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REVIEW 3 major objections 5 minor 43 references

Intertwined Charge and Spin Density Waves in Trilayer Nickelate La$_4$Ni$_3$O$_{10}$ Revealed by $^{139}$La NQR

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

Pith's one-line read 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

desk verdict 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. read the letter →

arxiv 2601.17663 v1 pith:HQS5UPNJ submitted 2026-01-25 cond-mat.supr-con cond-mat.str-el

classification cond-mat.supr-concond-mat.str-el PACS 76.60.-k71.45.Lr75.30.Fv
keywords nuclearquadrupoleresonancenickelatesuperconductorschargedensitywavespinLa4Ni3O10incommensurateorderfirst-orderphasetransitionspin-latticerelaxation
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

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.

What carries the argument

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

What would settle it

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.

Watch

Extended reading notes

Core claim

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

Load-bearing premise

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

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 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.

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 (3)
  1. [Section III, Fig. 4 discussion] 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.
  2. [Section III, Fig. 4(c) and text following Eq. (W_i)] 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.
  3. [Section III, Figs. 2–3] 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.
minor comments (5)
  1. [Fig. 4 caption] 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.
  2. [Data Availability] 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.
  3. [Section II, T1 analysis] 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.
  4. [Section III, incommensurability discussion] 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.
  5. [Throughout] Minor language issues: inconsistent use of 'polycrystal' vs 'polycrystalline', occasional article errors, and the notation 1/T1T should be typeset consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NQR analysis is a parameter-extraction consistency check anchored to independent external measurements.

full rationale

No significant circularity. The paper's central claims — an abrupt first-order-like DW transition near 133 K, incommensurate DW broadening, and coexistence of CDW and SDW with an internal field Bint ≈ 210 mT at the La(2) site — are based on new 139La NQR spectra and relaxation data, not on a quantity defined in terms of the conclusion. The line-shape decomposition W^i = W^i_CDW + W^i_SDW with W_CDW in 1:2:3 ratio is a standard quadrupole spin-Hamiltonian property (the three NQR transition frequencies for I=7/2 at η≈0 scale as 1:2:3); citing the authors' prior La3Ni2O7 work for this calculation is a self-citation, but the relation is independently derivable, and the same qualitative coexistence is supported by external neutron [23], STM [27], and µSR [28,29] measurements. The spectral simulation is a parameter-extraction consistency check (Bint and W_CDW are adjusted to match the three line shifts and broadenings), not a postdiction renaming a fitted parameter as a prediction. The paper itself flags the principal limitation — 'To conclusively determine the nature of the transition, it would be essential to conduct similar NQR measurements on high-quality single-crystal samples in the future' — and the data-availability statement notes raw data are not public; these affect verifiability and model dependence of the fitted Bint, but they are correctness risks, not circularity. No step in the derivation chain reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced. The investigation rests on standard NQR physics plus a two-parameter spectral model (B_int, W_CDW) whose scaling assumptions are inherited from the group's prior La3Ni2O7 work and whose uncertainties are not reported. The interpretive chain from broadening pattern to B_int ⊥ c to c-axis Ni moments depends on the assumed 1:2:3 CDW scaling and the B_int splitting calculation.

