Effect of polar distortions on the linear and nonlinear anomalous Hall conductivity of altermagnetic $\alpha$-MnTe

Amar Fakhredine; Carmine Autieri; Chanchal K. Barman; Mathews Benny; Sahar Izadi Vishkayi

REVIEW 2 major objections 1 minor 2 cited by

Effect of polar distortions on the linear and nonlinear anomalous Hall conductivity of altermagnetic $\alpha$-MnTe

T0 review · 2 major / 1 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read Polar lattice distortions substantially modify the anomalous Hall conductivity in altermagnetic α-MnTe.

desk verdict Polarization from surface distortions can affect AHC in α-MnTe, but the bulk E-field model may miss key surface symmetry features. read the letter →

arxiv 2606.12311 v2 pith:ECKH3GRN submitted 2026-06-10 cond-mat.mtrl-sci cond-mat.other

Mathews Benny , Sahar Izadi Vishkayi , Amar Fakhredine , Chanchal K. Barman , Carmine Autieri This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.other

keywords altermagnetismanomalousHallconductivitypolardistortionMnTeelectricfieldsurfacesymmetrynonlineareffect

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 investigates how the surface of α-MnTe breaks additional symmetries beyond the bulk, producing polar distortions along both the z and y axes along with weak ferrimagnetism along y. To capture this, the authors apply an in-plane electric field to the bulk crystal and compute its effect on the anomalous Hall conductivity. They find that the resulting lattice polarization alters the AHC value in a sizable way. Because the field also breaks inversion symmetry, this polar term appears together with the nonlinear anomalous Hall response. A reader would care if the finding holds because it adds an electric-field knob to the transport properties already expected from the altermagnetic order.

What carries the argument

The symmetry reduction to orthorhombic Amm2 on the surface, which permits polar lattice distortions that couple to and modify the anomalous Hall conductivity when an in-plane electric field is applied.

What would settle it

A first-principles calculation or transport measurement that finds the anomalous Hall conductivity of α-MnTe remains essentially unchanged when an in-plane electric field is applied would falsify the claim of a substantial polarization effect.

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Extended reading notes

Core claim

α-MnTe with Néel vector along y has a finite AHC and weak ferromagnetism along z. The surface reduces the space group from P6₃/mmc to Amm2, allowing polar distortions along z and y together with weak ferrimagnetism along y. Modeling the surface via an in-plane electric field applied to the bulk shows that lattice polarization substantially changes the AHC; the electric field simultaneously breaks inversion symmetry so the polar contribution coexists with the nonlinear anomalous Hall effect.

Load-bearing premise

The bulk response to an applied in-plane electric field is taken as an adequate stand-in for the actual surface polar distortions and their impact on the anomalous Hall conductivity.

Editorial extensions

If this is right

Lattice polarization induced by electric field changes the value of the anomalous Hall conductivity.
The polar contribution to the Hall response appears alongside the nonlinear anomalous Hall effect once inversion symmetry is broken.
Surface polar distortions along z and y, plus weak ferrimagnetism along y, appear once C₂ symmetry is lifted by the surface.
Altermagnets can exhibit additional transport channels when both magnetic order and electric-field-induced polarization are present.

Reading between the lines

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

Surface termination or substrate choice could be used to tune the anomalous Hall conductivity through controlled polar distortions.
Similar polarization effects may appear in other altermagnets that lose inversion symmetry at their surfaces or under external fields.
Time-resolved or gate-tuned transport experiments on thin films could separate the polar and nonlinear contributions to the Hall signal.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

The main takeaway is that the authors find lattice polarization from surface polar distortions can substantially modify the anomalous Hall conductivity in altermagnetic α-MnTe. They model this by applying an in-plane electric field to bulk MnTe as a stand-in.

The symmetry analysis is the part that holds up. They start from the bulk Néel vector along y, which already breaks C6 down to C2, then show the surface breaks that C2 further, leaving only time-reversed mirror symmetry and dropping the space group to Amm2. This produces polar distortions along both z and y plus weak ferrimagnetism along y. That step is clear and connects the Néel orientation to surface crystal symmetry in a way that had not been spelled out for this compound.

