Spin-noise spectroscopy as a tool for probing magnetic order

Julius Schlegel; Martin Evers; Ulrich Nowak

REVIEW 2 major objections 4 minor 31 references

Spin-noise spectroscopy as a tool for probing magnetic order

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Spin-noise spectroscopy reveals magnetic order and phase transitions from magnetization fluctuations.

desk verdict A solid numerical prediction of spin-noise signatures in ferro- and antiferromagnets, but the advertised correlation-time marker for the spin-flop transition rests on a Lorentzian fit the authors admit is unreliable exactly there. read the letter →

arxiv 2411.18342 v1 pith:2AFXZNS2 submitted 2024-11-27 cond-mat.mtrl-sci

Julius Schlegel , Martin Evers , Ulrich Nowak This is my paper · ORCID

classification cond-mat.mtrl-sci PACS 75.40.Gb75.50.Ee75.30.Ds

keywords spinnoisespectroscopymagnetizationfluctuationsatomisticmodelLandau-Lifshitz-Gilbertdynamicsferromagneticresonanceantiferromagnetflopmagnonmodesphasetransitions

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 argues that spin-noise spectroscopy—measuring the equilibrium fluctuations of a sample's magnetization—can serve as a practical probe of magnetic order in ferromagnets and antiferromagnets. Using numerical simulations of an atomistic spin model, it shows that the spectral noise power density has a Lorentzian resonance at the ferromagnetic resonance frequency in an easy-axis ferromagnet, and that this resonance vanishes at the Curie temperature. For an easy-axis antiferromagnet, two resonance peaks appear that track the two magnon branches, and the total noise power peaks at the spin-flop field. These features give experimentalists three measurable quantities—resonance frequency, correlation time, and noise amplitude—to detect phase transitions and magnon mode frequencies, particularly in antiferromagnets where the order parameter cannot be measured directly.

What carries the argument

The central object is the spectral noise power density $P_\beta(\omega)$ of the magnetization, computed as the Fourier transform of the magnetization autocovariance via the Wiener-Khinchin theorem from stochastic Landau-Lifshitz-Gilbert simulations. It is characterized by three parameters extracted from a Lorentzian fit (or sum of Lorentzians): the resonance frequency $\omega_0$, the half-width $\Gamma_\beta$ (inverse correlation time $\tau_\beta$), and the maximum spectral power (equivalently total noise power $P_{\text{tot}}$). The frequencies are matched to linear spin-wave theory dispersion relations for ferromagnets and antiferromagnets, which supply the interpretation of the peaks as magnon modes.

What would settle it

Run the same stochastic LLG simulation for an easy-axis antiferromagnet at $k_B T = 1|J|$ with fields across $B_{sf} \approx 0.45B_J$ and check whether the lower resonance frequency $\omega_-$ vanishes exactly at $B_{sf}$ and whether the total in-plane noise power $P_{\text{tot}}^x$ peaks at the spin-flop field; alternatively, a Faraday-rotation noise experiment on a uniaxial antiferromagnet thin film should see the two-peak splitting disappear and a single zero-frequency peak appear above the spin-flop field.

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Extended reading notes

Core claim

Within an atomistic spin model solved by stochastic Landau-Lifshitz-Gilbert dynamics, the spectral noise power density $P_\beta(\omega)$ of the magnetization is Lorentzian (or a sum of Lorentzians). For an easy-axis ferromagnet, below the Curie temperature the in-plane components show a resonance at the ferromagnetic resonance frequency $\omega_r = \gamma(2d_z + \mu_s B_z)/\mu_s$, which softens to zero at $T_C$; above $T_C$ all components are white noise at low frequency and $1/\omega^2$ at high frequency. For an easy-axis antiferromagnet, a finite field splits the resonance into two peaks corresponding to the two spin-wave branches $\omega_\pm(k)$, and the lower frequency goes to zero while the upper jumps at the spin-flop field $B_{sf} \approx 0.45B_J$; the total noise power in both $x$ and $z$ components peaks at $B_{sf}$. The correlation time $\tau_\beta = 1/\Gamma_\beta$ scales as $1/\alpha$ and shows distinct signatures: for the ferromagnet $\tau_z$ peaks at $T_C$, while for the antiferromagnet $\tau_x$ drops near the N\'eel temperature.

Load-bearing premise

The entire analysis assumes the numerically computed noise spectra can be accurately fitted by a Lorentzian (or a sum of Lorentzians).

