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REVIEW 3 major objections 4 minor 40 references

The second superconducting dome of LaFeAsO1−xMx develops a mixed-state linewidth maximum absent in the first dome, consistent with stronger Pauli-paramagnetic effects.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-14 12:25 UTC pith:IQY42AAH

load-bearing objection Clear comparative µSR result: SC2 shows a real nonmonotonic mixed-state linewidth that SC1 does not; the Zeeman assignment is plausible but rests on a model used outside its range. the 3 major comments →

arxiv 2607.10348 v1 pith:IQY42AAH submitted 2026-07-11 cond-mat.supr-con

Anomalous field evolution of the mixed-state linewidth in the second superconducting dome of LaFeAsO_(1-x)M_x (M={rm F,H})

Rustem Khasanov , Pierre Dalmas de R\'eotier , Samuele Sanna , Gianrico Lamura , Hubertus Luetkens , Matteo Moroni , Pietro Carretta , Rhea Kappenberger
show 4 more authors
Rowena Wachtel Bernd B\"uchner Sabine Wurmehl Nikolai D. Zhigadlo
This is my paper
classification cond-mat.supr-con
keywords muon spin rotationiron-based superconductorsvortex latticePauli paramagnetismLaFeAsOsuperconducting domesmixed statelinewidth
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 compares the internal magnetic-field distribution inside the vortex state of two related iron-based superconductors, one from each superconducting dome of the LaFeAsO1−xMx family, using transverse-field muon spin rotation. After the field-dependent normal-state background is removed, the superconducting linewidth of the low-doping sample falls steadily with applied field, the usual orbital-vortex behaviour. The high-doping sample instead shows a clear peak near 3 T at low temperature; that peak forms a ridge that moves to lower fields as temperature rises and disappears near Tc. The authors read the anomaly as an extra Zeeman-current contribution that appears only when Pauli-paramagnetic pair-breaking is strong. A reader cares because the result supplies direct microscopic evidence that the two domes are electronically distinct, not merely different doping levels of the same superconducting state.

Core claim

After normal-state subtraction the superconducting µSR linewidth σ_sc of LaFeAsO0.75H0.25 (second dome) shows a pronounced local maximum near 3 T at 4 K and a ridge of maxima H_σ,max(T) that shifts downward on warming and vanishes near Tc, while the first-dome compound LaFeAsO0.89F0.11 exhibits only the conventional monotonic decrease with field. The paper attributes the SC2 anomaly to an additional field-induced Zeeman contribution arising from enhanced Pauli-paramagnetic effects.

What carries the argument

The superconducting Gaussian relaxation rate σ_sc obtained by quadrature subtraction of the normal-state linewidth; its field dependence is then fitted with the approximate Ginzburg–Landau model of Dalmas de Réotier and Yaouanc that writes the vortex-lattice form factor as the sum of orbital and Zeeman Fourier components controlled by the reduced field and a dimensionless Zeeman weight R.

Load-bearing premise

The non-monotonic linewidth is ascribed to Zeeman currents by using a Ginzburg–Landau model formally justified only near the transition temperature, while the decisive data lie far below that range and require an ad-hoc two-component fit with large free R values.

What would settle it

A single-crystal TF-µSR or small-angle neutron-scattering measurement of the vortex form factor in LaFeAsO0.75H0.25 that recovers a strictly monotonic field dependence of the second moment would rule out an intrinsic Zeeman-induced maximum.

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

If this is right

  • SC1 and SC2 must be treated as electronically distinct regimes rather than a single continuous superconducting phase.
  • Pair-breaking in SC2 is dominated by paramagnetic rather than orbital effects, consistent with independent upper-critical-field data.
  • Contour maps of σ_sc(T,H) become a practical powder diagnostic for strong Pauli-paramagnetic contributions.
  • The ridge H_σ,max(T) tracks a roughly fixed fraction of Hc2(T), giving a route to the relative Zeeman weight without single crystals.

Where Pith is reading between the lines

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

  • Similar non-monotonic linewidths should appear in other heavily electron-doped iron pnictides that neighbour correlation-driven antiferromagnetic phases.
  • Single-crystal form-factor measurements would test whether the two-component R fit is an artefact of powder averaging.
  • If the fitted Zeeman weight is physical, the mixed-state free energy of SC2 may allow field-induced magnetic textures near the upper critical field.

