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REVIEW 3 major objections 4 minor 50 references

Mn3Sn's low-temperature transition is not a static spin glass but a growing ferromagnetic component with localized spin-fluctuation slowing.

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2026-08-04 18:45 UTC pith:YTCTB4IO

load-bearing objection Careful muSR experiment with genuinely new observations, but the headline no-glass result is a null result that needs a quantified sensitivity bound before it is sold as established. the 3 major comments →

arxiv 2608.01892 v1 pith:YTCTB4IO submitted 2026-08-03 cond-mat.str-el

Microscopic magnetic phase evolution in the Weyl semimetal Mn₃Sn revealed by μ^+SR

U. Miniotaite , O. K. Forslund , H. Luetkens , V. Rai , J. Persson , G. D. Morris , D. Zuhair , D. W. Tam
show 3 more authors
S. Nandi Y. Sassa M. M{\aa}nsson
This is my paper
classification cond-mat.str-el PACS 76.75.+i75.25.-m75.50.Lk
keywords muon spin relaxationMn3SnWeyl semimetalantiferromagnetismspin glasshelical magnetic orderinternal field distributionmagnetic phase coexistence
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper uses muon spin relaxation to re-examine the low-temperature magnetism of the Weyl semimetal Mn3Sn (composition Mn2.99Sn). It argues that the widely reported spin-glass-like state below 21 K is actually absent in this near-stoichiometric sample: instead, a ferromagnetic component grows while spin fluctuations slow down locally, suggesting the two phenomena are decoupled. The paper also finds that the incommensurate helical phase holds an asymmetric internal-field distribution, pointing to anharmonic distortions of the spin spiral, and that the helical and inverse-triangular antiferromagnetic phases coexist across a broad temperature range. A sympathetic reader would care because it resolves a long-standing microscopic ambiguity about what happens at low temperature in a prototypical antiferromagnetic Weyl semimetal.

Core claim

The central claim is that in Mn2.99Sn the transition at Tf = 21 K is not a static spin-glass freezing. Zero-field muon spin relaxation spectra show no static Kubo-Toyabe-type signature; instead, the relaxation rate of the fastest precession component peaks near Tf, indicating a slowing of spin fluctuations, while an exponentially relaxing component indicates an increasing ferromagnetic contribution. The paper interprets these as separate phenomena that may be decoupled from the static glassy freezing observed in Mn-excess samples. In the incommensurate helical phase, a globally fitted phase shift of 20.3 degrees in the precession signal is taken as evidence that the internal-field distributi

What carries the argument

Zero-field muon spin relaxation (mu+SR) is the central probe: implanted muons precess in local magnetic fields, and the time-dependent asymmetry spectrum encodes the distribution of internal fields and spin dynamics. The paper fits the spectra with three exponentially damped cosine components (three muon stopping sites), a fast exponential, a slow tail, and a static Gaussian Kubo-Toyabe term, with a shared initial phase phi. The fitted phase shift phi = 20.3 degrees is the key indicator of an asymmetric field distribution, and the temperature-dependent asymmetries of the three precession components track the coexistence and evolution of magnetic environments.

Load-bearing premise

The claim that the incommensurate helical phase has an asymmetric internal-field distribution rests on interpreting the fitted precession phase shift phi = 20.3 degrees as arising from anharmonicity, but the paper itself notes that muon implantation time uncertainty, wide field distributions, and incommensurate order can also cause phi to be nonzero.

