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arxiv: 2503.13600 · v2 · submitted 2025-03-17 · ❄️ cond-mat.supr-con

Critical spin fluctuations across the superconducting dome in La_(2-x)Sr_(x)CuO₄

Jacopo Radaelli , Oliver J. Lipscombe , Mengze Zhu , J. Ross Stewart , Aavishkar A. Patel , Subir Sachdev , Stephen M. Hayden This is my paper

Pith reviewed 2026-05-22 23:23 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords cupratesstrange metalspin fluctuationsneutron scatteringquantum phase transitionGriffiths phasespin density waveLa2-xSrxCuO4
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The pith

Critical spin fluctuations from a disordered spin density wave quantum phase transition explain the strange metal phase across the cuprate superconducting dome.

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

The paper presents neutron scattering data showing strongly temperature-dependent critical spin fluctuations with dynamical scaling in La2-xSrxCuO4 over a wide doping range that includes both underdoped and overdoped regimes. These fluctuations persist alongside the strange metal regime where electrical resistivity rises linearly with temperature. The data are shown to be consistent with the predictions of a spin density wave quantum phase transition occurring in a metal whose tuning parameter varies spatially due to disorder. Numerical computations of spin density waves in such a disordered metal produce an extended Griffiths phase whose scaling properties match the observed fluctuations and transport anomalies. A reader would care because the account ties the absence of conventional quasiparticles in the strange metal directly to low-energy spin excitations generated by the disordered critical point.

Core claim

Our neutron scattering observations and the strange metal behaviour are consistent with a spin density wave quantum phase transition in a metal with spatial disorder in the tuning parameter. Numerical computations using a theory of spin density waves in a disordered metal yield an extended Griffiths phase with scaling properties in agreement with experimental observations. Thus low-energy spin excitations and spatial disorder are central to the strange metal behaviour.

What carries the argument

The extended Griffiths phase generated by a spin density wave quantum phase transition in a metal with spatial disorder in the tuning parameter, which produces critical spin fluctuations whose scaling matches both the neutron scattering intensity and the linear resistivity.

If this is right

  • Strange-metal linear resistivity arises from scattering off the critical spin fluctuations of the disordered quantum critical point.
  • Dynamical scaling of the spin excitations holds uniformly across the entire superconducting dome.
  • Spatial disorder in the tuning parameter produces an extended region of critical behavior rather than an isolated quantum critical point.
  • Low-energy spin excitations remain central to transport even where superconductivity is fully suppressed by overdoping.

Where Pith is reading between the lines

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

  • Similar scaling signatures could appear in other families of strange metals once spatial disorder is accounted for in their phase diagrams.
  • Intentional introduction of controlled disorder into cuprate samples would provide a direct test of whether the width of the Griffiths phase can be tuned.
  • The same framework may connect the observed spin fluctuations to the suppression of quasiparticle coherence seen in other spectroscopies.
  • Extensions to finite magnetic fields could reveal how the Griffiths phase interacts with the superconducting dome.

Load-bearing premise

The measured neutron scattering intensity and its temperature dependence are generated by critical fluctuations of an underlying spin density wave quantum phase transition rather than by stripe order, phonons, or other unrelated mechanisms.

What would settle it

A neutron scattering measurement or numerical computation in which the temperature dependence of the spin fluctuation intensity fails to follow the predicted Griffiths-phase scaling for any choice of disorder parameters consistent with the material would falsify the central claim.

Figures

Figures reproduced from arXiv: 2503.13600 by Aavishkar A. Patel, Jacopo Radaelli, J. Ross Stewart, Mengze Zhu, Oliver J. Lipscombe, Stephen M. Hayden, Subir Sachdev.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: C in κ for ω > T is possibly also related to the crossover between these ‘foot’ and ‘fan’ regimes. In summary, we have observed critical spin fluctua￾tions with ω/T-scaling in an overdoped cuprate super￾conductor. When combined with earlier measurements [11] this shows that there is an extended region of crit￾ical spin-fluctuations in La2−xSrxCuO4. We have com￾pared our observations with numerical studies … view at source ↗
read the original abstract

Overdoped cuprate superconductors are strange metals above their superconducting transition temperature. In such materials, the electrical resistivity has a strong linear dependence on temperature ($T$) and electrical current is not carried by electron quasiparticles as in conventional metals. Here we demonstrate that the strange metal behaviour co-exists with strongly temperature-dependent critical spin fluctuations showing dynamical scaling across the cuprate phase diagram. Our neutron scattering observations and the strange metal behaviour are consistent with a spin density wave quantum phase transition in a metal with spatial disorder in the tuning parameter. Numerical computations using a theory of spin density waves in a disordered metal yield an extended `Griffiths phase' with scaling properties in agreement with experimental observations. Thus we establish that low-energy spin excitations and spatial disorder are central to the strange metal behaviour.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript presents neutron scattering data on spin fluctuations in La_{2-x}Sr_xCuO_4 across doping levels spanning the superconducting dome. It reports strongly temperature-dependent critical fluctuations exhibiting dynamical scaling that coexist with strange-metal transport (linear resistivity). The central claim is that these observations are consistent with a spin-density-wave quantum phase transition in a metal with spatial disorder in the tuning parameter; numerical solutions of the disordered SDW theory produce an extended Griffiths phase whose scaling properties match the experimental temperature and doping dependence.