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 transverse-field µSR study of the mixed-state internal-field distribution in two polycrystalline La1111 compositions: LaFeAsO0.89F0.11 (SC1, Tc ≈ 18.5 K) and LaFeAsO0.75H0.25 (SC2, Tc ≈ 23.7 K). After subtracting a field-dependent normal-state linewidth σn(H) = √(σnm^{2} + (kH)^{2}) attributed to nuclear moments plus anisotropic Knight-shift powder broadening, the residual superconducting linewidth σsc(H) is monotonic and decreasing for SC1, while SC2 develops a clear local maximum near 3 T at 4 K. Contour maps of σsc(T,H) show a ridge of maxima Hσ,max(T) that shifts to lower field on warming and vanishes near Tc. The authors interpret the SC2 anomaly within the Dalmas de Réotier–Yaouanc Ginzburg–Landau form-factor model that includes orbital and Zeeman currents, fitting a single component for SC1 and a two-component form with large Zeeman weights R for SC2, and conclude that SC2 hosts an enhanced Pauli-paramagnetic contribution absent in SC1.

Significance. If the non-monotonic σsc(H) in SC2 is intrinsic and correctly attributed to Zeeman currents, the work supplies a local-probe signature that the two superconducting domes of La1111 differ not only in doping and nesting but also in the dominant pair-breaking mechanism, consistent with recent high-field Hc2 results. The raw temperature- and field-dependent σ data, the identical normal-state k for both powders, and the clean SC1 control are valuable and well documented. The temperature-dependent ridge Hσ,max(T) is a falsifiable experimental feature independent of any particular model. The quantitative link to Pauli paramagnetism, however, rests on a phenomenological application of a model outside its stated validity range and on an ad-hoc two-component parameterization, so the interpretive claim is less secure than the experimental contrast itself.

major comments (3)
  1. Results and Discussion, Eqs. (3)–(4) and the accompanying text: the key 4 K data (T/Tc ≈ 0.17) are analyzed with the Dalmas de Réotier–Yaouanc form factor that the authors themselves note is formally justified only near Tc and for T > 0.56 Tc. Treating the model as a purely phenomenological fitting function is acceptable only if the limitations are stated more prominently and if the large fitted R values (R1 = 220, R2 = 120) and the second Hc2,2 = 8 T are not presented as microscopic evidence of enhanced Zeeman weight. A single-component description already fails for SC2; the two-component construction therefore needs either independent justification or a clearer statement that it is an empirical device rather than a quantitative extraction of R.
  2. Eqs. (1)–(2) and Figs. 3(a)–(d): the central claim that the SC2 local maximum is superconducting rests on quadrature subtraction of a normal-state background fitted only above Tc, with k assumed temperature-independent. In a powder the measured second moment already averages over crystallite orientations and demagnetization factors; any T-dependent change in Knight-shift anisotropy or inter-grain currents below Tc would leave a residual non-monotonicity unrelated to Zeeman currents. The identical k for both samples and the clean monotonic SC1 result are reassuring, yet intermediate-temperature normal-state isotherms (or at least a check that σn(H) remains linear just above Tc at several fields) would substantially strengthen the subtraction. Without such a control the attribution of the 3 T peak remains vulnerable.
  3. Fitting procedure for Eq. (4): Hc2,1 is fixed to literature values (60 T and 75 T) while Hc2,2 = 8 T for SC2 is introduced as a free scale with no independent experimental anchor. Because the position of the maximum is sensitive to the reduced field h = H/Hc2, the second component effectively absorbs the peak location. The manuscript should either motivate Hc2,2 from existing high-field data or demonstrate that the qualitative need for a large Zeeman contribution survives when Hc2,2 is constrained or removed.
minor comments (4)
  1. Fig. 2: the vertical scales and symbol sizes make the high-field plateaus difficult to compare between panels; a common y-range or an inset of the normal-state region would help.
  2. Fig. 3(e,f): the contour color scale saturates at high σsc; a logarithmic or more finely graded scale would better reveal the ridge Hσ,max(T).
  3. The Supplemental Information is cited for sample preparation and data-analysis details but is not available in the arXiv posting; the main text should at least summarize the Gaussian-fit assumptions and any multi-component spectral models used.
  4. Typographical consistency: “Dalmas de Réotier” appears with and without accents; “µSR” and “muon-spin rotation/relaxation” should be standardized.

