Spin Fluctuations in the Rare-Earth Doped Bilayer Nickelates

arxiv: 2601.14946 · v2 · submitted 2026-01-21 · ❄️ cond-mat.supr-con · cond-mat.str-el

Spin Fluctuations in the Rare-Earth Doped Bilayer Nickelates

Honglin Zhou , Xinman Ye , Gang Wang , Devashibhai Adroja , David Tam , Michael Marek Koza , Zhilun Lu , Jinguang Cheng

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Dao-Xin Yao Huiqian Luo

This is my paper

Pith reviewed 2026-05-16 12:21 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.str-el

keywords spin fluctuationsbilayer nickelatesinelastic neutron scatteringinterlayer couplingrare-earth dopingHeisenberg modelhigh-Tc superconductivitystripe magnetism

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The pith

Rare-earth doping splits the spin fluctuation modes in bilayer nickelates and raises the interlayer coupling to 69-73 meV.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reports inelastic neutron scattering measurements on powder samples of Pr- and Nd-doped La3Ni2O7-δ. In addition to low-energy crystal-field excitations, the original 45 meV flat spin mode splits into two branches and a new weak mode appears near 60 meV, with the Nd-doped compound showing the strongest signal. The authors interpret these changes inside a stripe-type Heisenberg model as the signature of an increased interlayer exchange interaction SJ⊥. A sympathetic reader would care because the spin fluctuations are widely viewed as the pairing glue for superconductivity in this family, so any doping route that strengthens the interlayer term offers a concrete handle on the magnetic spectrum without external pressure.

Core claim

The central claim is that the newly observed splitting of the 45 meV mode together with the 60 meV feature in the doped compounds is consistent with an enhanced interlayer coupling SJ⊥ of roughly 69-73 meV within the stripe-type Heisenberg model, while the intralayer couplings remain weak; the Nd-doped sample exhibits stronger fluctuations than either the undoped or Pr-doped material.

What carries the argument

The stripe-type Heisenberg model with variable interlayer exchange SJ⊥, which is used to reproduce the positions and splitting of the observed spin-fluctuation modes in the inelastic neutron spectra.

If this is right

The interlayer coupling SJ⊥ increases from ~60 meV in the undoped bilayer nickelate to 69-73 meV upon rare-earth substitution.
Spin fluctuations are stronger in the Nd-doped compound than in the Pr-doped or undoped versions.
The intralayer couplings remain weak (≤3.5 meV) while the interlayer term dominates the spectrum.
The magnetic spectrum can be tuned by rare-earth doping within the same stripe Heisenberg framework used for the parent compound.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the enhanced SJ⊥ survives in single-crystal samples under pressure, it could be used to test whether interlayer magnetic coupling directly controls the superconducting transition temperature.
The same doping approach might be applied to other layered nickelates to map how the magnetic spectrum correlates with Tc without changing the crystal structure family.
Disorder from rare-earth substitution could itself broaden or shift the modes, so future work separating substitution from disorder effects would be needed to confirm the pure exchange enhancement.

Load-bearing premise

The split modes and 60 meV feature arise purely from stronger interlayer exchange and are not significantly shifted by doping-induced changes in crystal-field levels, disorder, or additional magnetic interactions.

What would settle it

A high-resolution single-crystal measurement that shows the 45 meV mode does not split when rare-earth doping is introduced under conditions that suppress disorder, or a calculation that includes explicit crystal-field level shifts and still fails to produce the observed splitting.

read the original abstract

Spin fluctuations have been generally believed as the pairing glue of high-$T_c$ superconductivity. Recent inelastic neutron scattering (INS) studies have revealed a weak flat spin-fluctuation signal around 45 meV in the bilayer nickelate La$_3$Ni$_2$O$_{7-\delta}$, suggesting strong interlayer and weak intralayer magnetic couplings ($SJ_{\perp}\approx$ 60 meV, $SJ_{\parallel}\leq$ 3.5 meV) in contrast to cuprate and pnictide superconductors. Here, we report further INS studies on the Pr and Nd doped La$_3$Ni$_2$O$_{7-\delta}$ powder samples at ambient pressure. Besides the crystalline electric field excitations at low energies, we have found that the 45 meV flat mode splits into two modes in doped compounds, along with another weak mode at about 60 meV, where the spin fluctuations in La$_2$NdNi$_2$O$_{7-\delta}$ are stronger than La$_3$Ni$_2$O$_{7-\delta}$ and La$_2$PrNi$_2$O$_{7-\delta}$. Our results are consistent with an enhanced interlayer coupling $SJ_{\perp}$ within the stripe-type Heisenberg model framework, where the estimated $SJ_{\perp}$ value is in the range of about 69 to 73 meV for the rare-earth doped bilayer nickelates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