They then show that the electric field breaks inversion symmetry so the polarization term can add to the nonlinear AHE. The claim that this coexistence highlights richer transport behavior in altermagnets follows directly from the setup.

The soft spot is the modeling shortcut. The bulk crystal keeps its C2 symmetry under a uniform in-plane field, while the actual surface does not, and the y-directed polar mode plus the associated ferrimagnetism have no obvious counterpart. If those surface-specific pieces drive the AHC shift, the bulk proxy could give the wrong size or even the wrong sign. The abstract gives no numbers or error bars, so it is impossible to judge how large the mismatch is without the full calculations.

This paper is for people working on altermagnetic surfaces and spintronic transport. It raises a concrete question worth checking, so it deserves a serious referee. I would send it to peer review and ask the referees to focus on whether the electric-field model actually reproduces the surface distortions.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that the surface of altermagnetic α-MnTe (Néel vector along y) breaks C2 symmetry, reducing the space group to orthorhombic Amm2 and inducing polar distortions along both z and y plus weak ferrimagnetism along y. To model these surface effects accessibly, the authors apply an in-plane electric field to bulk MnTe and show that the resulting lattice polarization substantially modifies the anomalous Hall conductivity (AHC), with this contribution coexisting with the nonlinear AHE due to inversion-symmetry breaking.

Significance. If the bulk in-plane E-field proxy is shown to faithfully reproduce the surface Amm2 distortions and their quantitative impact on AHC, the result would establish an additional electric-field-tunable mechanism in altermagnets, extending beyond the standard symmetry-protected AHC and highlighting coexistence with nonlinear Hall effects in doped ionic semiconductors.

major comments (2)

[Abstract] Abstract (modeling simplification): the central claim that polarization 'substantially affect[s] the AHC' rests on replacing the surface (C2 broken, Amm2 symmetry with y- and z-polar modes plus y-ferrimagnetism) by a uniform in-plane E-field in bulk MnTe; the bulk retains C2 symmetry, so the y-directed polar distortion and associated ferrimagnetism have no direct counterpart, undermining the claimed effect size for the actual surface.
[Abstract] Abstract (quantitative support): no specific calculations, band-structure results, AHC values, or error bars are provided to quantify how large the polarization-induced change in AHC is relative to the zero-field case, leaving the 'substantially' qualifier unsupported.

minor comments (1)

[Abstract] The phrase 'as already demonstrated in the bulk' lacks a citation to the prior work establishing the finite AHC and weak ferromagnetism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We address each major comment below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract (modeling simplification): the central claim that polarization 'substantially affect[s] the AHC' rests on replacing the surface (C2 broken, Amm2 symmetry with y- and z-polar modes plus y-ferrimagnetism) by a uniform in-plane E-field in bulk MnTe; the bulk retains C2 symmetry, so the y-directed polar distortion and associated ferrimagnetism have no direct counterpart, undermining the claimed effect size for the actual surface.

Authors: We agree that the uniform in-plane E-field applied to bulk MnTe is a simplification that does not reproduce the full surface symmetry reduction to Amm2, including the y-directed polar distortion and associated weak ferrimagnetism, because the bulk retains C2 symmetry. The proxy is used to make the polarization effects computationally accessible while capturing the inversion-symmetry breaking and z-polar distortions that modify the AHC. We will revise the abstract and main text to explicitly note these limitations of the bulk proxy and clarify that the reported AHC changes illustrate the polarization contribution without claiming quantitative equivalence to all surface-specific modes. revision: partial
Referee: [Abstract] Abstract (quantitative support): no specific calculations, band-structure results, AHC values, or error bars are provided to quantify how large the polarization-induced change in AHC is relative to the zero-field case, leaving the 'substantially' qualifier unsupported.

