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REVIEW 3 major objections 5 minor 53 references

Evolution of magnetism in Ruddlesden-Popper bilayer nickelate revealed by muon spin relaxation

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Zero-field muon spin relaxation finds bulk commensurate long-range magnetic order in La1.9Pr1.1Ni2O6.97 below 161 K with a 3D Ising-like critical exponent, while oxygen-deficient La3Ni2O6.63 shows only short-range order below 30 K.

desk verdict Useful new muSR data on two bilayer nickelate compositions, but the paper must report the oscillating-signal amplitude before the bulk-order attribution is fully convincing. read the letter →

arxiv 2412.09003 v1 pith:YKB7LQ4H submitted 2024-12-12 cond-mat.str-el cond-mat.supr-con

K. W. Chen , X. Q. Liu , Y. Wang , Z. Y. Zhu , J. C. Jiao , C. Y. Jiang , Y. F. Guo , L. Shu This is my paper · ORCID
classification cond-mat.str-elcond-mat.supr-con
keywords muonspinrelaxationRuddlesden-PoppernickelatesLa3Ni2O7oxygenvacanciesmagneticorder3DIsingcriticalexponentdensitywavenickelatesuperconductivity
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 ambient-pressure magnetic measurements on two Ruddlesden-Popper bilayer nickelates, layered nickel-oxide compounds whose pressurized members superconduct. Using implanted muons as local magnetic probes, it finds that the nearly oxygen-stoichiometric compound La1.9Pr1.1Ni2O6.97 develops bulk, commensurate long-range magnetic order below 161 K, with a critical exponent $\beta = 0.33(2)$ close to the 3D Ising value. The oxygen-deficient compound La3Ni2O6.63, by contrast, shows only short-range magnetic order below about 30 K, on top of weaker vacancy-related moments at higher temperature. The authors conclude that oxygen-vacancy disorder, not just pressure or chemical pressure, controls whether the magnetic ground state is long-range and three-dimensional, and that this magnetic evolution tracks the sample-dependent superconductivity seen under pressure.

What carries the argument

The central probe is zero-field muon spin relaxation, in which implanted positive muons sit at local interstitial sites and precess in whatever internal magnetic field they feel; a coherent oscillating asymmetry is direct evidence of static ordered moments, and the precession frequency gives the local field strength. The data analysis separates magnetic and paramagnetic fractions using a Gaussian Kubo-Toyabe function, the standard relaxation form for static random local fields, together with cosine-precession terms, and the magnetic order parameter is taken as the extracted internal field $B_{\mathrm{int}}(T)$, fitted with the phenomenological power law described in the core discovery. Weak-transverse-field muon spin relaxation supplies the magnetic volume fraction as a function of temperature, and longitudinal-field decoupling distinguishes static local fields from fluctuating ones.

What would settle it

Cool a phase-pure, vacancy-free La1.9Pr1.1Ni2O7 sample below 161 K and search for a commensurate magnetic Bragg peak by neutron diffraction, and repeat the zero-field muon experiment on a sample with the La2NiO4 impurity removed. If no long-range Bragg peak appears or the 145 mT precession amplitude changes materially, the claim that the signal is bulk and intrinsic would be refuted.

Watch

Extended reading notes

Core claim

At zero field, the muon spin relaxation spectra of La1.9Pr1.1Ni2O6.97 develop an oscillating component below about 160 K, and a single cosine frequency at 2.4 K indicates commensurate magnetic order. Fitting the extracted internal field with $B_{\mathrm{int}}(T)=B_{\mathrm{int}}(0)[1-(T/T_N)^{\alpha}]^{\beta}$ gives $T_N=161.4(5)$ K, $B_{\mathrm{int}}(0)=145(1)$ mT, $\alpha=1.9(2)$, and $\beta=0.33(2)$, placing the transition near the 3D Ising universality class. In La3Ni2O6.63 no precession signal appears; the spectra are described above 30 K by a Kubo-Toyabe relaxation multiplied by an exponential, and below 30 K by a fast-relaxing component plus a long-time tail, signatures of short-range order, with longitudinal-field measurements showing static internal fields of order 1 mT above 30 K and about 100 mT below. The paper interprets the contrast as oxygen vacancies disrupting long-range order: the nearly vacancy-free Pr-doped sample behaves as a bulk 3D Ising magnet, while roughly 40% inner apical vacancies leave only short-range correlations.

