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arxiv: 2512.03814 · v2 · submitted 2025-12-03 · ❄️ cond-mat.mes-hall

Quantum-Geometric Fingerprints of Altermagnetic Order in Planar Magnetotransport

Zhichun Ouyang , Wei-Jing Dai , Zi-Ting Sun , Jin-Xin Hu , K. T. Law This is my paper

Pith reviewed 2026-05-17 02:24 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords altermagnetismplanar magnetotransportBerry curvaturequantum metricHall effectnonreciprocal transportquantum geometrytwo-dimensional magnets
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0 comments X

The pith

An in-plane Zeeman field in two-dimensional altermagnets with CnT symmetry generates transport responses whose angular periodicities and field powers directly reflect the altermagnetic order.

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

The paper demonstrates that planar magnetotransport offers a way to identify altermagnetic order without needing a net magnetization. It focuses on two-dimensional systems where the magnetic symmetry is CnT. An in-plane Zeeman field breaks the mirror and C2z symmetries that suppress intrinsic responses. This enables contributions from the Berry curvature and quantum metric to linear planar Hall, nonlinear planar Hall, and nonreciprocal longitudinal transport. The key result is that the dominant field dependence and angular harmonics are dictated by the specific altermagnetic wave symmetry like d-wave or g-wave.

Core claim

In two-dimensional altermagnets with CnT magnetic symmetry, an in-plane Zeeman field explicitly breaks the mirror and emergent C2z symmetries that otherwise suppress intrinsic Hall and second-order transport responses. The resulting magnetic field susceptibilities of the Berry curvature and quantum metric produce linear planar Hall, nonlinear planar Hall, and nonreciprocal longitudinal responses. Crucially, the leading magnetic field powers and angular periodicities of these responses are fixed by the underlying altermagnetic order. For d-, g-, and i-wave altermagnets, this yields distinct fingerprint patterns.

What carries the argument

Magnetic field susceptibilities of the Berry curvature and quantum metric that activate transport responses when an in-plane Zeeman field breaks the protective symmetries of the altermagnetic state.

If this is right

  • Linear and nonlinear planar Hall effects appear with field powers and angular dependencies set by the altermagnetic symmetry.
  • Nonreciprocal longitudinal resistance shows similar symmetry-determined characteristics.
  • These quantum-geometric responses provide symmetry-selective probes for altermagnetic order in two-dimensional materials.
  • Distinct patterns emerge for different wave symmetries such as d-wave, g-wave, and i-wave altermagnets.

Where Pith is reading between the lines

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

  • Similar symmetry-breaking approaches might reveal hidden orders in other classes of magnetic materials through transport.
  • These fingerprints could be combined with angle-resolved photoemission to map both geometry and order in the same sample.
  • Extending the analysis to include disorder effects would test the robustness of the predicted periodicities.

Load-bearing premise

The leading magnetic field powers and angular periodicities of the transport responses are strictly fixed by the altermagnetic order and that no other mechanisms such as disorder or higher-order terms alter these signatures in real samples.

What would settle it

Measuring the angular dependence of the nonlinear planar Hall conductivity in a candidate d-wave altermagnet and finding a periodicity that deviates from the expected one fixed by the order, such as missing the characteristic harmonics.

Figures

Figures reproduced from arXiv: 2512.03814 by Jin-Xin Hu, K. T. Law, Wei-Jing Dai, Zhichun Ouyang, Zi-Ting Sun.

Figure 1
Figure 1. Figure 1: FIG. 1. The schematic picture of the planar magnetotrans [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Band-normalized quantum metric component multi [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The nonreciprocal longitudinal conductivity [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The linear Hall conductivity of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. BCSD-induced 2nd-order Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

Identifying altermagnetic order through transport requires signatures that are sensitive to magnetic symmetry but do not rely on a net magnetization. Here we show that planar magnetotransport provides such quantum-geometric fingerprints. In two-dimensional altermagnets with $C_n\mathcal{T}$ magnetic symmetry, an in-plane Zeeman field explicitly breaks the mirror and emergent $C_{2z}$ symmetries that otherwise suppress intrinsic Hall and second-order transport responses. The resulting magnetic field susceptibilities of the Berry curvature and quantum metric produce linear planar Hall, nonlinear planar Hall, and nonreciprocal longitudinal responses. Crucially, the leading magnetic field powers and angular periodicities of these responses are fixed by the underlying altermagnetic order. For $d$-, $g$-, and $i$-wave altermagnets, we find distinct fingerprint patterns associated with quantum geometric susceptibilities. Our results establish planar magnetotransport as a symmetry selective probe of both band quantum geometry and altermagnetic order.

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 / 3 minor

Summary. The manuscript claims that planar magnetotransport in two-dimensional altermagnets with CnT magnetic symmetry yields quantum-geometric fingerprints of the order. An in-plane Zeeman field breaks mirror and emergent C2z symmetries that suppress intrinsic responses at B=0; the resulting susceptibilities of Berry curvature and quantum metric generate linear planar Hall, nonlinear planar Hall, and nonreciprocal longitudinal conductivities whose leading powers of |B| and angular periodicities (e.g., cos(2φ) for d-wave) are fixed solely by the altermagnetic symmetry. Distinct patterns are derived for d-, g-, and i-wave cases in the clean limit.

