Wideband wide-field imaging of spin-wave propagation using diamond quantum sensors

Daigo Takafuji; Jobu Matsuno; Junichi Shiogai; Kensuke Kobayashi; Kensuke Ogawa; Kento Sasaki; Kohei Ueda; Moeta Tsukamoto; Yusuke Mori

REVIEW 4 major objections 6 minor 1 cited by

Wideband wide-field imaging of spin-wave propagation using diamond quantum sensors

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Using the AC Zeeman shift of nitrogen-vacancy spins, the authors image off-resonant spin waves in a YIG film over detunings up to 567 MHz at a fixed bias field, extracting quantitative wavenumber and amplitude maps.

desk verdict A genuinely new widefield NV imaging regime for off-resonant spin waves, with solid wavenumber extraction and softer amplitude numbers at the largest detunings. read the letter →

arxiv 2411.17344 v2 pith:PKXOU726 submitted 2024-11-26 cond-mat.mes-hall

Kensuke Ogawa , Moeta Tsukamoto , Yusuke Mori , Daigo Takafuji , Junichi Shiogai , Kohei Ueda , Jobu Matsuno , Kento Sasaki

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Kensuke Kobayashi

This is my paper · ORCID

classification cond-mat.mes-hall

keywords NVcentersACZeemaneffectspinwaveswidefieldimagingYIGthinfilmmagnonicsquantumsensingmicrowavemagnetometry

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

This paper reports a method for wide-field imaging of spin waves that does not require the spin-wave frequency to match the resonance frequency of the diamond nitrogen-vacancy (NV) sensor spins. Instead of relying on Rabi oscillations, which only respond to resonant microwaves, the method records the AC Zeeman shift of the NV resonance produced by an off-resonant microwave field from the spin waves. Using this shift, the authors image surface spin waves in a 54-nm yttrium iron garnet film at a fixed bias field, over detunings from 47 MHz to 567 MHz, and extract both the wavenumber and the absolute amplitude of the spin waves. If the method holds, NV ensembles can serve as fixed-field quantitative spin-wave microscopes for materials whose magnon frequencies lie far from the NV resonance, including metallic ferromagnets and van der Waals magnets.

What carries the argument

The machinery is the AC Zeeman effect on NV centers: an off-resonant microwave field shifts the NV spin resonance frequency by $f_{\rm ACZ} = B_{\rm mw}^2/\Delta$, where $B_{\rm mw}$ is the microwave amplitude and $\Delta$ the detuning (Eq. 2). The paper detects this shift with a Carr-Purcell sequence of two $\pi$ pulses (CP-2): the signal microwave is applied between the pulses, and the accumulated phase yields a photoluminescence oscillation at frequency $f_{\rm ACZ}$. Because the signal enters as $B_{\rm mw}^2$ rather than through a Rabi resonance, the measurement works even when $\Delta$ far exceeds the Rabi frequency. The imaging stage then exploits interference between the spatially uniform reference microwave from the antenna and the spin-wave microwave field; fitting the total amplitude along the propagation direction (Eq. 3) separates $B_{\rm ref}(x)$ from $B_{\rm sw}(x)\cos(k_x x + \theta_0)$, and Eq. (5) converts $B_{\rm sw}$ into the spin-wave magnetization $m(x)$ via the dipolar decay factor $e^{-kz}(1-e^{-kd})$.

What would settle it

The claim would be settled by comparing the AC Zeeman images with an independent, quantitative amplitude measurement of the same propagating spin wave, e.g., Brillouin light scattering or a calibrated inductive antenna, across the full detuning range; a systematic mismatch at large wavenumbers or large detunings would indicate that the reference-field model or the dipolar transfer function is wrong. A simpler, parameter-level test is to repeat the extraction while varying the assumed $z_d$ within its stated $\pm 20$ nm uncertainty and verify that the resulting $\mu_0 m(x)$ values stay within the reported error bars, since Eq. (5) depends exponentially on this distance.

