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arxiv: 2606.26239 · v1 · pith:AQWHWTZEnew · submitted 2026-06-24 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci· cond-mat.other

Anomalous Hall viscosity of altermagnets

Iksu Jang , Rui Aquino , J\"org Schmalian , Rafael M. Fernandes This is my paper

Pith reviewed 2026-06-26 01:02 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-scicond-mat.other
keywords altermagnetsHall viscosityphononsBerry curvaturemagneto-acousticDirac pointsLifshitz transitionssymmetry breaking
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The pith

Phonon Hall viscosity at zero magnetic field distinguishes altermagnets from ferromagnets and antiferromagnets via finite tensor elements.

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

The paper shows that phonon Hall viscosity offers a direct probe of altermagnetism without an applied magnetic field. Finite elements in the Hall viscosity tensor arise uniquely in altermagnets due to their symmetry properties and serve as an unambiguous identifier. Microscopic calculations for d-wave and g-wave models reveal that the viscosity depends strongly on details of the electronic spectrum such as gapped Dirac points and Lifshitz transitions. These features trace to a strain-space Berry curvature monopole, providing an experimental signature accessible through magneto-acoustic measurements in insulating altermagnets.

Core claim

Altermagnets exhibit a nonzero phonon Hall viscosity at zero field generated by a strain-space Berry curvature monopole. This produces finite components of the viscosity tensor that are absent in ferromagnets and conventional antiferromagnets. Explicit computations in d-wave and g-wave microscopic models demonstrate that the magnitude and sign of the viscosity track electronic spectrum features including gapped Dirac points and Lifshitz transitions, in contrast to the multipolar momentum-space Berry curvature that characterizes altermagnets.

What carries the argument

Strain-space Berry curvature monopole that generates the anomalous Hall viscosity response under strain.

If this is right

  • Magneto-acoustic measurements can detect the broken symmetries and topology of insulating altermagnets.
  • The Hall viscosity shows strong sensitivity to gapped Dirac points and Lifshitz transitions in the electronic spectrum.
  • Finite elements of the viscosity tensor provide an unambiguous signature separating altermagnets from other magnetic classes.
  • The effect occurs at zero magnetic field and does not require external fields for observation.

Where Pith is reading between the lines

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

  • The strain-space formulation could be applied to compute similar responses in other classes of materials with momentum-space multipolar order.
  • Measurements on specific material realizations of d-wave or g-wave altermagnets would allow direct comparison with the model predictions.
  • Temperature or doping dependence of the viscosity could reveal additional signatures tied to the underlying band features.

Load-bearing premise

The chosen microscopic models for d-wave and g-wave altermagnets capture the dominant contributions to the phonon Hall viscosity without significant corrections from disorder or electron-phonon coupling details.

What would settle it

An experimental determination of the phonon Hall viscosity tensor in a candidate insulating altermagnet at zero field that finds all predicted finite elements to be zero would disprove the claim that these elements distinguish altermagnets.

Figures

Figures reproduced from arXiv: 2606.26239 by Iksu Jang, J\"org Schmalian, Rafael M. Fernandes, Rui Aquino.

Figure 1
Figure 1. Figure 1: FIG. 1. Non-dissipative stress components [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (b). Being sources of large Berry curvature, these gapped Dirac points determine not only the behavior of the momentum-space Berry curvature quadrupole [6, 11, 35, 65], but also the properties of the strain-space Berry curvature of Eq. (5). The latter, in turn, gives the non-zero Hall viscosity tensor elements in the altermagnetic phase, which according to our group theory analysis are [PITH_FULL_IMAGE:fi… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The four spin-polarized Dirac points of the Lieb lattice [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Hexagonal lattice model for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We show that the phonon Hall viscosity at zero magnetic field is a natural probe of altermagnetism. First, we demonstrate that the finite elements of the Hall viscosity tensor unambiguously distinguish altermagnets from ferromagnets and conventional antiferromagnets. We then microscopically compute the Hall viscosity in models for d-wave and g-wave altermagnets, and find a strong sensitivity to electronic spectrum features such as gapped Dirac points and Lifshitz transitions. This sensitivity reflects a strain-space Berry curvature monopole, which contrast to the multipolar character of the standard momentum-space Berry curvature in altermagnets. Since the Hall viscosity can be probed experimentally through magneto-acoustic measurements, it provides a compelling method to probe the broken symmetries and topology of insulating altermagnets.