Editorial extensions

If this is right

Spin-noise spectroscopy can detect the ferromagnetic-paramagnetic transition in easy-axis ferromagnets through the disappearance of the in-plane resonance peak at the Curie temperature.
In antiferromagnets, the two resonance frequencies $\omega_\pm$ and the total noise power provide a measure of the spin-flop field $B_{sf}$ at finite temperature.
The correlation time $\tau_\beta \propto 1/\alpha$ allows extraction of the Gilbert damping from noise spectra, since $\alpha P_\beta(\omega)$ collapses when plotted against $(\omega-\omega_0)/\alpha$.
The antiferromagnetic-paramagnetic transition leaves a clear trace: below the N\'eel temperature the in-plane and out-of-plane noise powers differ, while above it they coincide.
The same approach can be extended to other reorientation transitions, such as the Morin transition in hematite.
Because the noise variance scales as $1/N$, the method is most naturally applied to small probed volumes, as in a focused laser spot in Faraday-rotation or Kerr setups.

Reading between the lines

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

If the Lorentzian fit is unreliable near $B_{sf}$ and at low temperature, then the extracted parameters there are not well-defined; a more general spectral shape analysis may be needed to make those claims quantitative.
The symmetry $P_\beta(\omega)=P_\beta(-\omega)$ means the sign of the precession frequency cannot be resolved; polarization- or phase-sensitive detection schemes could break this ambiguity and distinguish the two magnon branches directly.
One could test the damping scaling experimentally: if $\tau_\beta \propto 1/\alpha$ holds across the transition, temperature- or doping-dependent damping should change the linewidth in a predictable way.
The predicted two-peak splitting in the antiferromagnet could be verified with a broadband optical noise measurement on a uniaxial antiferromagnet thin film across the spin-flop field.

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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

Short version: this is a solid, clearly written atomistic spin-dynamics study that makes a specific and plausible prediction: the spectral noise power density of the magnetization carries measurable signatures of the FM/PM and AFM/PM transitions and of the spin-flop field. The resonance frequencies and total noise power are robustly extracted and match linear spin-wave theory with mean-field temperature scaling. The main soft spot is the correlation-time peak at the spin-flop transition: the paper's own conclusion admits that close to the spin-flop transition the spectra deviate from a Lorentzian and cannot always be fit accurately. Since tau_x^- is defined through that Lorentzian fit, its reported peak at B_sf may be an artifact. That does not sink the central claim, because the spin-flop signature is also carried by the resonance frequency and total noise power, which are less lineshape-sensitive. The authors should either provide a non-Lorentzian analysis of that regime or soften the claim about tau_x^-.

What is new: previous spin-noise work on magnets was mostly experimental or used other theoretical approaches. This is a clean numerical demonstration in a standard atomistic model that spin-noise spectra can in principle reveal magnon frequencies, correlation times, and transition points. The damping scaling check in Appendix A is a nice self-consistency test, and Appendix D addresses the symmetry-drift issue in the flopped state carefully enough.

Weaknesses beyond the Lorentzian issue: no error bars on the extracted parameters, which matters for a numerical paper; no release of code or data, so reproducibility is limited; and finite-size effects are not quantified, even though the authors note the variance scales as 1/N. None of these are fatal. The mean-field comparison is approximate but used only as a rough benchmark.

Who this is for: people planning ultrafast spin-noise experiments on magnetic solids, and theorists building atomistic simulation tools for spintronics. It is not a breakthrough, but it is an honest mapping of what to expect. I would send it to a competent referee; the Lorentzian caveat is important enough that it should be addressed in revision.

Recommendation: engage with it as a serious-but-needs-revision paper. If the authors fix or hedge the tau_x^- claim and add error bars, it is a solid contribution.

Referee Report

2 major / 4 minor

Summary. The paper presents atomistic spin-dynamics simulations of equilibrium magnetization noise in an easy-axis ferromagnet and an easy-axis antiferromagnet, computing the spectral noise power density from the Landau-Lifshitz-Gilbert equation with thermal noise. The central claim is that spin-noise spectroscopy can be used to determine phase transitions, magnon mode frequencies, and correlation times by extracting three Lorentzian parameters: resonance frequency, correlation time, and total noise power. For the ferromagnet, the in-plane resonance frequency vanishes at the Curie temperature. For the antiferromagnet, the field dependence of the two resonance frequencies and of the total noise power are proposed as signatures of the spin-flop transition.

