review of: Levitated Sensor for Magnetometry in Ambient Environment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AZRWKZRW}},
  note         = {Machine review of arXiv:2504.21524}
}

abstract

Levitated particle systems have gained significant attention as a rapidly advancing platform for precision sensing, offering low-loss, highly isolated environments by eliminating mechanical contact and associated noise. Current room-temperature levitation techniques are primarily sensitive to acceleration, with magnetic sensing often relying on the Meissner effect, which is impractical under ambient conditions. Here, we demonstrate a diamagnetically stabilized magnetically levitated magnet magnetometer (LeMaMa), where the motion of the magnet is detected optically. Leveraging strong spin-lattice coupling in the ferromagnet to suppress spin-projection noise and minimizing dissipation through levitation, we achieve a sensitivity of 32 fT $/Hz^{1/2}$. This sensitivity is adequate for a wide range of applications in biology, chemistry, and fundamental physics, matching the performance of leading technologies like SQUIDs and atomic magnetometers, while offering the distinct advantage of operating at room temperature and under Earth's magnetic field.

Figures

Figures reproduced from arXiv: 2504.21524 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: , we demonstrate the ability to adjust the resonance frequency by varying the leading magnetic field using a set of coils generating a uniform field along the z-axis. By tuning the magnetic field Bz from 1.42 mT to 2.12 mT, we successfully shift the resonance frequen…

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Forward citations

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Pith tools

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

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