Circularity Check

2 steps flagged

Experimental nonmonotonic σ_sc is independent, but large fitted R values are then presented as evidence of enhanced Zeeman/Pauli effects that the co-author model associates with large R by construction.

specific steps
  1. fitted input called prediction [Results and Discussion, Eqs. (3)–(4) and fits to Figs. 3(c,d)]
    "the substantially larger fitted R values obtained for the x_H = 0.25 sample further indicate that the anomalous field evolution in SC2 is associated with a much stronger Zeeman contribution to the mixed-state field distribution."

    R_i are free parameters in the phenomenological two-component fit of Eq. (4) to the measured σ_sc(H). Within the imported model a local maximum appears only when R is sufficiently large; therefore reporting the large fitted R as ‘indicating’ stronger Zeeman simply restates the fit that was required to reproduce the peak, rather than supplying an independent determination of the Zeeman strength.

  2. self citation load bearing [Results and Discussion, paragraph introducing the model of Ref. 16]
    "we analyze the data in Figs. 3(c) and 3(d) within the framework developed by Dalmas de Réotier and Yaouanc [16]. … A key result of the theory is that, when R becomes sufficiently large, the linewidth of the field distribution may develop a maximum at an intermediate reduced field"

    The sole theoretical link that converts the observed non-monotonic linewidth into a claim of enhanced Pauli-paramagnetic (Zeeman) currents is the form-factor calculation of Ref. 16, co-authored by a present author. Once that framework is adopted, large R is fitted and re-interpreted as evidence of the same effect the model was constructed to describe; the interpretive chain therefore rests on an overlapping-author citation whose domain of validity (near T_c) is acknowledged not to cover the 4 K data.

full rationale

The core experimental contrast (monotonic σ_sc(H) in SC1 vs local maximum near 3 T and temperature-shifting ridge H_σ,max(T) in SC2 after quadrature subtraction of the high-T normal-state form) does not depend on any model fit and is therefore non-circular. The subsequent interpretation, however, imports the Dalmas de Réotier–Yaouanc Ginzburg–Landau form factor (Ref. 16, co-authored by one present author), parameterizes σ_sc(H)/σ_sc(0) as a weighted sum of two model components (Eq. 4), freely adjusts the dimensionless Zeeman weights R_i (and a second ad-hoc H_c2 = 8 T) until the SC2 peak is reproduced, and then cites the resulting large R as indicating a stronger Zeeman contribution. That step is a mild instance of fitted-input-called-indication: large R is required by construction of the model to generate a local maximum, so the numerical values do not constitute an independent prediction or measurement. The paper itself flags the model’s formal domain (near T_c, T > 0.56 T_c) and treats the description as phenomenological, keeping the circularity modest rather than load-bearing for the raw observation. No self-definitional loop, uniqueness theorem, or renaming of a known result is present. Score 3 reflects one clear but non-central fitted-as-evidence step plus the overlapping-author model citation.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central experimental claim rests on standard TF-µSR analysis plus a normal-state subtraction. The interpretive claim that the anomaly is Zeeman-driven imports an approximate Ginzburg–Landau model outside its formal range and introduces several free parameters (R_i, ω, a second Hc2) fitted only to the SC2 data. No new microscopic entities are postulated; the free-parameter and model-assumption burden is moderate and concentrated in the interpretation rather than the raw observation.

