{"id":"6237529e-2585-4f21-a321-a3e69345438e","arxiv_id":"2411.17344","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Using the AC Zeeman effect, NV diamond sensors imaged propagating spin waves in a YIG film at detunings up to about 557 MHz from the NV resonance at a fixed magnetic field.","lead":"Diamond nitrogen-vacancy sensors usually detect magnetic waves only when the wave frequency exactly matches the sensor's spin resonance. This paper shows they can image spin-wave propagation in a magnetic film across a broad frequency range using the AC Zeeman effect, without changing the magnetic field.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Amplitude extraction at the largest detunings rests on an unvalidated separation of a seven-parameter fit of the reference and spin-wave fields; this, not the wavenumber claim, is the load-bearing weak point.","rationale":"The reader's weakest assumption correctly identifies the amplitude-extraction chain as the fragile part of the paper: reference-field dominance, uniform reference phase, and knowledge of zd are load-bearing, and the authors flag reference-field mismodeling and the omitted PSF correction. My stress-test sharpens this into a more specific issue: at the largest detunings, the data contain too few interference fringes for the seven-parameter Eq. (3) fit to separate Bref and Bsw reliably. This is not an objection to the core demonstration, which is convincing: the frequency-dependent fringe spacing follows the spin-wave dispersion, and the two independent experiments give consistent effective magnetization values. The concern is confined to the quantitative amplitude and to the absolute conversion to m(x), where the transfer function's exponential sensitivity at high k amplifies any Bsw error. Because the paper's headline includes quantitative imaging, this uncertainty matters; however, it is disclosed and partially bounded by the authors, and it does not undermine the wideband detection claim. A direct reference-field measurement or a synthetic identifiability analysis would settle whether the extracted amplitudes are trustworthy. If the amplitudes shift by more than ~20% under the test, the verdict should remain conditional rather than accept; if they are stable, the conditional caveat can be lifted. I therefore recommend no change to the reader's conditional verdict, while asking the authors to provide the requested re-analysis as a condition of full acceptance. No code or data are currently available, which makes the proposed independent re-analysis the only practical check. I found no need to question the authors' honesty or the validity of the AC Zeeman mechanism itself; the issue is a quantitative calibration gap, not a conceptual flaw.","tokens_in":27908,"tokens_out":15247,"duration_ms":165171,"concrete_test":"Re-analyze the Sec. IV and V datasets with an independently determined reference field. One practical route is to use the CST stripline model of Appendix H as the reference profile and refit Bmw(x) with only Bsw(x), kx, and theta0 free. Alternatively, drive the same stripline at a frequency where spin-wave excitation is suppressed (or use a nonmagnetic control sample) and measure Bref(x) directly; then fit the interferometric images with that measured reference. In addition, perform a synthetic identifiability study for fsw=1800 and 1860 MHz: generate noisy data from Eq. (3), then fit with alternative Bref forms (simple exponential, stretched exponential, and CST profile) and with bootstrap resampling.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is quantitative wideband spin-wave amplitude imaging via Eq. (3) and Eq. (5). The wavenumber part of the claim is well supported by the dispersion fit and by the consistency of the extracted effective magnetization. The amplitude part, however, depends on an unvalidated decomposition of the measured Bmw(x) into a stretched-exponential reference field Bref(x)=B0ref exp(-((x-x0)/lref)^pref) and a decaying spin-wave term Bsw(x)=B0sw exp(-(x-x0)/ld)cos(kx x+theta0). At the key widest-detuning frame, fsw=1800 MHz (Delta=556.7 MHz), the field of view contains only about two interference fringes (Fig. 4a), so a seven-parameter fit cannot robustly separate an exponential Bsw from a stretched-exponential Bref. Any reference-model error propagates directly into Bsw(x) and is then amplified into m(x) through the strong transfer function D(k,z)=exp(-kz)(1-exp(-kd)) at the largest k. The authors themselves acknowledge sensitivity to the reference model (Sec. IV, where fsw=2280 MHz shows decay-length anomalies, and Appendix I, where the predicted oscillatory k-dependence is absent) and also disclose an uncorrected 10-20% PSF-induced underestimation at high k. No independent calibration of Bsw is provided, and no code or data are available for an external check. Thus the quantitative amplitude values are the load-bearing uncertainty; the detection and the wavenumber extraction are not in question.