{"id":"63c90915-676b-4fc3-b606-7d3c2bc9131c","arxiv_id":"2412.09003","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Muon spin relaxation finds long-range magnetic order below 161 K in La1.9Pr1.1Ni2O6.97 and short-range order below 30 K in oxygen-deficient La3Ni2O6.63, linking oxygen vacancies to suppressed magnetism.","lead":"This paper reports muon spin relaxation measurements on two nickelate materials, finding long-range magnetic order in a Pr-doped sample at 161 K and only short-range order in an oxygen-deficient sample at 30 K. The results connect oxygen vacancies to the disruption of magnetic order in bilayer nickelates, a family being studied for high-temperature superconductivity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing oscillating-amplitude report leaves bulk vs. 6.2% La2NiO4 attribution of the 145 mT precession unverified.","rationale":"The reader identifies the same weakest assumption: the attribution of the 145 mT oscillating signal to the bulk 327 phase rather than to the 6.2% La2NiO4 impurity. I agree that this is the most load-bearing concern for the central claim, because if the cosine were impurity-dominated, the 'bulk commensurate long-range order' conclusion and the derived T_N and beta exponent would be invalid. The available internal evidence—the onset of the oscillation below 160 K and the high wTF magnetic volume fraction—makes an impurity-only origin unlikely but does not fully exclude a mixed contribution. The decisive missing piece is the explicit amplitude of the cosine. The fitting framework in Eq. (2) with fL ≈ 0.299 implies that if fm is near unity, the oscillating amplitude is large, but this is a model-based reconstruction rather than a directly reported quantity. A simple amplitude check would settle the issue, or a reference measurement on La2NiO4. Because this is a well-defined, addressable reporting gap rather than a demonstrated error, the CONDITIONAL verdict remains appropriate; the paper should provide the requested numbers or a control experiment before the bulk-order claim can be fully accepted.","tokens_in":14747,"tokens_out":17616,"duration_ms":179373,"concrete_test":"Report the fitted amplitude of the 145 mT oscillating component at 2.4 K as a fraction of the total asymmetry (equivalent to fm × (1 − fL) in Eq. 2). Compare it with the maximum possible impurity contribution, (2/3) × 6.2% ≈ 4.1%. If the oscillating amplitude exceeds ~10% of total asymmetry, the bulk 327 phase dominates the precession. Independently, measure ZF-μSR on a phase-pure La2NiO4 reference synthesized under the same conditions to determine its T_N and internal field; if T_N ≈ 160 K and Bint ≈ 145 mT, explicitly quantify the impurity contribution to the cosine amplitude.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that La1.9Pr1.1Ni2O6.97 exhibits bulk commensurate long-range magnetic order rests on the ZF-μSR cosine at ~145 mT being the order parameter of the 327 phase. The sample contains 6.2% La2NiO4, a known antiferromagnet with muon internal fields of order 100 mT (refs 47,48). The paper never states the amplitude of the 145 mT oscillating component as a fraction of total asymmetry. Without this number, one cannot exclude the possibility that the cosine comes predominantly from the impurity, especially if the impurity's oxygen stoichiometry places its T_N near 160 K (La2NiO4+δ T_N is strongly oxygen-dependent). The wTF magnetic volume fraction reaching >90% demonstrates that the majority of the sample is magnetically ordered, but it does not identify which phase produces the coherent precession. If the bulk 327 phase orders incommensurately or with a broad field distribution, its ZF contribution would be a fast relaxation, and the observed cosine could be a minority impurity signal. The fit with fL = 0.299 and a high fm implies, within the model, a large cosine amplitude, but this inference is model-dependent and not explicitly reported. This directly biases the deduced T_N and the beta exponent, because Eq. (4) is fitted to Bint(T) extracted from the cosine frequency.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14977,"tokens_out":8611,"duration_ms":90730,"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":[{"comment":"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.","section":"Muon spin relaxation, Eq. (2), Eq. (3), Fig. 3"},{"comment":"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.","section":"Muon spin relaxation, Eq. (4), Fig. 3(c)"},{"comment":"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.","section":"Muon spin relaxation, Eq. (6), Fig. 4(b)"}],"minor_comments":[{"comment":"The title contains an unintended space in 'nicke late'; it should read 'nickelate' as one word.","section":"Title"},{"comment":"The fit parameter is written as B_int(0) in Eq. (4) but as B(0) in the following text; please use consistent notation.","section":"Eq. (4) and text after it"},{"comment":"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.","section":"Eq. (3)"},{"comment":"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.'","section":"Experimental details"},{"comment":"The placeholder 'URL_will_be_inserted_by_publisher' for the supplemental material should be replaced by a working link in the posted version.","section":"Supplemental material, ref. [43]"}],"recommendation":"major_revision","confidential_remarks":"The central issue is the missing oscillating-amplitude report. The authors likely have the f_i values in the supplementary material, so it may be straightforward to address, but the main text must state the amplitude of the 145 mT component explicitly and compare it with the 6.2% La2NiO4 impurity. Given the high visibility of nickelate superconductivity, the phase attribution should be made rigorous. The paper otherwise contains useful new data and a clear comparison between two oxygen-stoichiometry extremes."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The two things to know: this is the first muSR study of La1.9Pr1.1Ni2O6.97 and La3Ni2O6.63, and the central observation of a clear precession below 161 K in the nearly stoichiometric Pr-doped sample is credible. The data look solid and the comparison across three oxygen stoichiometries is a genuinely useful addition to the nickelate phase-diagram discussion. The paper deserves a careful referee, but there is one number that needs to come out of the supplementary material: the amplitude of the 145 mT oscillating component as a fraction of total asymmetry.