New INS spectra on Pr/Nd-doped bilayer nickelates show mode splitting and a 60 meV feature, but the jump in SJ_perp to 69-73 meV is not yet isolated from possible doping effects on crystal fields or disorder.

read the letter

The main takeaway is new powder INS data on the doped compounds. The 45 meV flat mode splits and a weak feature appears near 60 meV, with the Nd-doped sample showing stronger intensity than the Pr-doped or undoped cases. These peak positions are fresh observations relative to the earlier La3Ni2O7 work the abstract cites. The authors place them inside the stripe Heisenberg model and read out an increase in interlayer coupling SJ_perp from roughly 60 meV to the 69-73 meV range. That supplies a concrete number the subfield can test against other calculations or future single-crystal measurements. The low-energy CEF excitations are noted separately, which keeps the spin-fluctuation discussion focused. The experimental extension to doped powders at ambient pressure is the clear incremental advance here. The soft spot is the modeling step. The numerical claim for SJ_perp comes from matching the new energies to the model, yet the summary gives no raw spectra, fit residuals, error bars, or explicit checks that hold SJ_perp fixed at the undoped value while varying crystal-field parameters or adding random-exchange disorder. Powder averaging can hide or mimic splitting if those other terms shift, so the isolation of the interlayer term is not yet demonstrated. If the full manuscript contains those comparisons, the concern shrinks; if not, the range 69-73 meV remains provisional. This paper is for people already working on bilayer nickelate magnetism and its possible link to superconductivity. A reader who needs updated spectral features to benchmark calculations will get direct value from the reported mode positions. It deserves a serious referee because the data are new and the materials are timely, even though the modeling section will probably need tightening and additional figures before acceptance.

Referee Report

2 major / 2 minor

Summary. The manuscript reports inelastic neutron scattering measurements on powder samples of Pr- and Nd-doped La3Ni2O7-δ. In addition to low-energy crystal-electric-field excitations, the authors observe that the ~45 meV flat spin-fluctuation mode splits into two branches and that a new weak feature appears near 60 meV. They interpret these changes as evidence for an increase in the interlayer exchange parameter SJ⊥ from ~60 meV (undoped) to 69–73 meV within a stripe-type Heisenberg model, while intralayer couplings remain weak.

Significance. If the attribution of the mode splitting and 60 meV feature exclusively to enhanced SJ⊥ is confirmed, the work would demonstrate that rare-earth doping can selectively strengthen interlayer magnetic coupling in bilayer nickelates. This would supply a concrete experimental handle on the spin-fluctuation spectrum thought to be relevant to superconductivity in this family, complementing the earlier La3Ni2O7-δ results.

major comments (2)

[Results and discussion of INS spectra on doped samples] The numerical claim SJ⊥ ≈ 69–73 meV is obtained by matching the observed mode positions to the stripe Heisenberg model, yet the manuscript provides neither the raw powder-averaged spectra, the explicit fitting procedure, error bars on the extracted energies, nor a quantitative comparison of model predictions versus data. Without these steps the quoted range cannot be independently verified.
[Interpretation within the stripe Heisenberg model] The interpretation that the splitting of the 45 meV mode and the new ~60 meV feature arise solely from raising SJ⊥ assumes that doping affects only the interlayer exchange. No model calculations are shown that vary crystal-field parameters, introduce random-exchange disorder from rare-earth substitution, or alter intralayer J∥ while keeping SJ⊥ fixed at the undoped value; such calculations are required to demonstrate that alternative mechanisms cannot reproduce the observed spectral changes in powder data.

minor comments (2)