Load-bearing premise

The load-bearing premise is that the ~145 mT precession signal comes entirely from the bulk bilayer nickelate phase, not from the 6.2% La2NiO4 impurity or from moments near oxygen vacancies; if those contributed, the deduced transition temperature and critical exponent would be biased.

Editorial extensions

If this is right

  • The near-stoichiometric bilayer nickelate has an intrinsic, bulk, commensurate magnetic ground state below 161 K that cannot be dismissed as an impurity artifact.
  • Oxygen vacancies convert that ground state to short-range order, so comparisons of magnetic and superconducting properties among bilayer nickelate samples must control oxygen content.
  • The narrower magnetic transition and 3D Ising-like exponent in the cleaner sample imply that structural perfection strengthens interlayer magnetic coupling.
  • Ambient-pressure magnetism in the clean phase provides a baseline against which pressure-induced changes in the spin-density-wave state can be interpreted.

Reading between the lines

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

  • A neutron diffraction experiment on La1.9Pr1.1Ni2O6.97 below 161 K should reveal a commensurate magnetic Bragg peak; if it shows only diffuse scattering, the bulk long-range interpretation would need revisiting.
  • The same muon protocol applied to other rare-earth bilayer nickelates with systematically varied oxygen content could map how $T_N$ and the critical exponent change with vacancy concentration, testing whether 3D Ising behavior is generic to vacancy-free samples.
  • The vacancy picture suggests that eliminating apical-oxygen vacancies, rather than applying pressure alone, may be the key to enhancing interlayer coupling and superconductivity, a prediction that synthesis and transport experiments could test.
  • The small 10 mT precession component attributed to vacancy-adjacent sites could serve as a muon-visible measure of oxygen disorder across different growth batches.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports zero-field (ZF), longitudinal-field (LF), and weak-transverse-field (wTF) muon spin rotation/relaxation experiments on two Ruddlesden-Popper bilayer nickelates: nearly oxygen-stoichiometric Pr-doped La1.9Pr1.1Ni2O6.97 and strongly oxygen-deficient La3Ni2O6.63. The authors claim that La1.9Pr1.1Ni2O6.97 undergoes a transition to bulk commensurate long-range magnetic order below TN = 161.4(5) K, with an internal field B_int(0) = 145(1) mT and a critical exponent beta = 0.33(2) consistent with the 3D Ising value, while La3Ni2O6.63 shows only short-range magnetic order below about 30 K with an additional broad magnetic response at higher temperatures. The paper connects these magnetic ground states to oxygen-vacancy concentration and structural perfection, and relates the evolution of magnetism to the sample-dependent superconducting properties under pressure.

Significance. If the central attribution is correct, the paper provides direct microscopic evidence that oxygen stoichiometry controls the magnetic ground state in bilayer Ruddlesden-Popper nickelates: a nearly vacancy-free Pr-doped sample hosts bulk long-range magnetic order with an Ising-like order parameter, while a strongly oxygen-deficient sample exhibits only short-range order. This is a valuable contribution to the ongoing discussion of magnetism and superconductivity in La3Ni2O7-based materials. The study is strengthened by new ZF-μSR data on two compositions, a clear precession signal with order-parameter-like temperature dependence, wTF volume-fraction measurements, and a comparison with the authors' earlier PRL (ref. [11]). The main weakness is that the main text does not report the amplitude of the 145 mT oscillating component as a fraction of total asymmetry, which is needed to rule out the 6.2% La2NiO4 impurity as the source of this precession.