Authors: The abstract is concise by design and does not contain the detailed numerical results. The manuscript body presents the first-principles band structures, polarization values, and AHC computations with and without the electric field. To better support the claim, we will revise the abstract to include a brief quantitative statement on the magnitude of the AHC modification based on the calculations already reported in the main text. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity; modeling choice is not a derivation that reduces to inputs

full rationale

Abstract and description contain no equations, parameters, or derivations. The approach of using bulk in-plane E-field to proxy surface polar distortions is presented as a simplification for accessibility, not as a fitted or self-defined result. No self-citations, ansatzes, or uniqueness theorems are invoked in a load-bearing way. The central claim (polarization affects AHC) rests on external computation rather than reducing to its own inputs by construction. This matches the expected non-finding for papers without shown derivations.

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

Abstract provides no details on free parameters, axioms, or invented entities.

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Cite this review

Pith. "Pith review of Effect of polar distortions on the linear and nonlinear anomalous Hall conductivity of altermagnetic $\alpha$-MnTe." pith.science (2026). https://pith.science/paper/ECKH3GRN

@misc{pith2026260612311,
  author       = {Pith},
  title        = {Pith review of: Effect of polar distortions on the linear and nonlinear anomalous Hall conductivity of altermagnetic $\alpha$-MnTe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ECKH3GRN}},
  note         = {Machine review of arXiv:2606.12311}
}

abstract

Altermagnetic $\alpha$-MnTe with N\'eel vector along the $y$-axis exhibits a finite anomalous Hall conductivity (AHC) and weak ferromagnetism along the $z$-axis. As already demonstrated in the bulk, there is the breaking of the C$_6$ symmetry by the in-plane N\'eel vector, leaving a C$_2$-type magnetic symmetry. The surface of $\alpha$-MnTe breaks the C$_2$, leaving only a time-reversed mirror symmetry with respect to the $x=0$ plane. Therefore, we demonstrate that on the surface, the interplay between breaking of the crystal symmetry and N\'eel vector orientation produces a reduction of the space group from hexagonal P6$_3$/mmc to orthorhombic Amm2. As a result, the surface exhibits not only a polar distortion along the $z$-axis, but also a polar distortion and a weak ferrimagnetism along the $y$-axis. To describe the surface of MnTe in an accessible way, we simplify the problem and examine the effect of the in-plane electric field in bulk MnTe. Moreover, as a doped ionic semiconductor, the properties of MnTe can be influenced by lattice polarization under an applied electric field. We investigate the interplay between the intrinsic anomalous Hall effect and lattice polarization, showing that polarization effects can substantially affect the AHC. Since the electric field breaks inversion symmetry, this contribution from the lattice polarization coexists with the non-linear anomalous Hall effect, highlighting the rich transport phenomenology of altermagnets.

Figures

Figures reproduced from arXiv: 2606.12311 by the authors.

**Figure 2.** FIG. 2. a) Top view of the MnTe crystal structure with centrosymmetric Space Group 194 (P6 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** FIG. 4. The relativistic altermagnetic band structure calcu [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 3.** Figure 3: FIG. 3. Non-magnetic band structures calculated by density [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 5.** Figure 5: FIG. 5. Anomalous Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: FIG. 7. Anomalous Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

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Forward citations

Cited by 2 Pith papers

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

Magnetic reconstruction of the altermagnet {\alpha}-MnTe(0001) surface driven by ligand holes
cond-mat.mtrl-sci 2026-08 conditional novelty 6.0 of 10

DFT calculations predict the α-MnTe(0001) surface orders with a ferromagnetic outermost Mn bilayer, 17 meV per surface lower in energy than the bulk antiferromagnetic stacking, driven by a ligand hole on Te.
Magnetotransport evolution and nonlinear Hall effect in altermagnetic MnTe
cond-mat.mtrl-sci 2026-08 conditional novelty 6.0 of 10

The authors find that high-order AMR and planar Hall harmonics in bulk MnTe appear only in the metallic regime, while a zero-field second-order nonlinear Hall effect persists and points to inversion-symmetry breaking.

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Reviewed June 27, 2026 · model on record in the stance chip above.