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Extended reading notes

Core claim

The central claim is that the AC Zeeman effect converts off-resonant microwaves into measurable shifts of the NV spin resonance, and that this shift can be used for quantitative wide-field imaging of off-resonant spin waves. At a fixed bias field $B_0 = 18.4$ mT (NV resonance at 2356.7 MHz), the authors sweep the spin-wave frequency from 1800 MHz to 2310 MHz and observe clear interference patterns whose period gives the spin-wave wavelength and whose amplitude, after fitting with Eq. (3), separates the reference microwave from the spin-wave microwave field. Converting the spin-wave field $B_{\rm sw}(x)$ to spin-wave magnetization $m(x)$ via the dipolar transfer function of Eq. (5) yields decay curves and a wavenumber dependence consistent with stripline excitation efficiency. The extracted effective magnetization $\mu_0 M_{\rm eff} = (169.5 \pm 0.7)$ mT matches the value obtained from resonant Rabi measurements $(169.6 \pm 0.7)$ mT, and the spin-wave amplitude scales linearly with input microwave power up to about 12 mT, consistent with linear spin-wave dynamics.

Load-bearing premise

The quantitative amplitude values depend on the reference microwave being much stronger than the spin-wave field, on its phase being uniform over the field of view, and on the NV-to-film distance $z_d = (878 \pm 20)$ nm being correct; a failure of any of these shifts the extracted spin-wave amplitude, and the authors also note that no point-spread-function correction was applied, which underestimates amplitudes at high wavenumbers by 10–20%.

Editorial extensions

If this is right

Spin-wave frequencies can be swept over hundreds of megahertz at a single bias field, so the dispersion relation of a magnetic film can be mapped without re-magnetizing the sample, eliminating the invasive field changes required by Rabi-based NV imaging.
The consistency of the effective magnetization extracted off-resonance ($\mu_0 M_{\rm eff} = 169.5 \pm 0.7$ mT) with the resonant value ($169.6 \pm 0.7$ mT) shows that the wavenumber extraction remains reliable across the entire off-resonant band.
The measured sensitivity of $\eta_{B_{\rm mw}} \approx 25~\mu\rm T/\sqrt{\rm Hz}$ at $\Delta = 100$ MHz means a 0.42 mT off-resonant spin-wave field can be resolved in seconds, and the paper's extrapolations indicate that with longer NV coherence times the same protocol could detect spin waves at tens of gigahertz.
The linear increase of the extracted spin-wave amplitude with input microwave power up to about 12 mT validates the quantitative interpretation and opens the way to wideband studies of nonlinear spin-wave dynamics.

Reading between the lines

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

Because the AC Zeeman signal is quadratic in the total microwave amplitude, the same protocol could be operated as a pure field sensor by injecting a calibrated reference tone through the antenna, decoupling the reference field from the excitation efficiency and potentially improving the spatial uniformity of the phase reference.
The method's phase sensitivity is not tied to any resonance condition, so it could be combined with spin-wave frequency mixing to image magnons that are far outside the NV response band, using the AC Zeeman effect as a linear readout of the mixed product.
A natural experimental extension is to replace the CP-2 sequence with longer dynamical decoupling sequences (e.g., XY8); the paper estimates this could push the detectable frequency range to tens of gigahertz, and the extracted spectra would provide a direct test of the Floquet expression in Eq. (7).
The authors note that at high wavenumbers the optical point-spread function reduces the apparent spin-wave amplitude by 10–20%; calibrating the PSF with a known stripline field distribution would turn the current demonstration into a fully quantitative method over the entire band.

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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

Bottom line: this is a real experimental step forward, not a repackaging. The AC Zeeman effect has been used before for single-NV and resonator microwave detection, but using it for widefield imaging of propagating spin waves at fixed bias field and detunings above 500 MHz is new and useful. The dispersion data are the strongest part of the paper: the extracted wavenumbers across eight frequencies fit a surface-spin-wave dispersion with a single free parameter, Meff = 169.5 mT, consistent with the value from the resonant Rabi protocol. That internal consistency is genuine evidence that the interference fringes are the spin waves.

The soft spot is the amplitude extraction at the largest detunings. At fsw = 1800 MHz (Δ = 556.7 MHz), the usable field of view contains roughly two fringes, and Eq. (3) has seven free parameters separating a stretched-exponential reference field from an exponentially decaying spin-wave term. That separation is not independently calibrated, and the authors admit the reference model is imperfect: they note anomalous decay lengths at 2280 MHz and the absence of the predicted oscillatory k-dependence in Appendix I. The uncorrected PSF adds another 10–20% uncertainty at high k. So the wavenumber claim is solid; the amplitude numbers at the far-off-resonant end are more like estimates. The power-dependence check in Sec. V is reassuring but it was done at Δ = 96.7 MHz, where the fit has plenty of fringes, so it does not validate the worst case.