major comments (3)
  1. [Muon spin relaxation, Eq. (2), Eq. (3), Fig. 3] The main text never reports the amplitude of the ~145 mT cosine component as a fraction of the total muon asymmetry. Because the sample contains 6.2% La2NiO4 (Fig. 1(a)), a known antiferromagnet with muon internal fields of order 100 mT (refs. 47,48), the observed cosine could in principle originate predominantly from this impurity if the bulk 327 phase orders incommensurately or with a broad field distribution. The wTF volume fraction fm > 90% (Fig. 3(d)) shows that the majority of the sample is magnetically ordered, but it does not identify which phase produces the coherent precession. Please report the fitted amplitude of the cosine component (e.g., fm(1-fL)f_i in the notation of Eqs. (2) and (3)) as a function of temperature, and demonstrate explicitly that this amplitude is too large to be accounted for by 6.2% of La2NiO4. This is required to validate the assignment of B_int(T), and hence TN and beta, to the bulk 327 phase.
  2. [Muon spin relaxation, Eq. (4), Fig. 3(c)] The order-parameter fit returns alpha = 1.9(2), beta = 0.33(2), and TN = 161.4(5) K, but the manuscript does not report the number of B_int(T) data points included in the fit, the temperature range, the uncertainties on B_int, or the correlation between the fitted parameters. Because the data exist only below 160 K and the transition is sharp, the deduced beta may be sensitive to the fitting range and to the treatment of points near TN. Please provide the fit residuals and a robustness check, such as varying the lower temperature cutoff or fixing alpha = 1, so that the claim that beta is close to the 3D Ising value can be properly evaluated.
  3. [Muon spin relaxation, Eq. (6), Fig. 4(b)] For La3Ni2O6.63, the paper states that the ZF and wTF spectra at 300 K split before and after applying the field, indicating ferromagnetism at 300 K. Equation (6) defines fm(T) = 1 - APM(T)/APM(300 K), thereby using the 300 K spectrum as a fully paramagnetic reference. If a ferromagnetic contribution is already present at 300 K, APM(300 K) may be reduced relative to the true paramagnetic asymmetry, which would bias the absolute fm values and the interpretation of the 'two-step transition.' Please clarify how the ferromagnetic component was accounted for or subtracted in the wTF analysis, or justify quantitatively that its effect on APM(300 K) is negligible.
minor comments (5)
  1. [Title] The title contains an unintended space in 'nicke late'; it should read 'nickelate' as one word.
  2. [Eq. (4) and text after it] The fit parameter is written as B_int(0) in Eq. (4) but as B(0) in the following text; please use consistent notation.
  3. [Eq. (3)] Please state the normalization condition on the weights f_i (for example, sum_i f_i = 1) and report the fitted f_i values for the fast precession component in the main text or in a table, since these values are central to the amplitude argument.
  4. [Experimental details] The sentence 'The reactants were reground and annealing at 900 ℃ for 3 times' should be corrected to 'The reactants were reground and annealed at 900 °C three times.'
  5. [Supplemental material, ref. [43]] The placeholder 'URL_will_be_inserted_by_publisher' for the supplemental material should be replaced by a working link in the posted version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are extracted from new μSR fits to measured spectra, and the prior work cited (ref [11]) is used only as an external comparison benchmark, not as an input to the fits.

full rationale

The paper's central results are derived from zero-field and weak-transverse-field muon spin relaxation measurements on two newly prepared polycrystalline samples. The order parameter B_int(T) is obtained by fitting the raw asymmetry spectra to Eq. (2) (Gaussian Kubo-Toyabe plus cosine precessions), and the temperature dependence is then fit to Eq. (4) to extract T_N = 161.4(5) K, α = 1.9(2), and β = 0.33(2). These quantities are free parameters of a least-squares fit to the measured spectra, not preset values or outputs of a model that was constructed to reproduce them. The β value is compared with the 3D Ising exponent only after the fit, so this is a post-hoc comparison, not a prediction built into the fitting procedure. The wTF magnetic volume fraction in Eq. (6) is calibrated against the 300 K paramagnetic amplitude, which is a standard and self-contained procedure. The only self-citation appears in the comparison with La3Ni2O6.92 from ref [11], which is published prior work by overlapping authors. That prior result is used as a benchmark to illustrate the 'evolution' with oxygen content; it is not fed into any of the fits or used to justify the assignment of the 145 mT precession to the bilayer phase. Therefore no load-bearing step reduces to its own input. The skeptic's concern about the unquantified amplitude of the oscillating signal (and the possible impurity contribution) is a legitimate empirical attribution issue, but it does not constitute circularity because the paper does not define 'bulk order' in terms of the precession amplitude; it is an assumption about which phase produces the signal, not a definitional or fitted loop. Consequently, the derivation chain is self-contained and the circularity score is 0.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard muon spin relaxation fitting models and on phenomenological order-parameter fits. The paper introduces no new particles or forces. The main fitted quantities that determine the claims are T_N, B_int(0), alpha, and beta, all extracted from the measured spectra. The comparison with prior data adds no circular dependency because the cited prior work is used as a benchmark, not as an input to the fits.