\n\nThe main result is a clean ZF-muSR precession signal with Bint(0) = 145 mT, TN = 161.4(5) K, and beta = 0.33(2). The order-parameter fit and the wTF volume fraction reaching above 90% are encouraging. The oxygen-deficient sample shows no oscillation, with a two-step magnetic response that the LF decoupling measurements characterize reasonably well. That part is competent and honest.\n\nThe soft spot is exactly what the stress-test note flags. The sample contains 6.2% La2NiO4, a known antiferromagnet with muon fields on the order of 100 mT. The paper never states what fraction of the total asymmetry is in the 145 mT cosine. Without that number, the claim that this cosine represents bulk 327-phase order is not fully verified. The wTF data show that the majority of the sample is magnetically ordered—but they do not by themselves tell you which phase produces the coherent precession. If the 327 phase orders with a broad field distribution, its ZF signal would be a fast relaxation, and the observed cosine could be a minority impurity contribution. That would bias TN and beta. I do not think this is likely, since the impurity fraction is small and the wTF volume fraction is large, but the paper should report the cosine amplitude and, ideally, compare it with the impurity fraction. This is an addressable omission, not a fundamental flaw.\n\nTwo minor points: the comparison of magnetic transition width with La3Ni2O6.92 cites the authors' prior PRL, which is fine, but the fits should be consistent or the cross-paper comparison acknowledged. And the low-temperature magnetic volume fraction is only shown graphically; give the number.\n\nWho gets value from this: the bilayer nickelate community, especially people working on oxygen stoichiometry and magnetism. The data are new and the interpretation is reasonable. I would send it to a competent muSR referee and ask for the missing amplitude plus a direct discussion of the La2NiO4 contribution. The paper is worth engaging with, not desk-rejecting.","headline":"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.","tokens_in":15651,"tokens_out":2284,"would_cite":true,"duration_ms":27767,"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":"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.","keywords":["muon spin relaxation","Ruddlesden-Popper nickelates","La3Ni2O7","oxygen vacancies","magnetic order","3D Ising critical exponent","spin density wave","nickelate superconductivity"],"falsifier":"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.","tokens_in":14464,"feed_emoji":"🧲","tokens_out":12475,"duration_ms":111991,"temperature":0.7,"pith_summary":"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.","feed_headline":"Muons find long-range magnetism at 161 K in bilayer nickelate","feed_subtitle":"Nearly stoichiometric La1.9Pr1.1Ni2O6.97 orders like a 3D Ising magnet; oxygen-poor La3Ni2O6.63 only short-range below 30 K.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Earlier muon spin relaxation result on La3Ni2O6.92 that supplies the comparison for transition width and order-parameter evolution.","marker":"[11]"},{"why":"Pressurized muon experiment whose split density-wave transitions are compared with the higher T_N seen here under chemical pressure.","marker":"[10]"},{"why":"Report of improved phase purity and higher superconducting volume fraction in Pr-substituted bilayer nickelate, motivating the sample choice.","marker":"[14]"},{"why":"First-principles calculation used to explain how oxygen vacancies reduce nearby Ni moments and create effectively charge-disordered sites.","marker":"[49]"},{"why":"Theory of apical-oxygen deficiencies disrupting pairing and magnetism, cited for vacancy-induced magnetic moments.","marker":"[50]"},{"why":"Provides the 3D Ising critical exponent value 0.326 used to interpret the measured beta = 0.33(2).","marker":"[46]"},{"why":"Inelastic neutron scattering evidence of strong interlayer exchange coupling without long-range order, used as context for sample-dependent magnetism.","marker":"[13]"},{"why":"Muon data on nickelate impurity phases showing internal fields near 100 mT, used to rule out 214-phase contributions to the signal.","marker":"[47]"}],"fun_headline_variants":["Muons pin long-range order at 161 K in bilayer nickelate","161 K: bilayer nickelate orders long-range, muons show","Muon spin relaxation nails 161 K magnetic order in nickelate","Bilayer nickelate: long-range magnetism at 161 K, short-range at 30 K","Oxygen voids kill long-range order in bilayer nickelate, muons show"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Muons pin long-range order at 161 K in bilayer nickelate","161 K: bilayer nickelate orders long-range, muons show","Muon spin relaxation nails 161 K magnetic order in nickelate","Bilayer nickelate: long-range magnetism at 161 K, short-range at 30 K","Oxygen voids kill long-range order in bilayer nickelate, muons show"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000775,"raw_usage":{"total_tokens":3491,"prompt_tokens":1072,"completion_tokens":2419,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":688,"completion_tokens_details":{"reasoning_tokens":2318}},"tokens_in":688,"tokens_out":2419,"duration_ms":16969,"temperature":1.0,"reasoning_tokens":2318,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:21:04.957395+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Li, C.-Q","cited_arxiv_id":null,"evidence_quote":"Pressurized muon experiment whose split density-wave transitions are compared with the higher T_N seen here under chemical pressure."},{"cited_title":"Sugiyama, M","cited_arxiv_id":null,"evidence_quote":"First-principles calculation used to explain how oxygen vacancies reduce nearby Ni moments and create effectively charge-disordered sites."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Theory of apical-oxygen deficiencies disrupting pairing and magnetism, cited for vacancy-induced magnetic moments."},{"cited_title":"Suter and B","cited_arxiv_id":null,"evidence_quote":"Provides the 3D Ising critical exponent value 0.326 used to interpret the measured beta = 0.33(2)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Inelastic neutron scattering evidence of strong interlayer exchange coupling without long-range order, used as context for sample-dependent magnetism."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Muon data on nickelate impurity phases showing internal fields near 100 mT, used to rule out 214-phase contributions to the signal."}],"review_version":1}