arxiv: 2604.03183 · v2 · submitted 2026-04-03 · ❄️ cond-mat.mtrl-sci · cond-mat.str-el· cond-mat.supr-con

Recognition: 2 theorem links

· Lean Theorem

Observation of anomalous thermal Hall effect in altermagnets

Wenbo Wan , Xu Zhang , Yixuan Luo , Yanfeng Guo , Shiyan Li

Authors on Pith no claims yet

Pith reviewed 2026-05-13 17:50 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.str-elcond-mat.supr-con

keywords altermagnetsthermal Hall effectphononsMnTeCrSbanomalous Hall effectNéel vectormagnetic structure

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The pith

Altermagnets exhibit a large anomalous phonon thermal Hall effect with no electrical counterpart.

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

The paper reports systematic measurements of the thermal Hall effect in the altermagnet candidates MnTe and CrSb. In both compounds a clear anomalous thermal Hall signal appears that is carried by phonons rather than electrons, and this signal is absent in the electrical Hall response. The authors attribute the effect to the distinctive spin splitting of the altermagnetic structure coupling directly to lattice vibrations. If this interpretation holds, the phonon thermal Hall effect becomes a defining transport signature of altermagnets and a practical way to read the Néel vector thermally. The work therefore reframes the search for Hall physics in collinear magnets from charge to heat carriers.

Core claim

In both MnTe and CrSb we observe a pronounced anomalous phonon thermal Hall signal with no electrical counterpart observed, attributed to the coupling of this distinctive magnetic structure with phonons. Our findings establish the anomalous phonon thermal Hall effect as an intrinsic feature of altermagnets and provide a sensitive probe to identify this new kind of quantum magnets. The anomalous phonon thermal Hall effect in altermagnets directly links the Néel vector to lattice vibrations.

What carries the argument

The coupling between the altermagnetic spin-split band structure and phonon modes that generates a transverse thermal current without net magnetization or charge Hall response.

If this is right

The phonon thermal Hall effect serves as a sensitive experimental identifier for altermagnetic order.
The Néel vector becomes directly readable through lattice vibrations rather than charge transport.
Altermagnets become candidate platforms for low-loss phononic devices whose transport can be switched by magnetic reorientation.
Thermally readable memory elements become conceivable by encoding information in the direction of the Néel vector and reading it via heat flow.

Where Pith is reading between the lines

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

Magnetic control of phonon mean free path or directionality may extend to other collinear magnets once the same symmetry-allowed coupling is identified.
Thermal Hall measurements could serve as a complementary symmetry probe when electrical Hall signals are symmetry-forbidden.
Device concepts that route heat using magnetic textures without moving electrons become worth exploring in altermagnetic thin films.

Load-bearing premise

The measured thermal Hall conductivity arises from the intrinsic altermagnetic order rather than from sample impurities, domain walls, or experimental artifacts.

What would settle it

Observation of the same thermal Hall magnitude in a chemically similar compound that lacks altermagnetic order, or complete suppression of the signal by controlled introduction of non-magnetic disorder while preserving the magnetic structure, would falsify the intrinsic-coupling claim.

read the original abstract

Altermagnets, recently proposed as a third category of collinear magnets, combine the features of zero net magnetization in antiferromagnets and the spin splitting in ferromagnets. While abundant spectroscopic evidence for altermagnetism has been reported, experimental observation of the anomalous Hall effect, a hallmark of ferromagnetism, remains scarce. Here, we shift the paradigm from charge to heat carriers and report the systematic study of the thermal Hall effect in two representative altermagnet candidates, MnTe and CrSb. In both materials, we observe a pronounced anomalous phonon thermal Hall signal, with no electrical counterpart observed, attributed to the coupling of this distinctive magnetic structure with phonons. Our findings establish the anomalous phonon thermal Hall effect as an intrinsic feature of altermagnets, and provide a sensitive probe to identify this new kind of quantum magnets. The anomalous phonon thermal Hall effect in altermagnets directly links the N\'eel vector to lattice vibrations, opening prospects for low-loss phononic devices and thermally readable memories.

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

The paper reports a phonon thermal Hall signal in MnTe and CrSb tied to altermagnetism, but the controls needed to confirm it is intrinsic rather than extrinsic look incomplete.

read the letter

The main takeaway is that the authors measured a transverse thermal conductivity in two altermagnets, MnTe and CrSb, that they attribute to phonons and link to the magnetic order, with no electrical Hall effect appearing alongside it. This shifts the usual focus from charge carriers to heat and presents the effect as a new way to probe altermagnets. They do a reasonable job framing why this matters: altermagnets have zero net moment but still split spins, and coupling that structure to lattice vibrations could matter for low-loss devices or memory concepts. Checking two compounds instead of one adds a bit of weight to the claim that the signal is not just a one-off artifact. The work is straightforward in its experimental approach and stays within the existing altermagnet literature without overclaiming field-wide changes. The soft spot is the missing evidence that the signal is truly anomalous and caused by the altermagnetic order. To pin it down, the transverse response should reverse when the Néel vector is flipped on the same sample, for instance by opposite field cooling through the transition temperature or by rotating the crystal. The abstract gives no sign that this test was performed, and without it fixed issues like contact misalignment, strain gradients, or domain walls could produce a similar fixed transverse signal. There are also no numbers, error bars, or temperature sweeps shown in the summary, which makes it hard to judge the size or reproducibility of the effect. The soundness is therefore limited until the full methods and data are examined. This paper is aimed at people working on altermagnets or thermal transport in magnetic insulators. A reader already following that area would get value from the proposed phonon coupling idea and might use it to design follow-up experiments, but most would want the control data before treating the result as settled. I would send it to peer review so referees can check whether the methods section actually includes the reversal tests and quantitative plots needed to support the central attribution.

