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Microscopic evidence of charge- and spin-density waves in La$_3$Ni$_2$O$_{7-\delta}$ revealed by $^{139}$La-NQR

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper uses 139La nuclear quadrupole resonance to show that the density wave in La3Ni2O7−δ is a simultaneous charge- and spin-density wave order below about 153 K.

desk verdict Phase-selective NQR data make a plausible case for simultaneous CDW and SDW in La3Ni2O7, but the CDW leg rests on a splitting ratio from an unresolved line. read the letter →

arxiv 2501.11248 v2 pith:IPYPYWTD submitted 2025-01-20 cond-mat.supr-con cond-mat.str-el

J. Luo , J. Feng , G. Wang , N. N. Wang , J. Dou , A. F. Fang , J. Yang , J. G. Cheng
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Guo-qing Zheng R. Zhou
This is my paper · ORCID
classification cond-mat.supr-concond-mat.str-el
keywords La3Ni2O7nickelatesuperconductorsnuclearquadrupoleresonancechargedensitywavespinorder139La-NQR
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 139La nuclear quadrupole resonance measurements on the bilayer nickelate La3Ni2O7−δ, a superconductor with Tc near 80 K under pressure. By resolving the La(2) site of the 327 phase from intergrowth impurity phases, the authors show that below TDW≈153 K the ±5/2↔±7/2 NQR line splits while the ±3/2↔±5/2 line only broadens, and they attribute this pattern to a unidirectional, commensurate charge modulation rather than to a magnetic field. At the same temperature, a magnetic line broadening appears and the spin-lattice relaxation rate increases sharply, which they take as evidence for formation of magnetic moments. The paper concludes that charge- and spin-density waves form simultaneously in the 327 phase, a result that constrains the electronic correlations thought to be relevant for the superconductivity.

What carries the argument

The central object is the 139La NQR line shape at the La(2) site of La3Ni2O7, measured at zero field. The discriminating step is the comparison of the line splitting of the ±5/2↔±7/2 and ±3/2↔±5/2 transitions: a magnetic internal field shifts all quadrupole transitions by the same amount, whereas charge modulation scales the splitting with the transition frequency (ratio 1.5 for equal asymmetry parameters η). The magnetic contribution to the linewidth is then isolated with the ad hoc decomposition wtot = $\sqrt$((m·wquad)^2 + (wmag)^2), with m=2 for the ±3/2↔±5/2 and m=3 for the ±5/2↔±7/2 transition, and its onset below TDW plus the 1/T1 enhancement provide the SDW signature.

What would settle it

Measure the lowest NQR transition (±1/2↔±3/2) in a single crystal below 153 K: if the splitting is purely charge-derived, the three transitions must split in a fixed ratio set by the quadrupole interaction, while a magnetic field would add the same frequency shift to all transitions; a pattern requiring a magnetic field would overturn the charge-order interpretation.

Watch

Extended reading notes

Core claim

Below TDW≈153 K, the 139La-NQR spectrum at the La(2) site of the 327 phase displays a distinct splitting of the ±5/2↔±7/2 transition while the ±3/2↔±5/2 transition only broadens. Comparing the observed splitting ratio (about 2) with simulations for a purely magnetic internal field and for charge modulation (expected ratio 1.5), the authors conclude the splitting is mainly a charge density wave, with possible minor contributions from EFG asymmetry or a small in-plane field. Simultaneously, the magnetic contribution to the linewidth, extracted via a FWHM decomposition, grows below TDW, and 1/T1 is enhanced by nearly two orders of magnitude at the transition, indicating spin fluctuations and the formation of ordered moments. The paper concludes that a commensurate, unidirectional CDW and an SDW coexist in the DW state of La3Ni2O7−δ.

Load-bearing premise

The conclusion that the line splitting comes from charge order rather than magnetism depends on the expected ratio of splittings being 1.5; the measured ratio is about 2, and the gap is closed by assuming an unspecified difference in the electric-field-gradient asymmetry between the two split sites or a small in-plane magnetic field, neither of which is measured.

Editorial extensions

If this is right

  • If correct, the density wave state in La3Ni2O7−δ is not a single order parameter but a coexistence of charge and spin density waves below TDW≈153 K.
  • The commensurate, unidirectional character of the CDW, similar to cuprate stripe order, constrains electronic-structure models and rules out a purely Fermi-surface-nesting picture for the CDW.
  • The 1/T1T drop to about 1% of its high-temperature value below 50 K implies that most of the Fermi surface is gapped in the DW state, so superconductivity must emerge from the remaining carriers.
  • The assignment of the ~133 K transition to the intergrowth 4310 phase explains why transport sometimes sees two transitions in polycrystalline samples, decoupling the intrinsic 327 response.
  • The strong spin fluctuations approaching TDW suggest the density wave is driven by magnetic correlations, which is relevant for the pairing mechanism if superconductivity competes with the DW.

