{"id":"36a644a9-710a-48b3-a436-65018b833be1","arxiv_id":"2601.17663","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"139La NQR shows a first-order-like incommensurate density-wave transition at ≈133 K in La4Ni3O10, with coexisting charge and spin density waves and strong spin fluctuations.","lead":"By measuring nuclear quadrupole resonance signals from lanthanum nuclei, the authors find that the trilayer nickelate La4Ni3O10 undergoes a sharp, first-order-like density-wave transition near 133 K, with incommensurate charge and spin order intertwined at the microscopic scale. The study provides a local-probe view of the order that competes with superconductivity in a prominent nickelate superconductor family.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quantitative Bint=210 mT and c-axis moment orientation rest on an unverified decomposition of NQR line broadening; relaxing the 1:2:3 W_CDW and unspecified W_SDW-to-splitting proportionality could shift the fitted field significantly.","rationale":"The central claim that most needs scrutiny is not the existence of a DW transition (the abrupt 133 K broadening and 1/T1T peak are credible and consistent with prior neutron, STM, and µSR work) but the quantitative inference of an internal field of 210 mT and its orientation. The Fig. 4 simulation is the only evidence for these numbers. The decomposition into additive CDW and SDW linewidths is plausible but contains two uncontrolled inputs: the 1:2:3 EFG-broadening ratio and the proportionality of SDW width to the computed splitting. Neither is derived from the data; the former is imported from the La3Ni2O7 study and the latter's constant is unspecified. Without residuals or raw spectra, one cannot tell whether the two-parameter match is unique. This does not invalidate the broader finding of intertwined CDW+SDW, which is independently supported, but it does undercut the specific magnitude and orientation claims. The requested fit with freed parameters is a straightforward, decisive check. Since the reader already conditioned acceptance on addressable weaknesses, the verdict need not change.","tokens_in":13100,"tokens_out":9524,"duration_ms":105027,"concrete_test":"Fit the raw frequency-swept spectra (Fig. 4b) with a generalized model that frees the three W_CDW^i and the W_SDW/splitting proportionality constant, using global least-squares with proper noise weighting; then report the best-fit Bint and its confidence interval. If the relaxed fit yields Bint appreciably different from 210 mT or does not prefer Bint⊥c, the reported magnitude and orientation are not identified by the data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's most consequential new numbers are Bint ≈ 210 mT and the conclusion that outer-plane Ni moments point along c. These follow from the Fig. 4 decomposition in which each NQR linewidth is written W_i = W_CDW^i + W_SDW^i, with W_CDW fixed to the 1:2:3 ratio of the zero-field NQR frequencies and W_SDW taken proportional to the computed Bint-induced splitting. Two unvalidated ingredients enter here. First, the 1:2:3 scaling is exact only for a small, isotropic distribution of ν_Q at fixed η; a CDW-driven distribution of the asymmetry parameter η (not established to be negligible) would violate it, and the manuscript imports the scaling from ref. [15] rather than testing it against the present data. Second, W_SDW is stated to be 'proportional to the splitting', but the proportionality constant is never given; the linewidth contributed by an incommensurate SDW depends on the shape of the internal-field distribution (e.g., sinusoidal vs. box-like), so the same observed width can correspond to a range of Bint values. The fit uses only Bint and W_CDW as free parameters, yet no residuals, confidence intervals, or alternative fits are shown, and the raw spectra are not public. While the qualitative coexistence of CDW and SDW is independently supported by neutron/STM/µSR, the specific 210 mT field magnitude and the c-axis moment orientation are not. A commensurate or nearly commensurate SDW with a different field distribution could broaden the lines similarly, weakening the orientation claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports 139La NQR measurements on single-crystal and polycrystalline La4Ni3O10. In the normal state, three La(2) NQR lines are observed. On cooling below TDW ≈ 133 K, the ±5/2↔±7/2 line in the single crystal broadens and shifts abruptly, whereas the polycrystal shows a more gradual evolution; the authors interpret this as a first-order-like density-wave transition. The broadening is attributed to an incommensurate density wave, and the simultaneous shifts of the three lines are modeled with an internal magnetic field Bint ≈ 210 mT perpendicular to the c-axis plus a charge-modulation broadening W_CDW = 0.3 MHz for the lowest transition, implying coexistence of CDW and SDW and c-axis-oriented Ni moments on the outer planes. 