Significance. If the symmetry-derived leading terms survive, the work supplies falsifiable, parameter-free predictions that link altermagnetic order directly to measurable planar responses via quantum geometry. This strengthens experimental routes to detect altermagnetism without net magnetization and provides concrete angular harmonics and field scalings that can be tested in 2D materials.

major comments (2)
  1. [Section IV] The central claim that leading powers and angular periodicities are strictly fixed by altermagnetic order holds only in the clean intrinsic limit. Section IV (model calculations for d-, g-, and i-wave cases) presents results assuming no disorder, but does not estimate the disorder strength at which extrinsic skew-scattering or side-jump terms (which can enter at the same or lower order in B with different harmonics) remain subdominant. This is load-bearing for the applicability of the fingerprints to real samples.
  2. [§3.2] §3.2 (susceptibility derivation): the explicit expansion of the quantum-metric contribution to the nonlinear conductivity is not shown in sufficient detail to confirm that no additional symmetry-allowed terms modify the claimed leading |B| power or angular dependence once the Zeeman field is included.
minor comments (3)
  1. [Figure 3] Figure 3: the angular plots would benefit from explicit overlay of the predicted cos(2φ) or cos(4φ) curves to make the periodicity matching visually immediate.
  2. [Results] The notation for the in-plane field angle φ is introduced in the abstract but should be restated at the beginning of the results section for clarity.
  3. A brief comparison table summarizing the distinct leading harmonics for d-, g-, and i-wave orders would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the constructive comments on our manuscript. We address each major comment point by point below, with a focus on strengthening the presentation of our symmetry-based results.

read point-by-point responses

  1. Referee: [Section IV] The central claim that leading powers and angular periodicities are strictly fixed by altermagnetic order holds only in the clean intrinsic limit. Section IV (model calculations for d-, g-, and i-wave cases) presents results assuming no disorder, but does not estimate the disorder strength at which extrinsic skew-scattering or side-jump terms (which can enter at the same or lower order in B with different harmonics) remain subdominant. This is load-bearing for the applicability of the fingerprints to real samples.

    Authors: We agree that the analysis is performed in the clean intrinsic limit, as explicitly stated throughout the manuscript. The central claim concerns the symmetry-fixed leading powers and angular periodicities of the quantum-geometric contributions, which are independent of microscopic details in that limit. Extrinsic skew-scattering and side-jump terms are sample- and disorder-dependent; while they may appear at comparable orders in |B|, their angular harmonics are not constrained by the altermagnetic symmetry in the same way and can be distinguished experimentally through the distinct patterns we derive (e.g., cos(2φ) for d-wave). In the revised manuscript we will add a dedicated paragraph in Section IV clarifying the regime of validity, noting that the intrinsic fingerprints should dominate in sufficiently clean, high-mobility samples and that the symmetry-enforced angular dependencies provide a route to separate them from extrinsic effects. A quantitative estimate of the critical disorder strength would require material-specific scattering calculations outside the present symmetry-focused scope. revision: partial

  2. Referee: [§3.2] §3.2 (susceptibility derivation): the explicit expansion of the quantum-metric contribution to the nonlinear conductivity is not shown in sufficient detail to confirm that no additional symmetry-allowed terms modify the claimed leading |B| power or angular dependence once the Zeeman field is included.

    Authors: We appreciate the request for greater transparency in the derivation. In the revised manuscript we will expand §3.2 to present the full explicit expansion of the quantum-metric susceptibility entering the nonlinear conductivity. This will include the intermediate steps showing how the in-plane Zeeman field breaks the relevant mirror and C2z symmetries, generating the leading |B| term with the angular periodicity dictated solely by the altermagnetic order, while confirming that no additional symmetry-allowed contributions alter this leading behavior. revision: yes

Circularity Check

0 steps flagged

Symmetry-allowed quantum-geometric susceptibilities yield independent predictions; no circular reduction

full rationale

The derivation proceeds from the definition of CnT altermagnetic symmetry (an external input) to the explicit breaking of mirror and C2z by an in-plane Zeeman field, which then permits Berry-curvature and quantum-metric susceptibilities at specific orders in B. These orders and angular harmonics follow directly from representation theory applied to the quantum geometric tensors; they are not obtained by fitting any parameter to the target observables nor by renaming a prior result. No self-citation is invoked as a load-bearing uniqueness theorem, and the clean-limit calculation is presented as a symmetry fingerprint rather than a statistical prediction. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard symmetry properties of altermagnets and quantum geometry; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Two-dimensional altermagnets possess CnT magnetic symmetry that permits specific mirror and C2z protections in the absence of an in-plane field.
    Invoked to explain why the Zeeman field is required to activate the responses.

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