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High-resolution Measurements of Thermal Conductivity Matrix and Search for Thermal Hall Effect in La$_2$CuO$_4$

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Pith's one-line read This paper reports that high-resolution field-sweep measurements resolve no thermal Hall signal in La2CuO4 between 2 and 20 K in fields up to 10 T, setting an upper bound 10 to 30 times smaller than previously reported signals.

desk verdict A careful null result that challenges a high-profile thermal Hall claim, but the unquantified hysteresis residual in the in-out subtraction keeps the bound from being fully closed. read the letter →

arxiv 2507.21403 v1 pith:GTUKMPXB submitted 2025-07-29 cond-mat.str-el

Jiayi Hu , Haozhi Xu , Juntao Yao , Genda Gu , Qiang Li , N. P. Ong This is my paper · ORCID
classification cond-mat.str-el
keywords thermalHalleffectconductivityLa2CuO4cupratesfield-sweepprotocolchiralphononshysteresismetamagnetictransition
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 attempts to establish that the thermal Hall effect in the parent cuprate La2CuO4, previously reported to be large and attributed to chiral phonons, is not intrinsic: using a high-resolution field-sweep protocol, the authors resolve no transverse thermal gradient in the range 2 to 20 K and 0 to 10 T. The claimed conservative upper bound, |kappa_xy/T| < 1e-4 $Wm^{-1}$$K^{-2}$, is 10 to 30 times smaller than the signal reported by Grissonnanche et al. (2020). The longitudinal conductivity kappa_xx/T agrees with previous studies in magnitude and temperature dependence, including a weak hysteresis tied to the metamagnetic transition of canted spins. If correct, the result challenges the chiral-phonon interpretation of the cuprate thermal Hall effect and points to sample differences or extrinsic artifacts as the source of the earlier signal.

What carries the argument

The field-swept (FS) protocol is the load-bearing experimental mechanism: instead of cooling in a fixed field, H is stepped in increments of 0.1 to 1 T with T rigorously regulated, waiting 3 to 8 minutes after each step so that magnetocaloric and eddy-current temperature spikes (1 to 6 mK, relaxing in 1 to 10 ms) die out before data are acquired. The in-out antisymmetrization, deltaTxy(H) = 1/2 (DeltaTxy(H) - DeltaT*xy(-H)), cancels the longitudinal contamination alpha deltaTxx under the assumption deltaTxx(H) = deltaT*xx(-H). The authors also perform in-situ thermometer calibration under field, with heat current off, to correct for the magnetoresistance of the thermometers.

What would settle it

A direct measurement of the hysteresis-loop asymmetry: if the difference between up-sweep and down-sweep branches of deltaTxx, evaluated at the same |H|, exceeds the claimed transverse resolution (about 30 microK at 2.3 K), then the in-out antisymmetrization is not exactly cancelling longitudinal contamination, and the null result could be questioned. Alternatively, repeating the measurement on the same crystals at H = 15 T and finding no signal would directly contradict the 15-T report, while finding a signal would reveal a steep field threshold.

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Extended reading notes

Core claim

The central claim is a null result with a quantified bound: in as-grown La2CuO4 crystals with Neel temperature near 255 K, neither field-sweep nor temperature-sweep protocols resolve a thermal Hall conductivity, and the conservative upper bound on |kappa_xy/T| is 1e-4 $Wm^{-1}$$K^{-2}$ across 2 to 20 K in H up to 10 T. The authors emphasize that their resolution is 10 to 30 times smaller than the magnitude reported in Ref. [8], where kappa_xy/T was approximately 3e-3 W/$mK^{2}$ near 7 K in 15 T, and that their resolution is independent of T from 2 to 10 K, incompatible with the exponential decay claimed previously. They attribute the high resolution to the field-sweep protocol, in which the bath temperature is actively regulated, post-step relaxation spikes (magnetocaloric and eddy-current) are waited out, and the in-out antisymmetrization cancels longitudinal contamination. The paper also documents an unexplained weak anomaly near 7 K in kappa_xx/T and a field-induced up-turn in kappa_xx at low T, while noting that the absence of a resolvable Hall signal is intrinsic and not an experimental artifact.