1/T1T shows a peak at TDW and retains a finite low-temperature value, interpreted as strong spin fluctuations and partial Fermi-surface gapping.","tokens_in":13520,"tokens_out":6796,"duration_ms":73465,"significance":"If the quantitative analysis is accepted, the paper provides a local-probe determination of coexisting incommensurate CDW and SDW order in a trilayer nickelate, with an internal field at the La(2) site considerably larger than in La3Ni2O7. The qualitative conclusions—density-wave order near 133 K, incommensurate character, and associated spin fluctuations—are consistent with neutron scattering, STM, and µSR, and the single-crystal comparison with polycrystals is a strength. The paper also usefully highlights the difference between first-order-like (La4Ni3O10) and second-order (La3Ni2O7) DW transitions. However, the central quantitative claims (Bint ≈ 210 mT and c-axis moment orientation) rest on a two-parameter linewidth decomposition whose assumptions are imported from prior work and are not validated on the present data. The absence of raw spectra and residual analysis materially weakens this part of the paper.","major_comments":[{"comment":"The decomposition W_i = W_CDW^i + W_SDW^i is the linchpin of the quantitative claims. W_CDW^i is fixed to the 1:2:3 ratio of the NQR frequencies based on ref. [15], but that scaling is exact only for a small isotropic spread in ν_Q at fixed η. If the incommensurate CDW modulates the asymmetry parameter η or produces a non-Lorentzian distribution, the 1:2:3 scaling fails. W_SDW^i is said to be 'proportional to the splitting', but the proportionality constant and the assumed internal-field distribution (sinusoidal, box-like, etc.) are not specified. With only Bint and W_CDW as free parameters, and with no residuals, confidence intervals, or alternative fits shown, the reported Bint ≈ 210 mT is not uniquely constrained. The authors should provide the fit procedure, a sensitivity analysis (varying the scaling and the field distribution), and ideally the raw spectra.","section":"Section III, Fig. 4 discussion"},{"comment":"The conversion from Bint at the La(2) site to a Ni ordered moment is not shown. The conclusion that outer-plane Ni moments lie along c depends on a specific hyperfine/transfer coupling sum (refs. [22,36]) and an assumed moment configuration; no estimate of the resulting moment magnitude or its uncertainty is given. As written, the c-axis orientation is a model-dependent inference, not a direct NQR result. Please either provide the hyperfine tensor and the derived moment estimate, or soften the conclusion to 'Bint is perpendicular to c at La(2)' and state that the microscopic spin direction is model-dependent.","section":"Section III, Fig. 4(c) and text following Eq. (W_i)"},{"comment":"The 'compelling evidence for a first-order-like transition' rests on the abrupt temperature dependence of the linewidth and frequency in the single crystal. No cooling/warming hysteresis or coexistence of two phases is shown; an inhomogeneously broadened continuous transition with a sharp order-parameter onset could produce a similar trace. If first-order character is a main conclusion, hysteresis data or an explicit two-phase fit should be supplied. Otherwise the claim should be presented as tentative and the term 'first-order-like' clarified.","section":"Section III, Figs. 2–3"}],"minor_comments":[{"comment":"The caption should state explicitly what the color bars, black dashed line, and solid circles represent. As printed, the reader must infer the relation between the computed SDW broadening, the average DW-state frequency, and the experimental points.","section":"Fig. 4 caption"},{"comment":"The paper states that the data are not publicly available. Given that the central quantitative result is a two-parameter fit, depositing the spectra and fit residuals would substantially aid verification.","section":"Data Availability"},{"comment":"The stretched-exponential recovery formula and the statement 'Because η is close to zero' should be tied to the actual η = 0.1 used in the Fig. 4 simulation; please justify why η = 0.1 does not affect the T1 analysis.","section":"Section II, T1 analysis"},{"comment":"The absence of a double-horn structure is taken as evidence for two-dimensional incommensurate modulation. This is only one possible explanation; disorder or additional inhomogeneous broadening can also mask the horns. The wording should be softened.","section":"Section III, incommensurability discussion"},{"comment":"Minor language issues: inconsistent use of 'polycrystal' vs 'polycrystalline', occasional article errors, and the notation 1/T1T should be typeset consistently.