free parameters (4)
  • B_int (internal magnetic field at La(2) site) = ≈ 210 mT, perpendicular to c-axis
    Chosen so the simulated shifts and broadenings of all three NQR transitions match the 7.3 K single-crystal spectrum; no uncertainty or degeneracy analysis reported.
  • W_CDW (charge-modulation broadening for ±1/2↔±3/2 transition) = 0.3 MHz
    Second tuning parameter of the Fig. 4 simulation, alongside B_int; the CDW broadening of the other transitions is set by the assumed 1:2:3 frequency scaling.
  • v_q and η for the La(2) NQR calculation = v_q = 5.27 MHz, η = 0.1
    Adopted as inputs to the spectral simulation in Fig. 4; v_q is derived from the measured NQR frequencies but η is assumed, and the combined effect on the B_int estimate is not varied.
  • Stretched-exponential factor β = Temperature-dependent, not tabulated
    Fitted per temperature in the T1 analysis via the stretched-exponential recovery formula; β drops rapidly below TDW and is used to support the DW-modulation interpretation.
assumptions (6)
  • standard math NQR recovery-curve formula for I = 7/2 with η ≈ 0 (Chepin & Ross, ref [34])
    Used to fit T1 from saturation-recovery data; η assumed close to zero so its influence on the recovery curve is ignored.
  • domain assumption CDW-induced NQR broadening scales with transition frequency in the ratio 1:2:3
    Imported from the authors' prior La3Ni2O7 NQR paper (ref [15], same group); this scaling is load-bearing for the W_CDW decomposition in the Fig. 4 simulation.
  • standard math FWHM of the convolution of two Lorentzians is the sum of their individual FWHMs
    Used to write W_i = W_CDW^i + W_SDW^i and to split total widths into charge and spin contributions.
  • domain assumption The La(2) site is sensitive only to the magnetic moments of the outer NiO2 planes
    Stated in Section III to explain why the second µSR SDW transition near 90 K is not observed; also underpins the interpretation of B_int as arising from outer-plane moments.
  • domain assumption An internal magnetic field perpendicular to the c-axis shifts ±1/2↔±3/2 and ±3/2↔±5/2 to higher frequencies and barely affects ±5/2↔±7/2
    NQR perturbation calculation pattern taken from ref [15]; the core of the argument that B_int ⊥ c and that Ni moments point along c.
  • domain assumption The abrupt single-crystal transition is intrinsic, while the gradual polycrystal behavior is a sample-quality effect
    Used to elevate the single-crystal first-order-like signature over the polycrystal gradual change; supported by the narrower single-crystal linewidth but not independently verified.

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Cite this review

Pith. "Pith review of Intertwined Charge and Spin Density Waves in Trilayer Nickelate La$_4$Ni$_3$O$_{10}$ Revealed by $^{139}$La NQR." pith.science (2026). https://pith.science/paper/HQS5UPNJ

@misc{pith2026260117663,
  author       = {Pith},
  title        = {Pith review of: Intertwined Charge and Spin Density Waves in Trilayer Nickelate La$_4$Ni$_3$O$_10$ Revealed by $^139$La NQR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HQS5UPNJ}},
  note         = {Machine review of arXiv:2601.17663}
}
abstract

The discovery of superconducting transitions in pressurized La$_3$Ni$_2$O$_{7}$ and La$_4$Ni$_3$O$_{10}$ has highlighted the pivotal role of density wave (DW) orders in nickelate superconductors. To gain a comprehensive understanding of the superconducting state, it is essential to elucidate the nature of the DW order. In this study, we utilized $^{139}$La nuclear quadrupole resonance (NQR) to investigate the charge density wave (CDW) and spin density wave (SDW) orders in both single-crystal and polycrystalline La$_4$Ni$_3$O$_{10}$. Near $T_{\rm{DW}} \approx 133$ K, an abrupt change in both the linewidth and frequency of the La(2) site in the single-crystal sample provides compelling evidence for a first-order-like phase transition. The pronounced broadening of the NQR lines indicates the incommensurate nature of the DW order. Furthermore, the spin-lattice relaxation rate divided by temperature 1/$T_1$$T$ exhibits a strong enhancement at $T_{\rm{DW}}$, indicating the strong spin fluctuations above the first-order DW transition. These observations suggest an intricate interplay between incommensurate CDW and SDW orders. Our findings offer critical insights into the microscopic mechanisms of the DW state in La$_4$Ni$_3$O$_{10}$ and establish an essential framework for exploring the interplay between DW and superconducting phases in nickelate superconductors.

Figures

Figures reproduced from arXiv: 2601.17663 by the authors.

Figure 1
Figure 1. FIG. 1: (a) Crystal structure of La [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The temperature-dependent [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The temperature-dependent NQR frequency (a) and full width at half maximum(FWHM) (b) of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (a) Theoretical simulation of the NQR frequencies at the La(2) site with an internal magnetic field [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (a) Red dots and blue symbols represent the 1 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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