Significance. If established, the results would provide a theoretical foundation for using ultrafast spin-noise spectroscopy as a probe of magnetic order, particularly for antiferromagnets where the order parameter is difficult to measure directly. The paper's strengths include the use of a standard stochastic LLG framework with a fluctuation-dissipation-consistent noise term, comparison against linear spin-wave theory and mean-field temperature scaling as external benchmarks, and careful appendix tests of damping dependence and of the in-plane drift of the Néel vector above the spin-flop field. The significance is moderated by the fact that the central quantitative claims rest on Lorentzian fits, and the manuscript itself states that such fits are not always accurate close to the spin-flop transition and at low temperatures, which is exactly the regime where the most distinctive correlation-time signature is claimed.

major comments (2)

[§V and Fig. 4b] The claim that the lower-branch correlation time τ_x^- peaks at the spin-flop field B_sf is based on Lorentzian fits of the spectral noise power, but the concluding section explicitly states that 'close to the spin-flop transition' the spectra deviate from a Lorentzian and that 'it is not always possible to accurately fit a Lorentzian to the data.' Since τ_x^- is defined only through the Lorentzian form (Eqs. 8–9), the reported peak at B_sf may be an artifact of forcing a Lorentzian onto a non-Lorentzian spectrum. Please provide a lineshape-robust extraction of the correlation time (for example, directly from the autocovariance function or from spectral moments), or qualify the spin-flop correlation-time claim and show that the peak persists under the alternative measure.
[Figs. 2 and 4; §II] The numerical results are presented without statistical uncertainties, and the text does not describe how the Lorentzian parameters are extracted from the spectra (e.g., fit range, weighting, number of spectra averaged, or the fitting criterion). With only Nav = 50 realizations, the spectral estimates carry nontrivial statistical error, and without error bars the agreement with mean-field estimates in Fig. 2a, the non-monotonic temperature dependence of τ in Fig. 2b, and the peak positions in Fig. 4 cannot be quantitatively assessed. Please add error bars or confidence intervals and specify the fitting procedure.

minor comments (4)

[§I] The sentence 'novel experimental methods are are sought for' contains a duplicated 'are' and should be rephrased.
[§IV] The phrase 'gaped quadratic branch' should read 'gapped quadratic branch.'
[Fig. 1 caption] The term 'brown noise' is used without definition; please define it explicitly as a spectral density proportional to ω^{-2}.
[Appendix D] The phrase 'locks the magnets ground state' should be 'locks the magnet's ground state.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the numerical noise spectra are independent first-principles outputs compared against external spin-wave theory and mean-field benchmarks.

full rationale

The paper's central predictions are not equivalent to its inputs. The spectral noise power density Pβ(ω) is computed directly from stochastic LLG trajectories via Eq. (4), and the Lorentzian parameters in Eqs. (8)-(9) are a post hoc lineshape reduction, not fitted to any external target quantity. The resonance frequencies are then compared with independent linear spin-wave theory (Eqs. (10)-(12)) and with the standard mean-field scaling of Eq. (11); the agreement is a nontrivial numerical result. The mean-field scaling is cited to Ref. [25], which includes an author overlap, but it is a standard approximation used only for comparison; the main phase-transition signatures (vanishing resonance peak at TC, peak in total noise, spin-flop features at the Monte-Carlo-determined Bsf ≈ 0.45BJ) are directly visible in the simulated spectra and do not depend on that citation. Appendix C determines Bsf using independent Monte Carlo simulations, so the spin-flop field is not chosen to force the noise signatures. The paper explicitly flags a limitation in Sec. V: "it is not always possible to accurately fit a Lorentzian to the data" for systems at low temperatures and close to the spin-flop transition. This is an honest validity caveat for the correlation-time extraction, but it is not circular: the raw spectra remain the input and no fitted parameter is renamed as a prediction. Self-citations, e.g., Refs. [12], [24], [25], and [29], are motivational or standard results rather than load-bearing uniqueness claims or ansatz imports, so they do not raise the circularity score.

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

The central claim relies on standard statistical mechanics and atomistic spin models, plus approximate mean-field and spin-wave theory for interpretation. No ad hoc entities or fitted parameters are introduced; all model parameters are physical inputs from prior literature or chosen for the model.

assumptions (5)

standard math Wiener-Khinchin theorem relates autocorrelation and spectral noise power density.
Used in eq. (6) to connect the two central observables.
domain assumption Stochastic LLG equation with white noise obeying the fluctuation-dissipation relation describes equilibrium spin dynamics.
Central model, eq. (2), used to generate magnetization trajectories.
domain assumption Classical spins with Heisenberg exchange, uniaxial anisotropy, and Zeeman coupling are sufficient to capture spin noise in magnetic solids.
Model Hamiltonian eq. (1), assumed to represent real ferro- and antiferromagnets.
domain assumption Mean-field temperature scaling of exchange and anisotropy, J(T)=J<m>^2 and D(T)=d<m>^3, is valid for comparing finite-temperature simulation results to spin-wave theory.
Used in eq. (11) and in the antiferromagnet section to estimate temperature-dependent resonance frequencies.
domain assumption Linear spin-wave theory dispersion relations (eqs. 10, 12, B3, B5) remain approximately valid at finite temperatures with renormalized parameters.
Used to interpret the resonance peaks in the simulated noise spectra and to compare with mean-field estimates.