What would settle it

A longitudinal-field muSR measurement on a single crystal of Mn2.99Sn below Tf that resolves a static, quasistatic spin-glass component (e.g., a field-independent relaxing tail characteristic of frozen moments) would directly contradict the no-spin-glass claim. Similarly, observing a frequency-dependent shift in the ACMS peak position at Tf would indicate canonical spin-glass behavior, which the present data lack.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the low-temperature transition is not a spin glass, then the ZFC-FC bifurcation and ACMS peak in Mn3Sn should be reinterpreted as arising from ferromagnetic cluster formation or anisotropy, not from frozen spin disorder.
  • The ferromagnetic component and the spin-fluctuation slowing may be independent, implying that 'partial spin-glass' descriptions of Mn3Sn conflate two separate physical processes.
  • The asymmetric internal-field distribution in the helical phase supports the idea that the spin structure carries anharmonic and amplitude-modulated components, linking local muon measurements to neutron and X-ray scattering results.
  • The coexistence of helical and inverse-triangular local environments over a broad regime (150-275 K) suggests that reported easy-axis rotations are a consequence of changing phase fractions rather than a separate internal transition.
  • The persistent missing muon fraction in the commensurate phase indicates that a subset of muons sees very broad or very large local fields, which can be tested with longitudinal-field muSR or complementary spatial probes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • One testable extension: longitudinal-field muSR on single crystals could directly determine whether the unresolved missing fraction is due to domain walls by decoupling the muon spin from static local fields.
  • The decoupling of ferromagnetism from glassiness, if general, might apply to other Mn-based kagome antiferromagnets where excess magnetic ions are thought to drive glassy behavior, implying a need to re-evaluate similar low-temperature anomalies.
  • The phase-shift model, though empirical, could be replaced by a microscopic simulation of muon stopping sites in an anharmonic spin texture; such a calculation would validate or refute the anharmonicity interpretation without relying on the ambiguous phase parameter.
  • The paper's data imply that the magnetic phase diagram of Mn3Sn is more continuous than previously mapped, which could motivate re-examination of its temperature-dependent anomalous Hall and transport properties in the coexistence regime.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript reports a combined μ+SR and magnetization study of near-stoichiometric Mn2.99Sn. The authors determine the transition temperatures TN = 418 K, Tt ≈ 275 K, and Tf = 21 K, and map the magnetic phase evolution. The central claims are: (i) below Tf there is no static spin-glass state, but rather an increasing ferromagnetic component accompanied by a localized slowing of spin fluctuations; (ii) in the incommensurate helical phase, a fitted muon precession phase shift of φ = 20.3° indicates an asymmetric internal-field distribution, interpreted as evidence of anharmonic modification of the helical structure; (iii) a broad coexistence region between IC-helical and IT-AFM local environments; and (iv) a persistent missing asymmetry in the IT-AFM phase due to unresolved ultrafast depolarization. The paper includes a detailed F-test-based justification for the number of oscillatory components and a careful estimate of impurity contributions.

Significance. If the no-static-spin-glass conclusion is correct, the paper would revise the current interpretation of the low-temperature transition in Mn3Sn, separating an intrinsic FM response from the impurity-related spin-glass freezing reported in other samples. The strengths of the paper include the wide temperature range (5–475 K), the combination of ZF and TF μ+SR, the use of high-statistics spectra, the explicit impurity-fraction estimate from TF data and magnetization steps, and the F-test analysis of the number of oscillatory components. The paper also correctly notes the absence of a frequency-dependent AC-susceptibility shift, which independently argues against canonical spin-glass freezing. However, the two headline claims—the null result for a static spin-glass and the anharmonicity-induced asymmetric field distribution—require stronger quantitative support before they can be considered established.