Reading between the lines

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

  • Beyond the paper's claims, measuring the ±1/2↔±3/2 NQR transition could separate the CDW and magnetic contributions; a pure CDW predicts a specific ratio across all three transitions, while an internal field would shift them equally.
  • Beyond the paper's claims, the coexistence of CDW and SDW at one temperature suggests a coupled stripe state; high-pressure NQR could test whether both orders vanish together near the superconducting dome.
  • Beyond the paper's claims, the proposed assignment of the ~133 K transition to the 4310 intergrowth implies that phase-pure samples should show a single DW transition, which a comparative study could verify.
  • Beyond the paper's claims, the magnetic broadening extraction relies on a decomposition formula that is not independently validated; single-crystal NMR of the internal-field distribution would provide a direct check of the ordered moment.
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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. This paper reports 139La-NQR measurements on a polycrystalline La3Ni2O7−δ sample, exploiting the spectral selectivity of NQR to isolate the intrinsic 327 phase from the 214, 4310, and intergrowth phases. The authors assign the observed resonance peaks to the different phases using the temperature dependence of 1/T1T, and then focus on the La(2) site of the 327 phase. Below TDW ≈ 153 K they observe a well-resolved splitting of the ±5/2↔±7/2 transition while the ±3/2↔±5/2 transition only broadens; from the ratio of the fitted splittings (≈ 2 versus the CDW expectation of 1.5) they attribute the splitting to a unidirectional, commensurate charge modulation. They also report a nearly two-order-of-magnitude enhancement of 1/T1 near TDW followed by a decrease at lower temperatures, and an increase of the NQR linewidth below TDW, which they decompose with an explicitly 'ad hoc' formula into a temperature-dependent magnetic part and an essentially constant quadrupole part. From the magnetic broadening they estimate Bint ≈ 0.005 T at the La(2) site, and they conclude that charge- and spin-density-wave order form simultaneously at TDW. The paper candidly notes that precise parameters require future single-crystal work and that no CDW superlattice peaks have yet been seen by X-ray scattering.

Significance. The question addressed is timely and contested: the nature of the density-wave transition adjacent to the high-pressure superconducting dome of La3Ni2O7−δ is disputed (µSR/NMR/RIXS point to SDW; other NMR and infrared work point to CDW). The phase-selective strategy of this paper is a genuine methodological strength, since intergrowth contamination is a known confound in this material family. If the simultaneous CDW+SDW conclusion holds, the result is an important microscopic constraint on the electronic correlations of bilayer nickelates and would support the stripe-order analogy with the cuprates. The credible elements include the peak assignment via 1/T1T, the clean splitting of the ±5/2↔±7/2 line, the robust 1/T1 enhancement at TDW, and the authors' explicit disclosure of the ad hoc character of their linewidth decomposition. The main weakness is quantitative: the CDW attribution rests on a ratio whose denominator is extracted from an unresolved line, and the static SDW component rests on an unvalidated decomposition formula. These points are fixable within the manuscript's scope, but they are load-bearing for the headline claim.