[Abstract and results] The abstract states that spin fluctuations in La2NdNi2O7-δ are stronger than in the Pr-doped and undoped compounds, but the manuscript does not define the quantitative measure of “strength” (integrated intensity, peak height, etc.) or show the corresponding comparison.
[Model description] Notation for the exchange parameters is introduced as SJ⊥ and SJ∥ without an explicit definition of the spin magnitude S or the convention used for the Heisenberg Hamiltonian.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will revise the manuscript to incorporate the requested details and calculations.

read point-by-point responses

Referee: [Results and discussion of INS spectra on doped samples] The numerical claim SJ⊥ ≈ 69–73 meV is obtained by matching the observed mode positions to the stripe Heisenberg model, yet the manuscript provides neither the raw powder-averaged spectra, the explicit fitting procedure, error bars on the extracted energies, nor a quantitative comparison of model predictions versus data. Without these steps the quoted range cannot be independently verified.

Authors: We agree that the current manuscript lacks sufficient detail for independent verification of the SJ⊥ values. In the revised version we will add the raw powder-averaged INS spectra for both Pr- and Nd-doped samples, describe the explicit fitting procedure used to extract the mode positions (including background subtraction and resolution convolution), report error bars on the fitted energies, and include a quantitative overlay of the stripe Heisenberg model predictions versus the data at the relevant energy transfers. These additions will allow direct assessment of the 69–73 meV range. revision: yes
Referee: [Interpretation within the stripe Heisenberg model] The interpretation that the splitting of the 45 meV mode and the new ~60 meV feature arise solely from raising SJ⊥ assumes that doping affects only the interlayer exchange. No model calculations are shown that vary crystal-field parameters, introduce random-exchange disorder from rare-earth substitution, or alter intralayer J∥ while keeping SJ⊥ fixed at the undoped value; such calculations are required to demonstrate that alternative mechanisms cannot reproduce the observed spectral changes in powder data.

Authors: We acknowledge that the manuscript does not presently contain explicit calculations exploring alternative mechanisms. In the revision we will add model spectra within the stripe Heisenberg framework that (i) vary crystal-field parameters around the values used for the undoped compound, (ii) incorporate random-exchange disorder consistent with rare-earth substitution, and (iii) change intralayer J∥ while holding SJ⊥ fixed at the undoped value of ~60 meV. Direct comparison of these spectra to the measured powder data will be shown to demonstrate that the observed splitting and 60 meV feature are most consistently reproduced by an increase in SJ⊥ alone. revision: yes

Circularity Check

0 steps flagged

No circularity: SJ⊥ estimated by fitting stripe Heisenberg model to new INS peak positions in doped samples

full rationale

The paper reports new experimental observations (splitting of the 45 meV mode and a ~60 meV feature) in Pr/Nd-doped La3Ni2O7-δ powders. It then states that these features are consistent with raising the interlayer coupling parameter SJ⊥ from ~60 meV (undoped) to 69-73 meV inside an existing stripe-type Heisenberg model. This is a conventional parameter estimation step that takes fresh spectral data as input and adjusts one model constant to reproduce the observed energies. No equation in the provided text reduces to its own input by construction, no prediction is generated from a fitted subset and then re-used as evidence, and no load-bearing self-citation chain is invoked to justify the model form or the uniqueness of the interlayer term. The derivation therefore remains self-contained against external benchmarks (new INS data plus a pre-existing spin model).

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on assigning the observed neutron modes to spin fluctuations within a stripe-type Heisenberg model whose interlayer exchange is then adjusted to match the data; no new particles or forces are introduced.

free parameters (1)

SJ_perp = 69-73 meV
Interlayer exchange strength adjusted to reproduce the positions of the split modes and the 60 meV feature; reported range 69–73 meV.

axioms (1)

domain assumption Spin fluctuations in these nickelates are described by the stripe-type Heisenberg model with dominant interlayer coupling.
Invoked to convert observed mode energies into the quoted SJ⊥ values.

pith-pipeline@v0.9.0 · 5593 in / 1381 out tokens · 25186 ms · 2026-05-16T12:21:14.028265+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Based on an effective Heisenberg model by only considering the nearest-neighbor exchange couplings on the stripe-type antiferromagnetic orders, we conclude that the interlayer coupling SJ⊥ is enhanced to about 69 meV and 73 meV for Pr and Nd doped samples, respectively.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the spin excitations in La2NdNi2O7−δ are stronger than La3Ni2O7−δ and La2PrNi2O7−δ

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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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