Load-bearing premise

The in-out subtraction assumes the longitudinal contamination in the transverse channel is exactly antisymmetric under field reversal; the paper's own data show weak hysteresis in the longitudinal channel, and if that hysteresis is not perfectly antisymmetric, the subtraction could cancel a real signal or create a spurious one.

Editorial extensions

If this is right

  • The previously reported large, exponentially decaying thermal Hall signal in undoped La2CuO4 is not reproduced at fields up to 10 T, so chiral-phonon explanations based on that signal lose their main empirical support for this material.
  • Sample stoichiometry becomes a plausible controlling variable: if the effect is extrinsic, its magnitude should vary with preparation, and the paper names deoxygenation as one possible difference.
  • The 10 to 30 times tighter upper bound sets a new benchmark that future thermal Hall experiments on cuprate parent compounds must beat or explain.
  • The documented hysteretic contamination in the longitudinal channel implies that naive antisymmetrization of transverse gradients can produce spurious Hall-like signals, so the field-sweep protocol with careful relaxation control should become standard for small-signal searches.
  • The linear suppression of kappa_xx with H and the low-T up-turn above 7.5 T are new field-dependence features that invite theoretical explanation.

Reading between the lines

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

  • If the null result holds generally, the reported thermal Hall signals in other cuprate parent and pseudogap materials may also contain a large extrinsic component, such as resonant skew scattering by defects, rather than an intrinsic chiral-phonon response.
  • The hysteresis asymmetry the authors note could be tested directly: measuring the up- and down-sweep branches of deltaTxx at fixed T and checking whether the difference is antisymmetric under H -> -H would quantify the residual systematic error in any in-out subtraction.
  • The unexplained 7-K anomaly in kappa_xx/T may be a signature of a low-energy magnetic or structural mode; a targeted specific-heat or neutron-scattering measurement near 7 K could test whether it is intrinsic.
  • A direct extension would be to repeat the measurement at 15 T and below 2 K: if a signal still fails to appear, the upper bound would directly confront the conditions of the original report.
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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 / 6 minor

Summary. The manuscript reports high-resolution measurements of the longitudinal (κxx) and transverse (κxy) thermal conductivity in the parent cuprate La2CuO4, using both field-sweep (FS) and temperature-sweep (TS) protocols, for temperatures 2–20 K and magnetic fields up to 10 T. The authors find no resolvable thermal Hall signal and set a conservative upper bound |κxy/T| < 1×10^-4 W m^-1 K^-2, which is 10–30 times smaller than the signal reported by Grissonnanche et al. (2020) in the same material. The longitudinal conductivity κxx/T agrees well with previous studies, and weak hysteretic features near ±(4–7) T are observed and attributed to the metamagnetic transition of the weakly canted antiferromagnetic order.

Significance. If correct, this null result is significant for the ongoing debate on the thermal Hall effect in cuprate parent compounds and the chiral-phonon scenario. The paper's strengths include a detailed description of the FS protocol, explicit treatment of relaxation spikes, in-situ thermometer calibration with magnetoresistance correction, and the use of in-out symmetrization. The authors also provide a conservative upper bound and acknowledge the hazard of naive antisymmetrization. However, the central claim is not yet fully supported because key systematic uncertainties—specifically the hysteresis residual in the in-out subtraction and the statistical basis of the upper bound—are not quantified.