major comments (3)
  1. [Fig. 2(b) and the paragraph following Fig. 3] The CDW attribution rests on the ratio Δν(±5/2↔±7/2)/Δν(±3/2↔±5/2) ≈ 2, but the denominator of this ratio is not a directly observed splitting: the text states that for the ±3/2↔±5/2 transition 'only the line broadening can be observed down to 10 K', yet Δν for this transition is extracted from a two-Gaussian fit of an unresolved, featureless line. No error bars, goodness-of-fit comparison against a single broad line, or constraints on the two-Gaussian parameters are reported, so the discriminating ratio is a model output rather than an experimental observable. The reconciliation of the observed ratio with the CDW expectation of 1.5 is likewise not quantitative: the required difference in the asymmetry parameter η between the two split sites is not estimated, and the suggested small in-plane internal field requires a quantitative treatment, since according to the paper's own Fig. 3(b) an ab-plane field produces a much larger line splitting at the ±3/2↔±5/2 transition than at the ±5/2↔±7/2 transition. The manuscript itself concedes that precise parameters can only be obtained from future single-crystal work. Please report the fit statistics and error bars for Δν, quantify the η difference or field needed to reproduce the ratio, and discuss the alternative that a structural distortion (rather than a charge modulation) makes the two La(2) sites inequivalent.
  2. [Fig. 5 and the paragraph introducing the FWHM decomposition] The static magnetic order component of the SDW claim relies on the separation of the total linewidth into magnetic and quadrupole contributions via the explicitly 'ad hoc' formula wtot = sqrt((m·wquad)^2 + (wmag)^2), with m = 2 for the ±3/2↔±5/2 transition and m = 3 for the ±5/2↔±7/2 transition. Since both transitions are measured, a consistency check is available: the magnetic contribution should be the same for the two transitions if it arises from the same distribution of static fields, and the quadrupole contribution should scale with the transition index m. Without such a check, or a joint simulation of both lineshapes with a shared set of field and EFG distributions, the temperature-dependent 'magnetic' width in Fig. 5(a) and the derived estimate Bint ≈ 0.005 T remain model-dependent. The 1/T1 enhancement at TDW (Fig. 2(c)) independently supports enhanced spin fluctuations, but the claim that static moments form would be stronger if the decomposition were validated.
  3. [Paragraph on the 1D incommensurate CDW and Fig. 4] The conclusion that the charge modulation is commensurate follows from a comparison, reported only in the Supplemental Material, between a two-Gaussian fit and a simulation of a 1D incommensurate CDW, with no quantitative criterion given in the main text. Since this conclusion underlies the unidirectional stripe patterns proposed in Fig. 4 and the analogy with cuprate stripe order, please report the comparison statistic (e.g., reduced χ² or residuals) or explicitly label the commensurate character as a proposal.
minor comments (5)
  1. [Experimental methods (η statement)] The paper states 'Because η is close to zero, we ignore the influence of η on the recovery curve', but later uses η = 0.04 in the simulations of Fig. 3 and invokes a difference in η between the split sites to explain the observed splitting ratio; please state the value of η used and its uncertainty, and justify ignoring η for T1 while using it in the lineshape analysis.
  2. [Abstract] The abstract's wording that NQR measurements 'eliminate the influence of other structural phases' is stronger than what is demonstrated; the NQR spectra spectrally separate the different phases, but the phases remain present in the sample. Please rephrase to 'exclude the signals from' or 'suppress the contribution of' the other phases.
  3. [Text near 'Bint ∼ 0.005 T'] The sentence 'the observed internal field Bint at the La(2) site can be estimated from the magnetic line broadening as Bint ∼ 0.005 T' does not state the temperature at which this estimate is made, given the strong temperature dependence of wmag in Fig. 5(a), nor does it give an uncertainty; please add these.
  4. [Fig. 2(b)] Fig. 2(b) would benefit from a statement of the fitting procedure in the main text: number of spectral points, line shape used, and whether the two-Gaussian fits are constrained (e.g., equal widths or equal intensities), since the low-frequency transition is not visibly split.
  5. [Discussion of the absence of X-ray superlattice peaks] The discussion acknowledges that X-ray scattering has not observed CDW superlattice peaks so far; please add a sentence quantifying the expected diffraction intensity or otherwise explaining why the absence of an observable structural signature is compatible with the claimed modulation amplitude.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: CDW/SDW discrimination uses standard quadrupole calculations, not fitted outputs.

full rationale

The paper's central inference (line splitting below TDW implies CDW) is based on forward calculations from the standard NQR Hamiltonian, with stated parameters νQ = 5.92 MHz and η = 0.04, and on the nuclear gyromagnetic ratio γ = 6.0146 MHz/T. The expected splitting ratio of about 1.5 between the ±5/2↔±7/2 and ±3/2↔±5/2 transitions is derived from the Hamiltonian before comparison with data; it is not obtained by fitting the observed splitting. The observed ratio (~2) is reconciled by invoking an unquantified difference in η or a small in-plane internal field; this reduces the quantitative force of the CDW attribution but does not make the prediction equivalent to its input by construction. The magnetic broadening extraction uses an explicitly labeled 'ad hoc formula', wtot = sqrt((m·wquad)^2 + (wmag)^2), rather than presenting it as a derived first-principles result, and the SDW conclusion is additionally supported by the independently measured 1/T1 enhancement. The self-citation [10] for phase assignment is a minor reliance on prior STEM/NQR work by overlapping authors, but that prior work is empirical and not a theorem; the assignment is not the quantity being derived. No load-bearing step reduces a claimed prediction to its own input, so the paper is not circular beyond a normal, non-load-bearing self-citation.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its free parameters are the ad hoc explanatory degrees of freedom used to reconcile the observed splitting ratio with the CDW prediction (an unspecified η difference and a possible small in-plane internal field). The axioms are the standard NQR Hamiltonian, the prior assignment of the EFG principal axis, the ad hoc FWHM decomposition, the qualitative commensurability comparison, and the peak assignment to specific structural phases.

