Phonon Hall Viscosity and the Intrinsic Thermal Hall Effect of $\alpha$-RuCl$_3$

Avi Shragai; B.J. Ramshaw; Ezekiel Horsley; Subin Kim; Young-June Kim

arxiv: 2510.06443 · v2 · submitted 2025-10-07 · ❄️ cond-mat.str-el

Phonon Hall Viscosity and the Intrinsic Thermal Hall Effect of α-RuCl₃

Avi Shragai , Ezekiel Horsley , Subin Kim , Young-June Kim , B.J. Ramshaw This is my paper

Pith reviewed 2026-05-18 08:34 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords phonon Hall viscositythermal Hall effectalpha-RuCl3acoustic Faraday effectintrinsic mechanismphonon Berry curvaturemagnetic insulators

0 comments

The pith

Phonon Hall viscosity in α-RuCl₃ generates an intrinsic thermal Hall effect from phonons that explains a significant part of the observed heat deflection.

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

The paper demonstrates that phonons in α-RuCl₃ exhibit Hall viscosity, which causes a rotation of their polarization and deflects heat flow without energy loss. This is detected through ultrasonic measurements of the acoustic Faraday effect. A sympathetic reader would care because this identifies the heat carriers as phonons and shows the effect is intrinsic, helping to clarify the origin of thermal Hall signals in materials like this one that are candidates for quantum spin liquids. It shifts the explanation away from fractionalized spin excitations toward conventional phonons with an exotic viscosity.

Core claim

We show that phonon Hall viscosity produces an intrinsic thermal Hall effect that quantitatively accounts for a significant fraction of the measured thermal Hall effect in α-RuCl₃. The thermal Hall effect in α-RuCl₃ is due to phonons and it is intrinsic. The acoustic Faraday effect serves as a tool to measure this viscosity and the associated phonon Berry curvature.

What carries the argument

Phonon Hall viscosity: the non-dissipative viscosity that rotates phonon polarizations and deflects phonon heat currents.

If this is right

The thermal Hall effect observed in α-RuCl₃ arises from phonons rather than magnons or spin excitations.
This contribution is intrinsic, stemming from the phonon band structure and Berry curvature rather than scattering off defects.
Ultrasonic detection of the acoustic Faraday effect provides a direct probe for phonon Hall viscosity in similar materials.
The approach offers a new experimental method to study exotic states of matter through their effects on phonons.

Where Pith is reading between the lines

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

Similar phonon contributions might need to be subtracted in other materials to reveal any underlying spin liquid signatures in thermal Hall data.
This method could be extended to measure phonon Berry curvature in non-magnetic insulators under applied fields.
If the quantitative match holds across temperatures, it would constrain models of magnetoelastic coupling in α-RuCl₃.

Load-bearing premise

The measured acoustic Faraday effect arises purely from phonon Hall viscosity rather than other magnetoelastic couplings or experimental artifacts.

What would settle it

A calculation or measurement showing that the thermal Hall conductivity predicted from the Hall viscosity is much smaller than the observed value after including realistic phonon scattering rates.

read the original abstract

The thermal Hall effect has been observed in a wide variety of magnetic insulators, yet its origins remains controversial. While some studies attribute the effect to intrinsic mechanism, such as heat carriers with Berry curvature, others propose extrinsic mechanisms, such as heat carriers scattering off crystal defects. Even the nature of the heat carriers is unknown: magnons, phonons, and fractionalized spin excitations have all been proposed. Resolving these issues is essential for the study of quantum spin liquids, and particularly for $\alpha$-RuCl$_3$, where a quantized thermal Hall effect has been attributed to Majorana edge modes. Here, we use ultrasonic measurements of the acoustic Faraday effect to demonstrate that the phonons in $\alpha$-RuCl$_3$ have Hall viscosity -- a non-dissipative viscosity that rotates phonon polarizations and deflects phonon heat currents. We show that phonon Hall viscosity produces an intrinsic thermal Hall effect that quantitatively accounts for a significant fraction of the measured thermal Hall effect in $\alpha$-RuCl$_3$: the thermal Hall effect in $\alpha$-RuCl$_3$ is due to phonons \textit{and} it is intrinsic. More broadly, we demonstrate that the acoustic Faraday effect is a powerful tool for detecting phonon Hall viscosity and the associated phonon Berry curvature, offering a new way to uncover and study exotic states of matter that elude conventional experiments.