major comments (3)
  1. [§IV B2, §V] The central conclusion that there is no static spin-glass state below Tf is not quantitatively supported. The text states that a minority static glassy phase 'should result in a resolvable static component', but no fitted values of A_KT or Δ_KT below Tf are reported, and no sensitivity test is presented. This is important because the IC helical phase has a fitted asymmetry of only A_tot ≈ 0.17 against the instrumental asymmetry A0 ≈ 0.25 (Sec. IV B2), i.e. roughly 30% of the signal is unresolved or missing. A static spin-glass component with a broad local-field distribution would depolarize within the earliest time bins and could be hidden in this missing fraction or in the fast exponential A_F. Indeed, the paper itself invokes unresolved ultrafast depolarization to explain the missing fraction in the IT phase (Sec. IV B3). To support the no-glass claim, the authors should provide an exp
  2. [§IV B2 / §V] The claim that the IC helical phase has an asymmetric internal-field distribution indicative of anharmonicity is an over-interpretation of a fitted phase shift. The evidence is that Eq. (2) with a common phase φ = 20.3° fits better than the Bessel/Overhauser models tried; however, the paper itself states that 'uncertainty in muon implantation time, wide internal field distributions, and incommensurate magnetic order can cause φ ≠ 0'. None of these alternative origins is quantitatively ruled out. In particular, a phase-shifted cosine is an empirical function and does not directly encode an asymmetric P(B); the connection to a third-order anharmonic spin modulation is made after the fact. The authors should either fit a model that explicitly contains an asymmetric field distribution, or temper the abstract/conclusion to state that the phase shift is phenomenologically consistent with, but
  3. [§IV B2] The temperature-dependent phase constraint φ(T) = 20.3° × A_AF2(T)/A_AF2(5 K) is ad hoc. This constraint directly affects the fitted asymmetries A_AFi(T) across the IC-helical to IT-AFM crossover, and the spectral-weight redistribution attributed to coexisting local environments is obtained under this assumption. No physical model is given for why the phase should scale linearly with the AF2 asymmetry, and no robustness test is presented. The authors should justify this constraint, or test the stability of the AF2/AF1/AF3 asymmetry redistribution by allowing φ to vary freely at the high-statistics temperatures (e.g. 250 K) and by checking whether the crossover conclusions survive under alternative treatments of φ.
minor comments (4)
  1. [Appendix A, Table S1] The F-test is used with ndf ≈ 40,000. While the reported p-values are extremely small, the F-distribution assumes independent Gaussian residuals; μ+SR histogram residuals often contain slight systematic correlations. The authors should report the reduced χ² value alongside each F-test and state the assumption. The Fourier-transform heat map is a useful independent check, and it would strengthen the presentation to reference it explicitly when justifying the disappearance of AF2 at 275 K.
  2. [§IV B] The notation for the total asymmetry is inconsistent: the text refers to the total fitted asymmetry A_tot ≈ 0.17, the instrumental asymmetry A0 ≈ 0.25, and also uses A_tot in Eq. (2). Please clarify whether A_tot includes the fixed background A_BG and define the relationship between A_tot and the full instrumental asymmetry.
  3. [§IV B1] The values of λ_F are reported as ≈35 μs⁻¹ at 50 K and ≈10 μs⁻¹ at 5 K. The physical interpretation would be clearer if the authors gave the corresponding depolarization times in nanoseconds, since the phrase 'fast relaxation' may be misleading for these rates.
  4. [Data Availability] The statement that data and analysis are available 'upon reasonable request' is quite limited. For a paper whose conclusions rely heavily on fitting choices (especially the phase-shift and the KT upper bound), it would be preferable to provide the fitted parameters for all temperatures in a table or repository, together with the analysis scripts.

Circularity Check

0 steps flagged

No significant circularity: conclusions follow from free fits, model comparison, and external benchmarks; not from definitions or self-citations.

full rationale

The paper's central claims are empirical rather than definitional. Eq. (2) is a general phenomenological decomposition; the no-static-spin-glass conclusion is based on the observed absence of a static Gaussian Kubo-Toyabe signature and the absence of a frequency-dependent ACMS peak, not on A_KT being set to zero by construction. The phase-shift inference is likewise not circular: phi = 20.3 deg is a free fitted parameter; the paper compares the cosine-plus-phase model against symmetric Overhauser/Bessel models and invokes independent neutron/X-ray evidence [22,23] for anharmonic/amplitude-modulated components. It explicitly acknowledges other origins of phi != 0 (implantation time, wide internal-field distributions, incommensurate order). No load-bearing self-citation chain exists: the prior muon study [32] and neutron/X-ray works are external. The missing-fraction discussion is flagged tentative ('should be regarded as tentative'; 'we do not directly equate...'). The absence of a quantified upper bound on a static spin-glass fraction is a scientific limitation and a correctness risk, but not a circular reduction of the paper's inputs. Therefore score 0.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central cost of the paper is the phenomenological muSR fit model: a phase-shifted cosine with a fitted phase, an ad hoc phase-scaling rule, and an unquantified missing fraction. The no-glass claim rests on the assumption that a static spin glass would be resolvable in the muSR time window.