major comments (3)
  1. [IIA, III C2, Fig. 4] The in-out subtraction δTxy(H) = ½[ΔTxy(H) − ΔTxy*(−H)] removes longitudinal contamination αδTxx only if δTxx is exactly symmetric under field reversal. The hysteresis in ΔTxx presented in Fig. 4(a) violates this condition in the field interval ±(4–7) T, leaving a residual ½α[δTxx_up(H) − δTxx_down(−H)] in the extracted signal. The paper neither measures α nor translates the observed hysteresis into an upper bound on this residual in κxy/T units. Given the stated conversion 30 µK ↔ 4×10^-5 W m^-1 K^-2, a residual of only ~75 µK in the transverse channel would saturate the claimed bound. The authors' own remark that 'a naive antisymmetrization in ΔTxy could result in a misleading thermal Hall signal' (Sec. III C2) shows that this is a known hazard, yet no quantitative residual-subtraction analysis is provided. The null result is therefore not yet demonstrated to be robust against this systematic.
  2. [III C3, Fig. 3] The conservative upper bound is justified by the statement that averaging the curves 'by eye' suggests a weak signal of about 0.1×10^-3 W m^-1 K^-2, but that this conclusion is 'seen to be invalid' when the curves are displaced (Sec. III C3). This is not a quantitative analysis. For a null result that claims to improve on previous bounds by an order of magnitude, the bound should be derived from a statistical analysis (e.g., mean and standard deviation of κxy/T over the measured field and temperature range, and a test for a field-odd component). Such an analysis would also establish whether the apparent positive offsets at 5.5 and 10.6 K are statistically significant.
  3. [IIB, Fig. 2b] The temperature-sweep data are offered as confirmation of the FS null result, but the TS protocol does not apply the in-out cancellation and is therefore subject to the same longitudinal contamination and hysteresis effects, with no correction. Because the TS data are also substantially noisier (as acknowledged in Sec. IIIA), they cannot provide independent confirmation. The paper should either apply an equivalent quantitative cancellation analysis to the TS data, or explicitly exclude them from the upper-bound claim.
minor comments (6)
  1. [IIA, IIIA] Sec. IIA states a resolution of ±100 µK at 2.3 K, while Sec. IIIA quotes δTxy ≈ 30 µK; please reconcile these numbers and state the resolution consistently.
  2. [IIIA] The statement that the resolution bounds for ΔTxy are independent of T from 2 to 10 K appears to conflict with the later statement that the He-3 insert stability degrades at higher temperatures; please clarify the temperature dependence of the resolution.
  3. [IIIB] There are several typographical errors, e.g., 'nomincal' for 'nominal' in Sec. IIIB and 'thermal hall' for 'thermal Hall' in the abstract; these should be corrected.
  4. [IIIC2, Fig. 4] The caption of Fig. 4(a) is confusing: it says solid circles are the down sweep from 10 T to −10 T and hollow ones the up sweep, but the text in Sec. III C2 says 'Open and solid red circles correspond to up-field and down-field scans, respectively.' Please make the caption and text consistent.
  5. [Abstract, IIIA, IV] The abstract and Sec. IV quote the upper bound as 1×10^-4 W m^-1 K^-2, while Sec. IIIA says the resolution threshold is 10^-5 to 10^-4 W m^-1 K^-2; please state a single, precise number with the conditions under which it applies.
  6. [Data availability] No raw data or data repository is mentioned; given the importance of the null result, the authors should make the raw data for Figs. 2–4 available.

Circularity Check

0 steps flagged · score 1.0 of 10

Experimental null result is self-contained; no circular derivation beyond minor methodological self-citations.