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

2 major / 1 minor

Summary. The paper claims that the phonon Hall viscosity at zero magnetic field serves as a probe of altermagnetism. It shows that finite elements of the Hall viscosity tensor distinguish altermagnets from ferromagnets and conventional antiferromagnets, then computes the viscosity microscopically in tight-binding models of d-wave and g-wave altermagnets. The results exhibit strong sensitivity to electronic features such as gapped Dirac points and Lifshitz transitions, attributed to strain-space Berry curvature monopoles (contrasting with momentum-space Berry curvature multipoles). The authors suggest experimental access via magneto-acoustic measurements for insulating altermagnets.

Significance. If the central claim holds, the work identifies a symmetry-based, zero-field transport signature that could experimentally distinguish altermagnetic order and its associated topology. The strain-space Berry curvature perspective offers a new angle on altermagnetism beyond standard spin-split band structures, with potential implications for phonon-mediated probes in magnetic materials.

major comments (2)
  1. [Microscopic calculations section (likely §3 or §4)] The central claim that finite Hall viscosity elements 'unambiguously distinguish' altermagnets (abstract and §1) rests on computations in clean, specific tight-binding models for d- and g-wave cases. No analysis is provided showing that these non-zero tensor elements survive under disorder, realistic electron-phonon matrix elements, or additional interactions that could renormalize or cancel the distinguishing components while preserving the magnetic order (see skeptic note on weakest assumption).
  2. [Berry curvature discussion] § on strain-space Berry curvature: the mapping from gapped Dirac points/Lifshitz transitions to monopoles in strain space is presented as the origin of the viscosity, but it is unclear how this remains robust when the underlying electronic spectrum is perturbed (e.g., by finite temperature or weak disorder), which is load-bearing for the distinction from FM/AFM.
minor comments (1)
  1. [Eq. definitions] Notation for the viscosity tensor components should be clarified with explicit definitions in terms of the strain tensor to avoid ambiguity when comparing to standard literature on Hall viscosity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. Below we address the major points, clarifying the role of symmetry arguments versus model calculations and noting planned revisions for added discussion.

read point-by-point responses

  1. Referee: [Microscopic calculations section (likely §3 or §4)] The central claim that finite Hall viscosity elements 'unambiguously distinguish' altermagnets (abstract and §1) rests on computations in clean, specific tight-binding models for d- and g-wave cases. No analysis is provided showing that these non-zero tensor elements survive under disorder, realistic electron-phonon matrix elements, or additional interactions that could renormalize or cancel the distinguishing components while preserving the magnetic order (see skeptic note on weakest assumption).

    Authors: The claim that finite Hall viscosity elements unambiguously distinguish altermagnets is grounded in the symmetry analysis (Section 2), which shows these tensor components are permitted solely by the magnetic point groups of altermagnets and forbidden in ferromagnets and conventional antiferromagnets. The tight-binding computations (Section 3) illustrate that the elements are non-zero and sensitive to spectrum features in representative clean models. We agree that disorder, realistic electron-phonon matrix elements, and interactions are not analyzed; such effects lie outside the present scope and would require substantial further work. In the clean limit appropriate to high-quality insulating samples the symmetry-allowed terms remain. We will add a concise discussion of these modeling assumptions and their implications in the revised manuscript. revision: partial

  2. Referee: [Berry curvature discussion] § on strain-space Berry curvature: the mapping from gapped Dirac points/Lifshitz transitions to monopoles in strain space is presented as the origin of the viscosity, but it is unclear how this remains robust when the underlying electronic spectrum is perturbed (e.g., by finite temperature or weak disorder), which is load-bearing for the distinction from FM/AFM.

    Authors: The strain-space Berry curvature monopoles originate from the deformation-induced mapping of electronic features (gapped Dirac points, Lifshitz transitions) onto singularities in strain-parameter space. Finite temperature and weak disorder will broaden these features, yet the topological monopole character implies that the integrated contribution to the Hall viscosity remains finite provided the altermagnetic order (and associated symmetry breaking) is preserved. We will insert a short clarifying paragraph on the expected robustness under weak perturbations in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is model-driven and self-contained

full rationale

The paper computes the phonon Hall viscosity tensor explicitly from tight-binding models of d-wave and g-wave altermagnets, identifying non-zero elements via strain-space Berry curvature monopoles at gapped Dirac points and Lifshitz transitions. These calculations are performed directly on the chosen microscopic Hamiltonians without fitting parameters to target observables or renaming fitted quantities as predictions. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatzes smuggled via citation are invoked to force the distinguishing finite tensor elements. The distinction from ferromagnets and conventional antiferromagnets follows from symmetry analysis and the explicit model spectra rather than any definitional reduction or statistical forcing. The derivation chain remains independent of its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. Standard condensed-matter concepts such as Berry curvature are invoked but not detailed.

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discussion (0)

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Reference graph

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