free parameters (2)
  • Difference in EFG asymmetry parameter η between the two split La(2) sites in the CDW state = not specified
    Invoked in the discussion to explain why the observed splitting ratio (~2) exceeds the CDW prediction (1.5); no independent estimate is provided, making the CDW attribution less constrained.
  • Possible small internal magnetic field along the ab plane at La(2) sites = not fitted; later estimated at ~0.005 T from the same magnetic broadening
    Also invoked to reconcile the ratio deviation; the estimate is not an independent handle and is extracted from the same linewidth data.
assumptions (5)
  • standard math The zero-field quadrupole Hamiltonian HQ = e^2 qQ / [4I(2I-1)] [(3I_z^2 - I^2) + (η/2)(I_+^2 + I_-^2)] governs the 139La NQR spectrum.
    Standard NQR formalism from Abragam; used to compute the expected splitting ratios in Fig. 3. No alternative is considered.
  • domain assumption At the La(2) site, the principal axis of the electric field gradient is along the c-axis, as concluded by prior 139La NMR.
    This orientation is needed to calculate how big a magnetic internal field would split the two NQR transitions. It is taken from ref [18]; if the axis assignment is wrong, the magnetic-order scenarios in Fig. 3(a,b) are miscalculated.
  • ad hoc to paper The total NQR linewidth can be decomposed as wtot = sqrt((m·wquad)^2 + (wmag)^2), with m = 2 for the ±3/2↔±5/2 transition and m = 3 for the ±5/2↔±7/2 transition.
    This 'ad hoc formula' is introduced without derivation or validation; the magnetic broadening wmag, the main SDW evidence, is obtained from it.
  • ad hoc to paper The two-peak shape below TDW is better reproduced by two Gaussian lines than by the simulation of a 1D incommensurate CDW, so the CDW is commensurate.
    The commensurability claim rests on a visual or qualitative comparison in Supplementary Fig. 8; no quantitative goodness-of-fit criterion is reported.
  • domain assumption The resonance peaks assigned to La327(2), La327-i(2), La4310-i(2), and La4310(2) sites are correctly identified.
    The central data come from the La327(2) peak. Assignment relies on prior STEM/NQR work [10] and on new 1/T1T behavior in Supplementary Fig. 5; a misassignment would invalidate the phase-specific conclusions.

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Cite this review

Pith. "Pith review of Microscopic evidence of charge- and spin-density waves in La$_3$Ni$_2$O$_{7-\delta}$ revealed by $^{139}$La-NQR." pith.science (2026). https://pith.science/paper/IPYPYWTD

@misc{pith2026250111248,
  author       = {Pith},
  title        = {Pith review of: Microscopic evidence of charge- and spin-density waves in La$_3$Ni$_2$O$_7-\delta$ revealed by $^139$La-NQR},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IPYPYWTD}},
  note         = {Machine review of arXiv:2501.11248}
}
abstract

The recent discovery of superconductivity in La$_3$Ni$_2$O$_{7-\delta}$ with a transition temperature $T_c$ close to 80 K at high pressures has attracted significant attention, due particularly to a possible density wave (DW) transition occurring near the superconducting dome. Identifying the type of DW order is crucial for understanding the origin of superconductivity in this system. However, owing to the presence of La$_4$Ni$_3$O$_{10}$ and other intergrowth phases in La$_3$Ni$_2$O$_{7-\delta}$ samples, extracting the intrinsic information from the La$_3$Ni$_2$O$_7$ phase is challenging. In this study, we employed $^{139}$La nuclear quadrupole resonance (NQR) measurements to eliminate the influence of other structural phases in the sample and obtain microscopic insights into the DW transition in La$_3$Ni$_2$O$_{7-\delta}$. Below the DW transition temperature $T_{\rm DW} \sim$ 153K, we observe a distinct splitting in the $\pm$ 5/2 $\leftrightarrow$ $\pm$ 7/2 transition of the NQR resonance peak at the La(2) site, while only a line broadening is seen in the $\pm$ 3/2 $\leftrightarrow$ $\pm$ 5/2 transition peak. Through further analysis of the spectra, we show that the line splitting is due to a unidirectional charge modulation. A magnetic line broadening is also observed below $T_{\rm DW}$, accompanied by a large enhancement of the spin-lattice relaxation rate, indicating the formation of magnetically ordered moments in the DW state. Our results suggest a simultaneous formation of charge- and spin-density wave order in La$_3$Ni$_2$O$_{7-\delta}$ , thereby offering critical insights into the electronic correlations in Ni-based superconductors.

Figures

Figures reproduced from arXiv: 2501.11248 by the authors.

Figure 1
Figure 1. FIG. 1: (Color online) (a) The crystal structure of La [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (Color online) (a) The temperature dependence of the La [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (Color online) The calculated evolution of the NQR lines in the presence of the internal field along [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: (Color online) Illustration of possible CDW patterns below [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) The magnetic (a) and quadrupole (b) contribution to the FWHM extracted from the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Reviewed August 10, 2026 · model on record in the stance chip above.