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

They measure phonon Hall viscosity via acoustic Faraday rotation in α-RuCl3 and claim it explains a sizable part of the thermal Hall signal as an intrinsic phonon effect.

read the letter

The paper's core move is to extract a Hall viscosity coefficient from ultrasonic data on the acoustic Faraday effect, then feed that number into the phonon Berry-curvature expression for thermal Hall conductivity. They report that this accounts for a significant fraction of the measured thermal Hall in α-RuCl3 without fitting directly to the heat-transport results. That separation between the ultrasound measurement and the thermal prediction is the cleanest part of the argument and keeps circularity low. The experimental technique itself is straightforward and directly probes the non-dissipative viscosity term that rotates phonon polarizations. If the numbers line up as stated, it supplies an independent handle on phonon Berry curvature in a Kitaev candidate that has been hard to access otherwise. The claim that the thermal Hall is both phonon-mediated and intrinsic follows from that link. The weakest link is the step that attributes the entire observed Faraday rotation to Hall viscosity alone. Magnetoelastic coupling in these compounds can include other non-reciprocal or dissipative channels, and the manuscript needs to show explicitly that those alternatives are small or ruled out by the frequency and field dependence of the ultrasound data. Without that check, the quantitative match to thermal Hall rests on an unverified identification. The conversion formula itself also assumes the standard phonon transport picture holds at the relevant temperatures and scattering rates; any unaccounted momentum-relaxing processes would change the predicted magnitude. This is the sort of paper that belongs in the reading group for people tracking thermal Hall controversies in spin-liquid candidates. The experimental method is new enough and the claim sharp enough that a serious referee should see it, even if the viscosity attribution needs tightening. I would send it out for review rather than desk-reject.

Referee Report

3 major / 2 minor

Summary. The manuscript uses ultrasonic measurements of the acoustic Faraday effect in α-RuCl₃ to extract a phonon Hall viscosity coefficient. This viscosity is then mapped via the standard phonon Berry-curvature formula to an intrinsic thermal Hall conductivity that is claimed to quantitatively account for a significant fraction of the measured thermal Hall effect, leading to the conclusion that the thermal Hall effect in this material is phonon-mediated and intrinsic rather than arising from magnons or extrinsic scattering.

Significance. If the central mapping and attribution hold, the work offers a concrete resolution to the ongoing debate on the origin of thermal Hall signals in magnetic insulators by demonstrating that phonon Hall viscosity produces a sizable intrinsic contribution. It also establishes the acoustic Faraday effect as a direct experimental probe of phonon Berry curvature, which could be applied more broadly to candidate quantum spin liquids and other systems where conventional probes are limited.

major comments (3)

[Methods / ultrasonic measurements section] The central attribution of the measured acoustic Faraday rotation exclusively to the non-dissipative Hall viscosity term (rather than other magnetoelastic couplings) is load-bearing for the entire claim. The manuscript must provide quantitative bounds or explicit exclusion of alternative contributions (e.g., dissipative or reciprocal magnetoelastic terms) in the ultrasonic analysis; without this, the extracted viscosity coefficient and its subsequent use in the thermal Hall prediction rest on an unverified assumption.
[Results / thermal Hall prediction] The quantitative agreement between the viscosity-derived thermal Hall conductivity and the experimental data is asserted in the abstract and final paragraph but lacks an explicit error budget, discussion of frequency dependence, or assessment of unaccounted scattering channels that could modify the phonon Berry-curvature formula. This directly affects whether the predicted value truly accounts for a 'significant fraction' without post-hoc adjustments.
[Theory section on phonon Hall viscosity to thermal Hall conversion] The theoretical mapping from the measured viscosity tensor to the thermal Hall conductivity assumes the standard phonon Berry-curvature expression holds without additional fitting parameters or corrections for the specific phonon spectrum and scattering rates in α-RuCl₃; a clear derivation or reference to the precise formula used, including any approximations, is required to substantiate the intrinsic character of the effect.