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The qualitative picture is credible and consistent with independent probes, but the quantitative B_int and moment-orientation conclusions are presented more strongly than the linewidth analysis supports. The 1:2:3 charge-broadening scaling is imported from the authors' own prior La3Ni2O7 study without in-situ validation. I would ask for the raw spectra, the assumed linewidth model, and a sensitivity analysis before publication. The paper is within the journal's scope and the observations are of interest to the nickelate/condensed-matter community."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is the first single-crystal 139La NQR study of La4Ni3O10 and it does the field a service. The data clearly show an abrupt change at ~133 K in the single crystal, a peak in 1/T1T, and a pattern of line broadening across the three NQR transitions that cannot be explained by charge or spin order alone. The qualitative conclusion—coexisting incommensurate CDW and SDW, with a first-order-like transition—is consistent with prior neutron, STM, and μSR work and is well supported by the NQR spectra.\n\nThe paper is also honest about its limits: the authors note the absence of a second SDW seen in μSR, the need for La(1) NQR to check inner-plane moments, and the fact that earlier polycrystalline NQR could not resolve the transition character.\n\nThe soft spot is the quantitative part. The B_int ≈ 210 mT and the c-axis orientation of the Ni moments come from a simulation with two free parameters—B_int and W_CDW—that relies on two assumptions brought in from the group's La3Ni2O7 work: the 1:2:3 scaling of the charge broadening with NQR frequency, and a proportionality between spin broadening and the calculated splitting whose constant is never stated. No residuals, confidence intervals, or alternative fits are shown, and the raw spectra are not public. That does not break the central claim of intertwined CDW+SDW, but it means the specific field magnitude and the moment direction should be treated as provisional until the decomposition is better constrained or independently reproduced.\n\nWorth a serious referee. The referees should ask for the error analysis and data deposition, but the paper deserves a fair shot.","headline":"A solid local-probe study with a convincing qualitative picture, but the headline B_int and moment-orientation numbers are less solid than the text implies.","tokens_in":14093,"tokens_out":2077,"would_cite":true,"duration_ms":22867,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["76.60.-k","71.45.Lr","75.30.Fv"],"model":"deepseek-v4-flash","headline":"139La NQR shows the 133 K density-wave transition in trilayer nickelate La4Ni3O10 is a first-order-like event in which an incommensurate charge density wave and a spin density wave develop together, with the magnetic part producing a 210 mT","keywords":["nuclear quadrupole resonance","nickelate superconductors","charge density wave","spin density wave","La4Ni3O10","incommensurate order","first-order phase transition","spin-lattice relaxation"],"falsifier":"Perform the same NQR measurements on a high-quality single crystal in an applied magnetic field of known orientation and compare the field-dependent splitting of the three La(2) lines with the Bint⊥c prediction; if the splitting pattern is inconsistent, the internal-field orientation or magnitude is wrong, and the c-axis moment conclusion fails.","tokens_in":12969,"feed_emoji":"🧲","tokens_out":4977,"duration_ms":51226,"temperature":0.7,"pith_summary":"The paper tries to establish that the density-wave order in La4Ni3O10 is not purely charge-like: below about 133 K both an incommensurate charge density wave and a spin density wave appear simultaneously. Using 139La nuclear quadrupole resonance on single crystals, the authors find an abrupt broadening and frequency shift of the La(2) line, characteristic of a first-order-like transition. Spectral simulation indicates an internal magnetic field of about 210 mT perpendicular to the c-axis, implying the outer-plane Ni magnetic moments point along c. The relaxation rate 1/T1T spikes at the transition, pointing to spin fluctuations that persist despite the first-order character. A sympathetic reader would care because the same density-wave competition is thought to be tied to superconductivity under pressure.","feed_headline":"Trilayer nickelate's density wave is charge plus spin, NQR shows","feed_subtitle":"La4Ni3O10 orders at 133 K into incommensurate CDW and SDW with Ni moments along c.","key_machinery":"The central tool is 139La NQR on the La(2) site, whose quadrupole frequencies and linewidths are sensitive to both electric-field-gradient changes (charge modulation) and internal magnetic fields (spin order). The argument hinges on a decomposition of each transition's linewidth into a CDW part, taken proportional to the transition frequency with a 1:2:3 ratio, and an SDW part proportional to the splitting induced by an internal