Significance. If the quantitative mapping between neutron intensity, dynamical scaling, and the computed Griffiths-phase response holds without parameter tuning, the result would link the strange-metal regime directly to critical spin fluctuations from a disordered SDW QPT, supplying a concrete mechanism that accounts for both the neutron data and the absence of quasiparticles. The work supplies machine-checked numerical results for the disordered theory and falsifiable scaling predictions, which are strengths.

major comments (3)
  1. [§3] §3 and associated figures: the reported agreement between measured dynamical susceptibility and the Griffiths-phase scaling is presented without tabulated scaling exponents, error bars on the extracted exponents, or explicit criteria for data exclusion/background subtraction; without these the support for the central consistency claim cannot be verified.
  2. [§4] §4 (numerical computations): the spatial disorder distribution in the local tuning parameter is stated to be the sole free parameter, yet the text does not demonstrate that its width is independently constrained by transport or structural data at each doping; if the width must be adjusted separately to recover the reported T-dependence, the agreement is not a robust test of the mechanism.
  3. [Abstract, §2] Abstract and §2: the assignment of the observed neutron intensity to critical SDW fluctuations (rather than stripe order or phonons) rests on the assumption that the measured response is produced by the disordered QPT; no quantitative test is provided to rule out alternative origins.
minor comments (2)
  1. Notation for the dynamical susceptibility and the disorder distribution should be defined once in the text and used consistently in all figures.
  2. Figure captions should state the precise doping values, temperature range, and energy transfers used for each panel.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment of its potential significance. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [§3] §3 and associated figures: the reported agreement between measured dynamical susceptibility and the Griffiths-phase scaling is presented without tabulated scaling exponents, error bars on the extracted exponents, or explicit criteria for data exclusion/background subtraction; without these the support for the central consistency claim cannot be verified.

    Authors: We agree that additional quantitative details would improve verifiability. In the revised manuscript we will include a table of extracted scaling exponents together with their uncertainties for each doping level studied. We will also add explicit statements of the background-subtraction procedure and the criteria used to exclude data points in both the main text and the methods section. revision: yes

  2. Referee: [§4] §4 (numerical computations): the spatial disorder distribution in the local tuning parameter is stated to be the sole free parameter, yet the text does not demonstrate that its width is independently constrained by transport or structural data at each doping; if the width must be adjusted separately to recover the reported T-dependence, the agreement is not a robust test of the mechanism.

    Authors: The width is the single adjustable parameter and is fixed once by matching the overall intensity scale at a single reference temperature per doping; the theory then predicts the full temperature dependence without further adjustment. This predicted T-dependence matches the data across the dome. We will revise §4 to state this fitting procedure more clearly and to note the correlation of the chosen widths with doping, which is consistent with known structural inhomogeneity, although an independent transport-based constraint is not performed in the present work. revision: partial

  3. Referee: [Abstract, §2] Abstract and §2: the assignment of the observed neutron intensity to critical SDW fluctuations (rather than stripe order or phonons) rests on the assumption that the measured response is produced by the disordered QPT; no quantitative test is provided to rule out alternative origins.

    Authors: The identification is based on the momentum-space location at the expected SDW wavevector and on the strong temperature dependence that is incompatible with temperature-independent phonon scattering at these energies. Static stripe order is absent in the overdoped regime examined. We will expand §2 with a brief quantitative estimate showing that the observed integrated intensity and its temperature evolution exceed typical phonon contributions in LSCO by more than an order of magnitude. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The paper reports neutron scattering data on spin fluctuations across the doping dome and states that numerical solutions of a disordered SDW theory produce a Griffiths phase whose scaling matches the observations. No equations, parameter-fitting steps, or self-citation chains are exhibited in the provided text that reduce the reported agreement to a tautology or to inputs already containing the target scaling. The central claim rests on an external numerical computation whose disorder distribution is presented as part of the model rather than tuned post hoc to the neutron intensities; absent any quoted reduction showing that the scaling is forced by construction, the derivation does not meet the criteria for circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the spin density wave theory in a disordered metal to the cuprate system and on the interpretation of the neutron scattering signal as arising from critical fluctuations of that transition.

free parameters (1)
  • spatial disorder distribution in tuning parameter
    The model requires a distribution of local tuning parameters due to spatial disorder; its width or form is a free parameter needed to produce the extended Griffiths phase.
axioms (1)
  • domain assumption The low-energy spin excitations in overdoped LSCO are described by a spin density wave quantum phase transition in a metal with spatial disorder
    This theoretical framework is invoked to interpret the neutron scattering data and to generate the numerical scaling results.

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Forward citations

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