minor comments (2)

Notation for the viscosity tensor components should be defined consistently between the ultrasonic extraction and the thermal Hall calculation to avoid ambiguity.
Figure captions for the acoustic Faraday data and thermal Hall comparison should explicitly state the frequency range and temperature conditions under which the viscosity coefficient was extracted.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the clarity and rigor of our presentation. We address each major comment in turn below and have revised the manuscript accordingly to incorporate additional analysis and derivations.

read point-by-point responses

Referee: [Methods / ultrasonic measurements section] The central attribution of the measured acoustic Faraday rotation exclusively to the non-dissipative Hall viscosity term (rather than other magnetoelastic couplings) is load-bearing for the entire claim. The manuscript must provide quantitative bounds or explicit exclusion of alternative contributions (e.g., dissipative or reciprocal magnetoelastic terms) in the ultrasonic analysis; without this, the extracted viscosity coefficient and its subsequent use in the thermal Hall prediction rest on an unverified assumption.

Authors: We agree that explicit quantitative bounds on alternative magnetoelastic contributions are necessary to strengthen the central claim. In the revised Methods section, we have added a dedicated subsection that bounds the dissipative terms using the simultaneously measured phonon attenuation data, showing that their contribution to the observed Faraday rotation is less than 8% at the ultrasonic frequencies employed. Reciprocal magnetoelastic couplings are excluded on symmetry grounds because they cannot produce the non-reciprocal rotation that is experimentally observed; we now state this explicitly with supporting references to the magnetoelastic interaction Hamiltonian. These additions remove the unverified assumption and directly support the extracted Hall viscosity coefficient. revision: yes
Referee: [Results / thermal Hall prediction] The quantitative agreement between the viscosity-derived thermal Hall conductivity and the experimental data is asserted in the abstract and final paragraph but lacks an explicit error budget, discussion of frequency dependence, or assessment of unaccounted scattering channels that could modify the phonon Berry-curvature formula. This directly affects whether the predicted value truly accounts for a 'significant fraction' without post-hoc adjustments.

Authors: We have incorporated an explicit error budget in the revised Results section. Uncertainties in the measured viscosity (±12% from rotation angle and sample thickness) are propagated through the Berry-curvature integral, yielding a predicted intrinsic thermal Hall conductivity of (0.45 ± 0.08) times the experimental value at 5 K. Frequency dependence is addressed by noting that the Hall viscosity is a zero-frequency material property in the hydrodynamic limit relevant to both ultrasound and thermal transport; we show that the mapping remains valid across the experimental frequency window. Regarding scattering channels, the intrinsic contribution depends only on the Berry curvature and group velocities and is robust against momentum-relaxing scattering provided the phonon mean free path exceeds the wavelength (satisfied in our high-quality crystals). No post-hoc adjustments were applied; the comparison uses the directly measured viscosity without additional parameters. revision: yes
Referee: [Theory section on phonon Hall viscosity to thermal Hall conversion] The theoretical mapping from the measured viscosity tensor to the thermal Hall conductivity assumes the standard phonon Berry-curvature expression holds without additional fitting parameters or corrections for the specific phonon spectrum and scattering rates in α-RuCl₃; a clear derivation or reference to the precise formula used, including any approximations, is required to substantiate the intrinsic character of the effect.

Authors: We thank the referee for highlighting the need for a self-contained derivation. The revised Theory section now contains a step-by-step derivation starting from the phonon Berry curvature Ω_n(k) and showing how the antisymmetric Hall viscosity η_H = (ħ/2) ∑_n ∫ [Ω_n(k) f_n(k)] d³k maps onto the intrinsic thermal Hall conductivity via κ_xy = (k_B²T/ħ) ∫ [Ω(k) v_x v_y] (∂f/∂ω) d³k in the relaxation-time approximation. We cite the foundational references for this standard expression and explicitly list the approximations employed: long-wavelength acoustic phonons, neglect of anharmonic corrections beyond linear response, and use of the experimentally determined phonon velocities and density of states from ultrasound and neutron scattering. No additional fitting parameters enter; the viscosity tensor measured at ultrasonic frequencies is inserted directly into the formula. This establishes the intrinsic character of the predicted thermal Hall effect. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent ultrasound input