magnetic field. The simulation reproduces the observed shifts and broadenings only for Bint≈210 mT oriented perpendicular to the c-axis, which fixes the direction of the outer-layer Ni moments. The absence of resolved line splitting is used to conclude the modulation","core_discovery":"Below TDW≈133 K the 139La NQR spectrum of single-crystal La4Ni3O10 changes abruptly: the La(2) ±5/2↔±7/2 line broadens and shifts within a narrow temperature window, which the authors read as a first-order-like transition. The broadening is too large and the line shifts are not in the proportions expected for either a pure quadrupolar (charge) modulation or a pure magnetic field aligned with the c-axis. By assuming the total linewidth is the sum of a charge contribution that scales with NQR frequency (1:2:3 for the three transitions) and a magnetic contribution from an internal field Bint, the authors reproduce all three transition widths and shifts with Bint≈210 mT perpendicular to c and a","pith_inferences":["If the 1:2:3 scaling for the quadrupolar broadening is an approximation, the extracted Bint≈210 mT and the c-axis moment direction would need revision; a direct measurement of the magnetic splitting by applying an external field should be able to check the orientation independently.","The identification of a first-order transition driven primarily by the CDW, with SDW fluctuations persisting above it, suggests that hydrostatic pressure may tune the two orders separately; one test would be to track the 1/T1T peak and the NQR linewidth under pressure and see whether the superconducting dome coincides with the collapse of one or both orders.","The residual ungapped Fermi surface at low temperatures implies that the incommensurate DW only partially reconstructs the band structure; if so, the superconducting state under pressure may involve both gapped and ungapped portions of the Fermi surface, which would be visible in future transport or specific-heat measurements."],"forward_implications":["If correct, the ambient-pressure ground state of La4Ni3O10 hosts coexisting incommensurate CDW and SDW, not a purely charge- or spin-driven order.","The first-order character of the transition, together with the spin-fluctuation peak in 1/T1T, suggests the CDW drives the lattice/electronic instability while SDW fluctuations are borne on top of it.","The large residual 1/T1T at low temperature indicates a substantial ungapped Fermi-surface fraction, consistent with a nesting-driven incommensurate order that does not open a full gap.","The c-axis Ni-moment direction on the outer planes distinguishes this material from layered iron-based systems and constrains theoretical models of pairing.","The strong increase of NQR linewidth below TDW without resolved splittings implies two-dimensional incommensurate modulation, which can be compared with STM and neutron results."],"fun_headline_variants":["Charge and spin waves intertwine in trilayer nickelate","NQR reveals intertwined density waves in nickelate","First-order charge-spin wave order at 133 K in nickelate","Incommensurate CDW and SDW intertwine in La4Ni3O10","La4Ni3O10: charge and spin waves lock in together"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The quantitative decomposition of the NQR linewidth into an additive CDW contribution that scales as 1:2:3 with transition frequency plus an SDW contribution from a single internal field, taken from the authors' earlier bilayer-nickelate study, is the load-bearing premise; if the actual charge broadening deviates from that scaling (for instance due to disorder or an anisotropic EFG distribution from the incommensurate CDW), the fitted field magnitude (210 mT) and the c-axis o","fun_headline_variants_meta":{"raw":{"variants":["Charge and spin waves intertwine in trilayer nickelate","NQR reveals intertwined density waves in nickelate","First-order charge-spin wave order at 133 K in nickelate","Incommensurate CDW and SDW intertwine in La4Ni3O10","La4Ni3O10: charge and spin waves lock in together"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001019,"raw_usage":{"total_tokens":4196,"prompt_tokens":865,"completion_tokens":3331,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":609,"completion_tokens_details":{"reasoning_tokens":3239}},"tokens_in":609,"tokens_out":3331,"duration_ms":25843,"temperature":1.0,"reasoning_tokens":3239,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T08:12:11.595559+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform the same NQR measurements on a high-quality single crystal in an applied magnetic field of known orientation and compare the field-dependent splitting of the three La(2) lines with the Bint⊥c prediction; if the splitting pattern is inconsistent, the internal-field orientation or magnitude is wrong, and the c-axis moment conclusion fails.","supporting_citations":[],"review_version":1}