The 567 MHz in the abstract versus 556.7 MHz in Sec. IV is a minor slip, not a substantive flaw. The tens-of-gigahertz sensitivity projection is explicitly an extrapolation based on an assumed 50 µs coherence time; they label it as such.

This paper is for people working on NV magnetometry and magnonics; it gives them a protocol that could extend spin-wave imaging to metallic and van der Waals magnets. I would send it to a serious referee. The experimental demonstration is well executed and the main claim—that NV ensembles can image off-resonant spin waves at fixed bias field—holds up. The referee should push on the amplitude extraction: ask for a calibration check of Bref, a PSF correction, or a statement that amplitude values at the largest detunings are semiquantitative. If the authors can separate the robust wavenumber claim from the softer amplitude claim, the paper is a solid contribution.

Referee Report

4 major / 6 minor

Summary. This manuscript reports widefield imaging of spin waves in a 54 nm YIG film using NV centers and the AC Zeeman effect, demonstrating off-resonant detection at fixed bias field with detunings up to about 567 MHz. The authors present two-dimensional interference images between spin-wave and reference microwaves, fit one-dimensional line profiles with Eq. (3) to extract wavenumber, phase, and amplitude, validate the dispersion relation through a one-parameter fit that yields Meff = 169.5 mT consistent with their resonant Rabi-based measurement, show a linear power dependence of the extracted spin-wave amplitude, and estimate the sensitivity of the protocol for future applications. The central experimental demonstration of wideband imaging of off-resonant spin waves is convincing, while the quantitative amplitude extraction is the main weak point.

Significance. If the quantitative amplitude extraction is validated, this work substantially extends NV widefield spin-wave microscopy by removing the resonance-matching constraint, which is relevant for metallic ferromagnets and van der Waals magnets. The paper has several genuine strengths: the wavenumber claim is supported by two independent determinations of the effective magnetization (169.5 and 169.6 mT), the Floquet derivation in Appendix J provides a rigorous foundation for the AC Zeeman shift, the power-dependence experiment in Sec. V gives a scaling test, and the sensitivity analysis clarifies the practical limits of the protocol. The phase and wavenumber results are solid; the absolute amplitude values and their frequency dependence are not yet established to the same standard. I do not see a circularity problem in the central claim: Eq. (2) is taken from prior work, but the wideband imaging demonstration does not reduce to a fitted parameter.

major comments (4)

[Sec. IV, Eq. (3), Fig. 5] The quantitative amplitude claim rests on a seven-parameter fit of Eq. (3) that separates a stretched-exponential reference field Bref(x) from an exponentially decaying spin-wave term Bsw(x). At the largest detuning, fsw = 1800 MHz (Fig. 4a), the field of view contains only about two interference fringes, so the oscillatory component cannot be robustly separated from the reference envelope. The authors themselves point to sensitivity of the decomposition in Sec. IV (the anomalous decay lengths at fsw = 2280 MHz) and in Appendix I (the predicted stripline Fourier oscillations are absent in the measured amplitude). I request an explicit validation of the extracted Bsw(x), for example by measuring Bref with spin waves suppressed or at a frequency where no spin waves propagate, by a parameter-correlation or Monte Carlo analysis of the fit, or by fitting with an independently calibrated Bref profile. Without such a check, the absolute amplitude values in Fig. 5(d) and Fig. 6(c) are not quantitatively supported.
[Sec. IV, PSF discussion] The paper states that the spin-wave amplitude is underestimated by 10 to 20% at large wavenumbers because no point-spread-function correction is applied, and that this effect does not alter the essence of the results. Since Fig. 5(d) is presented as a quantitative frequency-dependent amplitude and is used in Appendix I to compare with numerical simulations, this systematic error is load-bearing for the amplitude claim. Please apply a PSF correction or, at minimum, quantify the k-dependent correction and show it as a systematic band or error bar in Figs. 5(d) and 6(c), and discuss how it affects the comparison with the stripline excitation model in Appendix I.
[Eq. (5), Appendix D] The conversion from Bsw(x) to the spin-wave amplitude m(x) uses the transfer function D(k,z) = exp(-kz)(1 - exp(-kd)) with z = zd = (878 +/- 20) nm, but no uncertainty propagation is reported. At the largest wavenumbers in Fig. 5(b) (k around 5-6 rad/um), the exponential factor exp(-kz) makes m(x) exponentially sensitive to zd; the quoted +/-20 nm alone translates into roughly a 10% uncertainty in the conversion, before adding PSF and fit uncertainties. Please propagate the uncertainties in zd, kx, and the ellipticity eta_kx into the reported m(x) values and state the resulting error bars in the figures and in the Appendix I comparison.
[Sec. V, Fig. 6(d)] The linear dependence of the extracted m0 on Hmw is offered as validation of the quantitative method, but it tests only the scaling of the fitted amplitude with input power, not the absolute accuracy of the Bref/Bsw decomposition. Because both Bref and Bsw scale linearly with the input microwave amplitude, a systematic error proportional to Bref would also produce a linear plot. Please state this limitation explicitly, or provide an independent calibration of Bsw, so that the power-dependence result is not overinterpreted as absolute validation.