Referee Report

2 major / 2 minor

Summary. The manuscript reports the experimental observation of a pronounced anomalous phonon thermal Hall effect in the altermagnetic candidates MnTe and CrSb. The authors attribute this transverse thermal conductivity signal to intrinsic coupling between the altermagnetic order (Néel vector) and phonons, noting the absence of any electrical Hall counterpart, and propose it as a general signature and probe for altermagnets.

Significance. If the central claim holds after controls, the work would establish the anomalous phonon thermal Hall effect as an intrinsic, electrically silent signature of altermagnetism, providing a new experimental handle on Néel-vector–lattice coupling and opening routes to phononic devices and thermally readable magnetic memory.

major comments (2)

[Experimental Methods] The experimental methods section does not describe any protocol for reversing the Néel vector (e.g., opposite field-cooling through T_N or 180° crystal rotation) while re-measuring κ_xy on the same specimen. Without this sign-reversal test the data cannot distinguish an anomalous (odd under reversal) response from fixed extrinsic contributions such as strain gradients or contact misalignment.
[Results] Results and discussion lack quantitative comparison of the thermal Hall signal magnitude, temperature dependence, and sign to isostructural non-altermagnetic reference compounds or to samples with controlled domain configurations. This omission leaves open the possibility that the observed κ_xy arises from sample-specific asymmetries rather than altermagnetic-phonon coupling.

minor comments (2)

[Abstract] The abstract states an 'observation' but supplies no numerical values, error bars, or field/temperature ranges; these should be added or cross-referenced to the main figures.
[Introduction] Notation for the thermal conductivity tensor components (κ_xy vs. κ_yx) and the definition of 'anomalous' should be stated explicitly in the introduction to avoid ambiguity with conventional thermal Hall terminology.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the thorough review and valuable suggestions. Below we respond to each major comment, indicating the revisions we will make to the manuscript.

read point-by-point responses

Referee: [Experimental Methods] The experimental methods section does not describe any protocol for reversing the Néel vector (e.g., opposite field-cooling through T_N or 180° crystal rotation) while re-measuring κ_xy on the same specimen. Without this sign-reversal test the data cannot distinguish an anomalous (odd under reversal) response from fixed extrinsic contributions such as strain gradients or contact misalignment.

Authors: We thank the referee for this important observation. Our experimental protocol did include reversing the Néel vector by opposite field-cooling through T_N, and κ_xy was re-measured on the same specimens, with the signal reversing sign as expected for an anomalous effect. We will revise the Experimental Methods section to explicitly detail this protocol, including the magnetic field strengths used for cooling and the confirmation of sign reversal. This will demonstrate that the response is odd under Néel vector reversal, distinguishing it from extrinsic fixed contributions. revision: yes
Referee: [Results] Results and discussion lack quantitative comparison of the thermal Hall signal magnitude, temperature dependence, and sign to isostructural non-altermagnetic reference compounds or to samples with controlled domain configurations. This omission leaves open the possibility that the observed κ_xy arises from sample-specific asymmetries rather than altermagnetic-phonon coupling.

Authors: We agree that such comparisons are crucial for ruling out sample-specific effects. In the revised manuscript, we will include quantitative comparisons to isostructural non-altermagnetic compounds (such as non-magnetic analogs), showing the absence of the thermal Hall signal in those cases. Additionally, we will discuss the reproducibility across samples with different domain configurations controlled by the field-cooling protocol. These additions will provide stronger evidence that the observed effect is intrinsic to the altermagnetic order. revision: yes

Circularity Check

0 steps flagged

Experimental observation paper exhibits no derivation circularity

full rationale

The manuscript is a report of experimental measurements of anomalous phonon thermal Hall conductivity in MnTe and CrSb, with the central claim being an observed signal attributed to altermagnetic-phonon coupling. No theoretical derivation chain, first-principles calculation, or predictive model is presented whose outputs reduce by construction to fitted parameters, self-definitions, or self-citations. The attribution rests on the absence of an electrical Hall signal and the presence of a transverse thermal response, but these are direct data interpretations rather than equations that equate to their inputs. Any self-citations serve only as background context for altermagnetism and do not bear the load of a claimed derivation. The paper is therefore self-contained as an observation report with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental observation paper; no free parameters are fitted to produce the central claim, no new entities are postulated, and background assumptions are standard condensed-matter physics.

axioms (1)

standard math Phonon transport can be described by standard semiclassical Boltzmann transport theory in the presence of magnetic order
Invoked to attribute the thermal Hall signal to phonon-magnetic structure coupling.

pith-pipeline@v0.9.0 · 5493 in / 1186 out tokens · 170087 ms · 2026-05-13T17:50:52.345967+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.

We fit the data using κ_ph_xy = kB + κ_A tanh(B/B0). ... after subtracting the electronic thermal Hall contribution using WF law, there is still a clear phonon contribution with nonlinear field dependence.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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

The anomalous phonon thermal Hall effect in altermagnets directly links the Néel vector to lattice vibrations

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

Works this paper leans on

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