free parameters (9)
  • T_N (La1.9Pr1.1Ni2O6.97) = 161.4(5) K
    Fitted from Eq. (4) to the temperature dependence of B_int; sets the claimed ordering temperature.
  • B_int(0) = 145(1) mT
    Zero-temperature internal field from Eq. (4) fit; the observed muon precession field.
  • alpha = 1.9(2)
    Phenomenological exponent in Eq. (4); affects the shape of B_int(T), deviates from the mean-field value of 2.
  • beta = 0.33(2)
    Phenomenological exponent in Eq. (4); central to the 3D Ising claim.
  • T_0 (VRH) = 3.1e6 K
    Localization temperature from the Mott variable-range-hopping fit to La3Ni2O6.63 resistivity; supports the disordered-vacancy picture, not the magnetic claim.
  • rho_0 (VRH) = 2.9e5 ohm cm
    Resistivity prefactor from the same VRH fit.
  • sigma_ZF (fixed) = 0.08 us^-1
    Fixed Gaussian relaxation rate in Eq. (2), chosen by hand rather than fitted.
  • f_L = 0.299
    Long-time tail fraction determined from ZF and wTF spectra, slightly below the polycrystalline 1/3 value; attributed to pelletization orientation.
  • sigma (La3Ni2O6.63) = 0.07 us^-1
    Fixed Gaussian relaxation rate in Eq. (7), chosen by hand.
assumptions (5)
  • domain assumption The Gaussian Kubo-Toyabe function describes muon relaxation from static nuclear dipolar moments.
    Used in Eqs. (2) and (7) to separate nuclear and electronic magnetic contributions.
  • domain assumption A single precession frequency in ZF-muSR implies commensurate magnetic order.
    Stated after Eq. (3): 'The oscillation can be fitted with single cosine function suggests a commensurate magnetic order.'
  • domain assumption The phenomenological order-parameter form B_int(T) = B_int(0)[1 - (T/T_N)^alpha]^beta captures the critical behavior.
    Eq. (4) is used to extract T_N, alpha, and beta; the extracted beta is then compared to the 3D Ising exponent.
  • domain assumption The 6.2% La2NiO4 impurity does not contribute significantly to the 145 mT precession signal.
    The paper argues from magnetization measurements that the impurity impact is minimal, but does not separate the muon signal by phase.
  • domain assumption Muon stopping sites are representative of the bulk magnetic order.
    All muon spin relaxation analyses assume the implanted muons sample the bulk of the material and that the local field distribution reflects the intrinsic magnetic order.

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Pith. "Pith review of Evolution of magnetism in Ruddlesden-Popper bilayer nickelate revealed by muon spin relaxation." pith.science (2026). https://pith.science/paper/YKB7LQ4H

@misc{pith2026241209003,
  author       = {Pith},
  title        = {Pith review of: Evolution of magnetism in Ruddlesden-Popper bilayer nickelate revealed by muon spin relaxation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YKB7LQ4H}},
  note         = {Machine review of arXiv:2412.09003}
}
abstract

Here we report the positive muon spin relaxation study on Pr-doped La$_{1.9}$Pr$_{1.1}$Ni$_2$O$_{6.97}$ and oxygen-deficient La$_3$Ni$_2$O$_{6.63}$ polycrystalline under ambient pressure. Zero-field $\mu^+$SR experiments reveal the existence of bulk long-range magnetic order in La$_{1.9}$Pr$_{1.1}$Ni$_2$O$_{6.97}$ with $T_{N}=161\ \rm{K}$, while La$_3$Ni$_2$O$_{6.63}$ exhibits a short-range magnetic ground state with $T_N=30\ \rm{K}$. The magnetic transition width of La$_{1.9}$Pr$_{1.1}$Ni$_2$O$_{6.97}$ revealed by weak-transverse-field $\mu^+$SR is narrower compared to La$_3$Ni$_2$O$_{6.92}$. Our $\mu^+$SR experiment results provide a comprehensive view on the correlation between magnetism and structure perfection in Ruddlesden-Popper bilayer nickelates under ambient pressure.

Figures

Figures reproduced from arXiv: 2412.09003 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Rietveld refinement of powder x-ray diffraction d [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Rietveld refinement of powder x-ray diffraction d [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Temperature dependence of ZF- [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Temperature dependence of ZF- [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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