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Cite this review

Pith. "Pith review of Spin-noise spectroscopy as a tool for probing magnetic order." pith.science (2026). https://pith.science/paper/2AFXZNS2

@misc{pith2026241118342,
  author       = {Pith},
  title        = {Pith review of: Spin-noise spectroscopy as a tool for probing magnetic order},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2AFXZNS2}},
  note         = {Machine review of arXiv:2411.18342}
}

read the original abstract

Spin noise spectroscopy is a technique to measure magnetization fluctuations, a subject of increasing relevance in ultrafast spintronics. We investigate numerically the equilibrium spin noise of ferro- and antiferromagnets within an atomistic spin model. The aim is to predict the possible outcomes of ultrafast spin-noise spectroscopy measurements and demonstrate what relevant information can be extracted. Specifically, we show how this method can be used to determine phase transitions, frequencies of magnon modes and correlation times.

Figures

Figures reproduced from arXiv: 2411.18342 by the authors.

**Figure 1.** Spectral noise power density Pβ of an easy-axis ferromagnet. Upper panel a) shows the noise of mz, lower panel b) of mx (my equivalent to mx). Both exhibit white noise at low frequencies and brown noise at high frequencies. However, the in-plane noise Px below the Curie temperature kBTC ≈ 1.48 |J| has a resonance at the ferromagnetic resonance frequency ωr. This frequency decreases with increasing temperature and v… view at source ↗

**Figure 2.** Characteristics for easy-axis ferro- (blue) and an [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Spectral noise power density Pβ of an easy-axis antiferromagnet for different magnetic fields Bz at fixed temperature kBT = 1 |J| below and above the spin-flop field Bsf ≈ 0.45BJ (see appendix C). a) out-of-plane z component, b) in-plane x component (Py equivalent). The latter shows the antiferromagnetic resonance frequencies ω ± r that have a distinctive field-dependence. For fields 0 < Bz < Bsf there are two pea… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: fig. 4: first of all, for finite field the in-plane components [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Dependence of the spectral noise power Pβ(ω) on the Gilbert damping α: we show αPβ over 1 α (ω−ω0) for ferromagnets (left panels) and antiferromagnets (right panels) for different values of α, where ω0 = ω FM,AFM r is the respective resonance frequency. The temperature…

**Figure 6.** Figure 6: Field dependence of the normalized Néel vector [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Comparison of an antiferromagnet in the spin-flop [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

H. Wang, C. Du, P. C. Hammel, and F. Yang, Antiferro- magnonic spin transport fromY3Fe5O12 into NiO, Phys. Rev. Lett.113, 097202 (2014)

work page 2014

[2] [2]

H. Wang, C. Du, P. C. Hammel, and F. Yang, Spin trans- 10 port in antiferromagnetic insulators mediated by mag- netic correlations, Phys. Rev. B91, 220410(R) (2015)

work page 2015

[3] [3]

Uchida, K

Z.Qiu, J.Li, D.Hou, E.Arenholz, A.T.N’Diaye, A.Tan, K.-i. Uchida, K. Sato, S. Okamoto, Y. Tserkovnyak, Z. Q. Qiu, and E. Saitoh, Spin-current probe for phase transi- tion in an insulator, Nature Communications7, 12670 (2016)

work page 2016

[4] [4]

Cramer, F

J. Cramer, F. Fuhrmann, U. Ritzmann, V. Gall, T. Ni- izeki, R. Ramos, Z. Qiu, D. Hou, T. Kikkawa, J. Sinova, U.Nowak, E.Saitoh,andM.Kläui,Magnondetectionus- ing a ferroic collinear multilayer spin valve, Nature Com- munications 9, 1089 (2018)

work page 2018

[5] [5]

Schlitz, T

R. Schlitz, T. Kosub, A. Thomas, S. Fabretti, K. Nielsch, D. Makarov, and S. T. B. Goennenwein, Evolution of the spin hall magnetoresistance in Cr2O3/Pt bilayers close to the Néel temperature, Applied Physics Letters112, 132401 (2018)

work page 2018

[6] [6]

Němec, M

P. Němec, M. Fiebig, T. Kampfrath, and A. V. Kimel, Antiferromagnetic opto-spintronics, Nature Physics14, 229 (2018)

work page 2018

[7] [7]

Starosielec and D

S. Starosielec and D. Hägele, Ultrafast spin noise spec- troscopy, Applied Physics Letters93, 051116 (2008)

work page 2008

[8] [8]

E. B. Aleksandrov and V. S. Zapasskii, Magnetic reso- nance in the Faraday-rotation noise spectrum, Zh. Eksp. Teor. Fiz.81, 132 (1981)

work page 1981