minor comments (6)

[Throughout] There are several typos and grammatical slips: "the the time-averaged" in Sec. I, "primely" in Sec. IV, "anisortopy" and "sueface" in Appendix B, and "Amp`ere" in Appendix D.
[Fig. 1] The axis label "Frecuency" should be "Frequency", and the panel labels "PulseOperation" and "MicrowaveSignal" are missing spaces.
[Eq. (3)] Please list explicitly which parameters are free in the fit and which are fixed for each dataset; in particular, state whether x0 is always fixed at 20 um and whether Bc_ref is set to zero for both the resonant and off-resonant analyses.
[Appendix I] The text refers to "Fig. H1(d) in the main text" for the off-resonant spin-wave amplitude; the intended reference appears to be Fig. 5(d). Please correct this cross-reference.
[Sec. III] The statement that the resonator frequency response contributes up to about 30% to the spin-wave amplitude would benefit from a quantitative estimate or a citation, since it is used to interpret the amplitude trends in Fig. 3(e).
[Data availability] No data availability or code availability statement is provided. Given that the quantitative claims depend on multi-parameter fitting, sharing the raw line profiles and fitting code would substantially strengthen the reproducibility of the paper.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central wideband imaging claim rests on independent measurements, dispersion consistency, and disclosed data-analysis assumptions, not on a fitted parameter or a self-citation chain.

full rationale

The paper's central claim is that the AC Zeeman effect allows widefield imaging of off-resonant spin waves over a wide frequency range up to a maximum detuning of 567 MHz at fixed bias field. The AC Zeeman frequency shift in Eq. (2) is a standard physical formula, and the paper independently derives a more rigorous expression in Appendix J using Floquet perturbation theory; it is not defined in terms of the measured spin-wave amplitude. The wavenumber extraction is validated by fitting the measured Bmw(x) with Eq. (3) and comparing the resulting kx(fsw) to the independent dispersion relationship Eq. (4). The only free parameter in that comparison is the effective magnetization Meff, and the fitted value (169.5 ± 0.7 mT) is consistent with the value obtained by the conventional Rabi protocol (169.6 ± 0.7 mT) and with an external literature value. This is an internal consistency check against an independent measurement channel, not a circular reduction. The amplitude extraction does involve fitting Bsw(x), Bref(x), kx, and phase via Eq. (3), but that is standard parameter estimation from raw data, and the paper explicitly discloses the load-bearing assumptions and limitations: reference-field mismodeling is acknowledged as affecting Bsw (Sec. IV and Fig. 5 discussion), and the absence of PSF correction is stated to cause a 10-20% underestimation at high wavenumber. Those are accuracy caveats, not demonstrations that the output is equivalent to the input by construction. Self-citations to Ref. [25] provide the pulse protocol and SCROFULOUS composite-pulse technique, but the paper re-derives or simulates the pulse-error tolerance in Appendix G and does not rely on the cited work for the spin-wave result itself. No uniqueness claim, imported ansatz, or renaming of a known result is load-bearing. The derivation chain is therefore self-contained with respect to circularity.