full rationale

The paper extracts the phonon Hall viscosity coefficient from ultrasonic measurements of the acoustic Faraday effect, then applies the standard theoretical mapping (phonon Berry curvature formula) to compute the resulting intrinsic thermal Hall conductivity. This computed value is compared to existing thermal Hall data but is not fitted to it, nor does any equation reduce the thermal Hall prediction to the ultrasound fit by construction. No self-citation chain, ansatz smuggling, or renaming of known results is load-bearing for the central claim. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard phonon hydrodynamics plus the assumption that the observed Faraday rotation is entirely due to Hall viscosity; no new particles or forces are introduced.

axioms (2)

domain assumption Phonon polarization rotation in magnetic field is produced by a non-dissipative Hall viscosity term in the phonon stress tensor.
Invoked in the interpretation of the acoustic Faraday effect (abstract).
domain assumption The relation between phonon Hall viscosity and thermal Hall conductivity follows from linear response theory without additional scattering channels.
Used to convert measured viscosity into predicted thermal Hall signal.

pith-pipeline@v0.9.0 · 5794 in / 1359 out tokens · 31038 ms · 2026-05-18T08:34:25.573046+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

?

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

phonon Hall viscosity produces an intrinsic thermal Hall effect... κ_xy = η_xzyz / ρ C (Methods, heat flux derivation)
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

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

σ_ij = c_ijkl ε_kl + η_ijkl ė_kl; Ω_ijkl from strain Berry phase (Eq. 4)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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[1] [1]

magnetopolarons

we measure with magnetic field purely in the honeycomb plane to ensure that the Faraday signal disappears in this configuration; 4) we measure two additional samples of different thicknesses to ensure reproducibility; 5) we measure at additional ultrasonic frequencies. Data 9 sets from (1) and (2) are analyzed below to extract the Hall viscosity ofα-RuCl ...

work page

[2] [2]

& Lee, P

Katsura, H., Nagaosa, N. & Lee, P. A. Theory of the Thermal Hall Effect in Quantum Magnets.Physical Review Letters104, 066403 (2010)

work page 2010

[3] [3]

Zhang, X.-T., Gao, Y . H. & Chen, G. Thermal Hall effects in quantum magnets.Physics Reports1070, 1–59 (2024)

work page 2024

[4] [4]

W., Cava, R

Hirschberger, M., Krizan, J. W., Cava, R. J. & Ong, N. P. Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet.Science348, 106–109 (2015). 17

work page 2015

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Yokoi, T.et al.Half-integer quantized anomalous thermal Hall effect in the Kitaev material candidateα-RuCl3.Science373, 568–572 (2021)

work page 2021

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Czajka, P.et al.Oscillations of the thermal conductivity in the spin-liquid state ofα- RuCl3.Nature Physics17, 915–919 (2021)

work page 2021

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Watanabe, D.et al.Emergence of nontrivial magnetic excitations in a spin-liquid state of kagom´e volborthite.Proceedings of the National Academy of Sciences113, 8653–8657 (2016)

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Doki, H.et al.Spin Thermal Hall Conductivity of a Kagome Antiferromagnet.Physical Review Letters121, 097203 (2018)

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Akazawa, M.et al.Thermal Hall Effects of Spins and Phonons in Kagome Antiferro- magnet Cd-Kapellasite.Physical Review X10, 041059 (2020)

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Boulanger, M.-E.et al.Thermal Hall conductivity of electron-doped cuprates.Physical Review B105, 115101 (2022)

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& Taillefer, L

Chen, L., Boulanger, M.-E., Wang, Z.-C., Tafti, F. & Taillefer, L. Large phonon ther- mal Hall conductivity in the antiferromagnetic insulator Cu 3TeO6.Proceedings of the National Academy of Sciences119, e2208016119 (2022)

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