free parameters (5)
  • R1 (Zeeman weight, SC1) = 19.0
    Single-component fit parameter quantifying relative Zeeman contribution for xF=0.11; set to 19.0 to describe the monotonic σ_sc(H).
  • R1, R2, ω (Zeeman weights and weight, SC2) = R1=220, R2=120, ω=0.60
    Two-component fit parameters for xH=0.25; R1=220, R2=120, ω=0.60 chosen to reproduce the local maximum near 3 T.
  • Hc2,2 (second upper-critical-field scale for SC2) = 8 T
    Ad-hoc second component Hc2 fixed at 8 T (while the main Hc2 is fixed at the literature 75 T) to allow the two-component description of the nonmonotonic curve.
  • k (Knight-shift broadening coefficient) = 0.0548(4) µs^{-1} T^{-1}
    Linear coefficient in the normal-state linewidth σ_n(H)=√(σ_nm^{2}+(kH)^{2}); fitted to high-T data and found identical for both samples.
  • σ_nm (nuclear contribution) = 0.10(1) and 0.15(1) µs^{-1}
    Field-independent nuclear linewidth extracted from normal-state fits; slightly different for the two samples.
axioms (4)
  • domain assumption Quadrature subtraction σ_sc=√(σ^{2}-σ_n^{2}) cleanly isolates the superconducting vortex contribution.
    Standard in TF-µSR literature (cited Refs. 30–34) and applied uniformly to both samples; any residual field-dependent normal-state term would distort σ_sc(H).
  • ad hoc to paper The Dalmas de Réotier–Yaouanc Ginzburg–Landau form factor with orbital plus Zeeman terms (Eq. 3) remains a valid phenomenological description of the linewidth even at T=4 K ≪ 0.56 Tc.
    The paper itself notes the model is formally justified only near Tc and for T>T*≃0.56 Tc, yet applies it to the base-temperature field sweeps that constitute the central claim.
  • domain assumption Literature Hc2 values (60 T for SC1, 75 T for SC2) can be fixed and still yield a meaningful comparison of R.
    Hc2 is taken from external high-field transport/magnetization studies (Refs. 11, 39, 40) rather than measured in the same experiment.
  • domain assumption Powder averaging and the Gaussian relaxation-rate approximation adequately capture the second moment of the vortex-lattice field distribution.
    Standard for polycrystalline TF-µSR; any strong anisotropy or disorder beyond the model would affect both samples similarly and is not expected to produce a peak only in SC2.

pith-pipeline@v1.1.0-grok45 · 17042 in / 3816 out tokens · 29007 ms · 2026-07-14T12:25:01.383800+00:00 · methodology

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read the original abstract

We report a transverse-field muon-spin rotation/relaxation ($\mu$SR) study of the internal-field distribution in the mixed state of LaFeAsO$_{0.89}$F$_{0.11}$ and LaFeAsO$_{0.75}$H$_{0.25}$, representative of the first (SC1) and second (SC2) superconducting domes of the LaFeAsO$_{1-x}M_x$ ($M={\rm F,H}$) family, respectively. Below the superconducting transition temperature $T_{\rm c}$, the linewidth of the internal-field distribution increases in both samples, indicating the formation of a vortex lattice. Above $T_{\rm c}$, the linewidth remains field dependent and increases approximately linearly with field, consistent with broadening of the powder spectrum caused by an anisotropic Knight shift. After subtraction of this normal-state contribution, the superconducting linewidth $\sigma_{\rm sc}$ exhibits qualitatively different field dependences in the two samples. At 4K, the SC1 ($x_{\rm F}=0.11$) sample shows the expected monotonic decrease with increasing field, whereas the SC2 ($x_{\rm H}=0.25$) sample develops a pronounced local maximum near 3T. A contour representation of $\sigma_{\rm sc}(T,H)$ further reveals a ridge of local maxima whose field position, $H_{\sigma,\max}(T)$, shifts to lower fields upon warming and disappears near $T_{\rm c}$. The anomalous field evolution observed in the SC2 sample is consistent with an additional field-induced contribution associated with enhanced Pauli-paramagnetic effects, highlighting the distinct electronic character of the two superconducting domes.

Figures

Figures reproduced from arXiv: 2607.10348 by Bernd B\"uchner, Gianrico Lamura, Hubertus Luetkens, Matteo Moroni, Nikolai D. Zhigadlo, Pierre Dalmas de R\'eotier, Pietro Carretta, Rhea Kappenberger, Rowena Wachtel, Rustem Khasanov, Sabine Wurmehl, Samuele Sanna.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic phase diagram of LaFeAsO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) to (f) Temperature dependence of the Gaussian relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) and (b) Field dependences of the Gaussian relaxation rate [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

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Reference graph

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