full rationale

The paper's central claim is an experimental null result: an upper bound |κxy/T| < 1e-4 Wm^-1K^-2 (Abstract; Sec. IIIA; Sec. IIIC3). This bound is extracted directly from measured transverse temperature gradients ΔTxy in field sweeps, with no fitted parameter fed back into the bound. The in-out antisymmetrization δTxy = 1/2[ΔTxy(H) − ΔTxy*(−H)] assumes δTxx(H) = δTxx*(−H); the paper itself flags hysteresis in the longitudinal channel and warns that 'a naive antisymmetrization in ΔTxy could result in misleading thermal Hall signals' (Sec. IIIC2, Fig. 4). That is an acknowledged systematic limitation, not a circular step: the null value is not defined to equal an input, and the result could in principle be wrong if the symmetry assumption fails. The protocols adopted from Refs. [13,14] (Princeton theses from the same laboratory) are methodological borrowings, not the source of the claimed physics; the result is benchmarked against the independent published value in Ref. [8] (Grissonnanche et al.), and the paper's κxx/T agrees with prior independent measurements. The exponential fit in Fig. S6 is a side analysis of κxx/T and does not enter the thermal-Hall upper bound. No equation in the paper reduces to its own input, and no fitted parameter is relabeled as a prediction. The only self-citation load is minor and methodological (Refs. 13,14), justifying at most a score of 1, not circularity.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new theoretical entities or free parameters central to the thermal Hall bound. The only free parameter fit appears in a supplementary analysis of kappa_xx/T. The main assumptions are standard experimental ones about the validity of temperature measurement and the symmetry of field-sweep contamination.

free parameters (1)
  • Exponential fit parameters for kappa_xx/T = T0 = 16.5 K; A and C not reported
    In the supplement (Fig. S6), the authors fit kappa_xx/T to A exp(-T/T0)+C with T0=16.5 K. This fit is used to argue that the thermal Hall signal does not decay exponentially with temperature, but it is not central to the main upper bound.
assumptions (3)
  • domain assumption The sample is in the diffusive heat transport regime, so Fourier's law applies and thermometers measure a well-defined local temperature gradient.
    Section II describes measuring temperature gradients across the sample and deriving thermal conductivities from them, assuming linear response.
  • domain assumption The longitudinal contamination deltaTxx is exactly antisymmetric under field reversal: deltaTxx(H) = deltaT*xx(-H).
    Section IIA: the in-out subtraction formula deltaTxy(H) = 1/2 (DeltaTxy(H) - DeltaT*xy(-H)) relies on this antisymmetry to cancel the longitudinal contribution.
  • domain assumption The thermometers' magnetoresistance can be corrected by interpolating between their resistances at the higher and lower bounds of the measured temperature range.
    Section IIA describes this correction procedure, which assumes a smooth and reproducible magnetoresistance behavior that is captured by calibration sweeps with JQ off.

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Pith. "Pith review of High-resolution Measurements of Thermal Conductivity Matrix and Search for Thermal Hall Effect in La$_2$CuO$_4$." pith.science (2026). https://pith.science/paper/GTUKMPXB

@misc{pith2026250721403,
  author       = {Pith},
  title        = {Pith review of: High-resolution Measurements of Thermal Conductivity Matrix and Search for Thermal Hall Effect in La$_2$CuO$_4$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GTUKMPXB}},
  note         = {Machine review of arXiv:2507.21403}
}
abstract

We investigated the longitudinal thermal conductivity $\kappa_{xx}$ and thermal hall conductivity $\kappa_{xy}$ in La$_2$CuO$_4$ at temperatures $T$ between 2 and 20 K in magnetic fields $H$ up to 10 T. Within the temperature and field intervals studied, we do not resolve any thermal Hall signal with a conservative upper bound of $|\kappa_{xy}/T| <1\times10^{-4}$ ${\rm Wm^{-1}K^{-2}}$. The longitudinal thermal conductivity $\kappa_{xx}/T$ agrees well with previous studies, in both magnitude and $T$ dependence. In both channels, we performed measurements using the field-sweep protocol. To achieve high resolution, we carefully took into account relaxation effects after each step-increase in $H$. At low $T$, we find a linear decrease in $\kappa/T$ vs. $H$, as well as weak hysteresis near the meta-magnetic transition of the spin degrees.

Figures

Figures reproduced from arXiv: 2507.21403 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
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Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Reference graph

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