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":28188,"tokens_out":4146,"duration_ms":40545,"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":[{"comment":"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.","section":"Sec. IV, Eq. (3), Fig. 5"},{"comment":"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.","section":"Sec. IV, PSF discussion"},{"comment":"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.","section":"Eq. (5), Appendix D"},{"comment":"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.","section":"Sec. V, Fig. 6(d)"}],"minor_comments":[{"comment":"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.","section":"Throughout"},{"comment":"The axis label \"Frecuency\" should be \"Frequency\", and the panel labels \"PulseOperation\" and \"MicrowaveSignal\" are missing spaces.","section":"Fig. 1"},{"comment":"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.","section":"Eq. (3)"},{"comment":"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.","section":"Appendix I"},{"comment":"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).","section":"Sec. III"},{"comment":"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.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nThe 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.\n\nThis 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.","headline":"A genuinely new widefield NV imaging regime for off-resonant spin waves, with solid wavenumber extraction and softer amplitude numbers at the largest detunings.","tokens_in":28812,"tokens_out":2538,"would_cite":true,"duration_ms":23963,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["NV centers","AC Zeeman effect","spin waves","widefield imaging","YIG thin film","magnonics","quantum sensing","microwave magnetometry"],"falsifier":"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.","tokens_in":27664,"feed_emoji":"🧲","tokens_out":9510,"duration_ms":74803,"temperature":0.7,"pith_summary":"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.","feed_headline":"Quantum sensors image spin waves across a 567-MHz band","feed_subtitle":"Off-resonant spin waves in a YIG film are imaged at fixed bias field, yielding phase and amplitude maps.","key_machinery":"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 $e^{-kz}(1-e^{-kd})$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Demonstrates single-NV detection of off-resonant microwaves via the AC Zeeman effect, the basis of the protocol.","marker":"[24]"},{"why":"Supplies the widefield AC Zeeman measurement protocol, the CP-2/SCROFULOUS pulse sequence, and the sensitivity evaluation used in this paper.","marker":"[25]"},{"why":"Establishes the quantitative spin-wave stray-field imaging formalism, including the dipolar transfer function used in Eq. (5).","marker":"[12]"},{"why":"Provides the widefield NV imaging of spin waves with wavenumber-resolved dispersion that this work extends to off-resonant frequencies.","marker":"[13]"},{"why":"Demonstrates off-resonant detection of ferromagnetic resonance with NV centers and gives the rigorous AC Zeeman frequency-shift expression used in Eq. (7).","marker":"[9]"},{"why":"Provides the YIG effective magnetization value used to validate the fitted $\\mu_0 M_{\\rm eff}$.","marker":"[35]"},{"why":"Supplies the argument that stripline excitation efficiency falls with increasing wavenumber, used to interpret the measured spin-wave amplitude decay.","marker":"[36]"}],"fun_headline_variants":["AC Zeeman effect widens NV spin-wave imaging by 567 MHz","Diamond sensors see spin waves 567 MHz off-resonance at fixed field","Off-resonant spin waves imaged wide-field with diamond NV centers","Diamond quantum imager captures spin waves across 567-MHz band"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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%.","fun_headline_variants_meta":{"raw":{"variants":["AC Zeeman effect widens NV spin-wave imaging by 567 MHz","Diamond sensors see spin waves 567 MHz off-resonance at fixed field","Off-resonant spin waves imaged wide-field with diamond NV centers","Diamond quantum imager captures spin waves across 567-MHz band"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000538,"raw_usage":{"total_tokens":2578,"prompt_tokens":939,"completion_tokens":1639,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":555,"completion_tokens_details":{"reasoning_tokens":1558}},"tokens_in":555,"tokens_out":1639,"duration_ms":12320,"temperature":1.0,"reasoning_tokens":1558,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:15:05.821350+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Li, C.-J","cited_arxiv_id":null,"evidence_quote":"Demonstrates single-NV detection of off-resonant microwaves via the AC Zeeman effect, the basis of the protocol."},{"cited_title":"Ogawa, S","cited_arxiv_id":null,"evidence_quote":"Supplies the widefield AC Zeeman measurement protocol, the CP-2/SCROFULOUS pulse sequence, and the sensitivity evaluation used in this paper."},{"cited_title":"Bertelli, J","cited_arxiv_id":null,"evidence_quote":"Establishes the quantitative spin-wave stray-field imaging formalism, including the dipolar transfer function used in Eq. (5)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the widefield NV imaging of spin waves with wavenumber-resolved dispersion that this work extends to off-resonant frequencies."},{"cited_title":"Van der Sar, F","cited_arxiv_id":null,"evidence_quote":"Demonstrates off-resonant detection of ferromagnetic resonance with NV centers and gives the rigorous AC Zeeman frequency-shift expression used in Eq. (7)."},{"cited_title":"Chang, P","cited_arxiv_id":null,"evidence_quote":"Provides the YIG effective magnetization value used to validate the fitted $\\mu_0 M_{\\rm eff}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the argument that stripline excitation efficiency falls with increasing wavenumber, used to interpret the measured spin-wave amplitude decay."}],"review_version":1}