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

No new physical entities are introduced. The main fitted inputs are Meff, the Eq. (3) fit parameters, and the zd calibration, all of which are standard analysis parameters. The axioms are standard magnonics and NV-sensing assumptions, made explicit in the appendices.

free parameters (4)

Effective magnetization Meff = 169.6 +/- 0.7 mT (resonant); 169.5 +/- 0.7 mT (wideband)
Fitted via the dispersion relation Eq. (4); used for theoretical dispersion lines and enters the ellipticity/transfer function in amplitude conversion.
Eq. (3) line-profile fit parameters = kx, Bsw0, ld, theta0, Bref0, lref, pref
Wavenumber and spin-wave amplitude values are extracted from these fits; the claimed quantitative results inherit their uncertainty.
NV-to-YIG distance zd = 878 +/- 20 nm
Calibrated by fitting the stripline stray field (Appendix D); used exponentially in the transfer function Eq. (5), so absolute amplitudes depend on it.
Sensitivity constant eta_Bmw = 25 uT / sqrt(Hz)
Fitted from standard error versus integration time (Eq. 6); used for the future applicability projection, not for the main imaging claim.

assumptions (4)

domain assumption Landau-Lifshitz-Gilbert equation with small-amplitude linearization
Appendix B derives the spin-wave dispersion and transfer function from the LLG equation, assuming linear precession and uniform magnetization across the film thickness.
domain assumption Reference microwave phase is uniform across the field of view and Bref >> Bsw
Appendix C uses this to approximate the total microwave amplitude as Bref(x) + Bsw(x) cos(kx + theta), which is the basis of the fitting model Eq. (3).
domain assumption AC Zeeman shift is described by the first term of Eq. (2) for the detunings used
The paper assumes Delta >> frabi and Delta small compared to NV spin resonance frequencies; more rigorous Floquet treatment (Appendix J) shows corrections become important at larger detuning.
domain assumption SCROFULOUS composite pulses compensate Rabi amplitude errors up to roughly +/- 50%
Appendix G restricts the field of view to x = 1.95-14.3 um where this assumption holds; outside this region the measured amplitudes would be unreliable.

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Pith. "Pith review of Wideband wide-field imaging of spin-wave propagation using diamond quantum sensors." pith.science (2026). https://pith.science/paper/PKXOU726

@misc{pith2026241117344,
  author       = {Pith},
  title        = {Pith review of: Wideband wide-field imaging of spin-wave propagation using diamond quantum sensors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKXOU726}},
  note         = {Machine review of arXiv:2411.17344}
}

read the original abstract

Imaging spin-wave propagation in magnetic materials in a wide frequency range is crucial for understanding and applying spin-wave dynamics. Recently, nitrogen-vacancy (NV) centers in diamond have attracted attention as sensors capable of quantitatively measuring the amplitude and phase of coherent spin waves. However, the conventional sensing protocol has been limited to detecting spin waves whose frequencies match the resonance frequency of the NV spins. We demonstrate that by utilizing the AC Zeeman effect, it is possible to image spin waves propagating in a yttrium iron garnet (YIG) thin film over a wide frequency range up to a maximum detuning of 567 MHz without changing the external magnetic field. Our results expand the applicability of NV centers for spin-wave sensing and pave the way for quantitative investigations of the dynamics in various magnetic materials, such as metallic ferromagnets and van der Waals magnets.

Figures

Figures reproduced from arXiv: 2411.17344 by the authors.

**Figure 2.** FIG. 2. Results of imaging resonant spin-wave propagation using the conventional protocol based on the Rabi oscillation at external magnetic [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. One-dimensional analysis results of sensing resonant spin [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Results of imaging off-resonant spin-wave propagation using the AC Zeeman effect at spin-wave frequencies [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. One-dimensional analysis of sensing off-resonant spin-wave [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 7.** Figure 7: FIG. 7. Evaluation of the sensitivity of off-resonant spin-wave [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 6.** Figure 6: FIG. 6. Off-resonant spin-wave amplitude dependence on the mi [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Forward citations

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

Entanglement-assisted multiparameter estimation with a solid-state quantum sensor
quant-ph 2025-05 conditional novelty 6.0 of 10

A room-temperature NV-center experiment simultaneously estimates amplitude, detuning, and phase of a microwave drive from one sequence, with sensitivity improving linearly in interrogation time.

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