free parameters (4)
  • Muon precession phase shift phi = 20.3 degrees at 5 K; fixed for 5-150 K, then scaled as phi(T)=20.3 deg * A_AF2(T)/A_AF2(5 K)
    Fitted at base temperature; the anharmonicity and asymmetric-field conclusion depends on this parameter, but other physical origins for a nonzero phase are acknowledged in the paper.
  • Missing fraction of initial asymmetry = about 20% of sample-related asymmetry
    Inferred from the gap between fitted total asymmetry (0.17 to 0.20) and full instrumental asymmetry (0.25); the attribution to ultrafast depolarization is tentative.
  • Mn2-xSn impurity fraction = about 1%
    Estimated from the magnetization step at T_im = 200 K compared to bulk Mn2Sn magnetization; used to argue impurities do not explain the muon signal.
  • Background asymmetry A_BG = about 0.033 (from the 5 K TF baseline)
    Fixed in ZF fits from the residual TF asymmetry; affects the absolute scale of the missing-fraction estimate.
axioms (5)
  • standard math In a powder, two-thirds of internal-field components perpendicular to the initial muon spin cause precession while one-third parallel produce a non-oscillating tail.
    Used to interpret the oscillatory and tail components in Eq. (2).
  • domain assumption A static spin-glass phase, even at minority volume fraction, would produce a resolvable static Gaussian Kubo-Toyabe component in ZF-muSR.
    Underlies the primary conclusion that no static spin-glass exists; the paper does not quantify the sensitivity limit for detecting a small static fraction.
  • domain assumption The T_im = 200 K magnetization feature is an extrinsic Mn2-xSn impurity, not intrinsic to the main Mn3Sn phase.
    Used to exclude impurity contributions from the ZF muon signal; based on prior literature and a roughly 1% fraction estimate.
  • domain assumption The three observed precession frequencies correspond to three distinct muon stopping sites predicted for Mn3Sn.
    Adopted from the high-pressure muon study by Bhattacharya et al.; the paper does not perform independent site calculations.
  • standard math The F-test for nested models remains meaningful with ndf about 40,000 and chi2/ndf near 1.
    Used to justify the number of frequency components; with such large ndf, even tiny absolute chi2 reductions are statistically flagged, so the practical significance is questionable.

pith-pipeline@v1.3.0-daily-deepseek · 14850 in / 17149 out tokens · 181534 ms · 2026-08-04T18:45:16.410268+00:00 · methodology

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read the original abstract

We report a comprehensive muon spin relaxation ($\mu^+$SR) and bulk magnetization study of the antiferromagnetic (AFM) Weyl semimetal Mn$_3$Sn (composition Mn$_{2.99}$Sn). Mn$_3$Sn is reported to exhibit a commensurate inverse triangular (IT) AFM phase, an incommensurate (IC) helical AFM phase, and a proposed low-temperature spin-glass-like state. In our sample, we establish the respective transition temperatures for these phases to be $T_\mathrm{N} = 418$ K, $T_\mathrm{t} \approx 275$ K, and $T_\mathrm{f} = 21$ K. Investigating the low-temperature regime below $T_\mathrm{f}$, we find no evidence of a static spin-glass state. Instead, the sample exhibits an increasing ferromagnetic (FM) component accompanied by a localized slowing of spin fluctuations, indicating that these phenomena may be decoupled. In the IC helical AFM phase, fitting the zero-field (ZF) spectra reveals an asymmetric internal magnetic-field distribution, indicating that the magnetic structure is heavily modified by anharmonicity. Upon warming above 150 K, a continuous redistribution of muon spectral weight reveals a broad regime of coexisting local magnetic environments associated with the IC helical and IT-AFM phases. In the commensurate IT-AFM phase above $T_\mathrm{t}$, a persistent missing fraction in the initial asymmetry indicates that a subset of implanted muons, corresponding to roughly 20% of the sample-related asymmetry, undergoes unresolved ultrafast depolarization. Finally, we observe temperature-driven shifts in muon site populations above 325 K. Ultimately, our results show a highly dynamic magnetic landscape in Mn$_3$Sn, demonstrating how its complex magnetic orders often coexist and evolve continuously with temperature.

Figures

Figures reproduced from arXiv: 2608.01892 by D. W. Tam, D. Zuhair, G. D. Morris, H. Luetkens, J. Persson, M. M{\aa}nsson, O. K. Forslund, S. Nandi, U. Miniotaite, V. Rai, Y. Sassa.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (c) shows the real part of the ACMS of Mn3Sn between 5 K and 80 K. A distinct peak is observed at Tf = 21 K. Notably, our results do not show a frequency￾dependent shift for this peak. IV. MUON SPIN SPECTROSCOPY RESULTS A. Transverse Field To measure the N´eel temperature and estimate pos￾sible minority/background contributions, we first con￾ducted µ +SR measurements in an applied transverse field (TF) of … view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

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