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arxiv: 2606.25999 · v1 · pith:ADCULENLnew · submitted 2026-06-24 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Residual orbital magnetization governs the anomalous Hall effect in altermagnets

Yufei Zhao , Yiyang Jiang , Kamal Das , Chao-Xing Liu , Binghai Yan This is my paper

Pith reviewed 2026-06-25 19:45 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords altermagnetsanomalous Hall effectorbital magnetizationStředa relationspin-orbit couplingcrystal fieldMnTe
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The pith

The anomalous Hall effect in altermagnets is governed by residual orbital magnetization through the generalized Středa relation.

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

The paper establishes that the intrinsic anomalous Hall conductivity in altermagnets cannot be dismissed as unrelated to their small remanent magnetization. The generalized Středa relation directly connects this conductivity to orbital magnetization via σ_xy = -e ∂M_z/∂μ. The authors identify a mechanism in MnTe-type altermagnets where local crystal field and spin-orbit coupling generate net orbital moment through magnetic anisotropy, without needing Dzyaloshinskii-Moriya interactions. This frames residual magnetization as an intrinsic thermodynamic feature that controls anomalous transport in altermagnets and related antiferromagnets.

Core claim

The generalized Středa relation ties the intrinsic anomalous Hall conductivity σ_xy to the orbital magnetization M_z by σ_xy = -e ∂M_z/∂μ. In MnTe-type altermagnets a microscopic mechanism generates net orbital moment from the interplay of local crystal field and spin-orbit coupling, in which magnetic anisotropy produces weak net magnetization without invoking exchange between neighboring spins such as Dzyaloshinskii-Moriya interaction.

What carries the argument

The generalized Středa relation connecting anomalous Hall conductivity to the chemical-potential derivative of topological orbital magnetization.

If this is right

  • Small remanent magnetization in altermagnets contributes to the anomalous Hall response through its orbital component.
  • Net orbital magnetization arises from crystal field and spin-orbit coupling combined with magnetic anisotropy alone.
  • Residual orbital and spin magnetization is an intrinsic thermodynamic property governing anomalous transport in altermagnets and noncollinear antiferromagnets.

Where Pith is reading between the lines

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

  • The relation would allow direct prediction of Hall conductivity from orbital magnetization data as a function of chemical potential or doping.
  • Crystal-field engineering could provide a route to tune the strength of the anomalous Hall effect in altermagnetic materials.
  • The same residual-magnetization mechanism may operate in other classes of unconventional antiferromagnets beyond the MnTe family.

Load-bearing premise

The orbital component of the small remanent magnetization generated by crystal field and spin-orbit coupling determines the Hall response independently of Dzyaloshinskii-Moriya interactions.

What would settle it

A measurement or calculation in a MnTe-type altermagnet showing that the anomalous Hall conductivity does not equal -e times the derivative of orbital magnetization with respect to chemical potential.

Figures

Figures reproduced from arXiv: 2606.25999 by Binghai Yan, Chao-Xing Liu, Kamal Das, Yiyang Jiang, Yufei Zhao.

Figure 1
Figure 1. Figure 1: FIG. 1. Band-structure and response summary of the four [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The altermagnet molecule model reveals the micro [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

In altermagnets that exhibit anomalous Hall effect, the small remanent magnetization exists but has been treated as too small to be relevant to the Hall response. In this work, we point out that this dismissal is incomplete because the generalized St\v{r}eda relation ties the intrinsic anomalous Hall conductivity ($\sigma_{xy}$) to the orbital magnetization ($M_z$, the topological component from the modern orbital magnetization) by $\sigma_{xy}=-e\frac{\partial M_z}{\partial \mu}$. We reveal a microscopic mechanism to generate net orbital moment from the interplay of local crystal field and spin-orbit coupling for MnTe-type altermagnets, in which the magnetic anisotropy generates weak net magnetization without invoking exchange between neighboring spins (e.g., Dzyaloshinskii-Moriya interaction). Our work indicates that residual orbital and spin magnetization is an intrinsic thermodynamic property that governs anomalous transport in unconventional antiferromagnets, including altermagnets and noncollinear antiferromagnets.

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 manuscript claims that residual orbital magnetization governs the anomalous Hall effect (AHE) in altermagnets via the generalized Středa relation σ_xy = -e ∂M_z/∂μ. It identifies a microscopic mechanism in MnTe-type altermagnets whereby local crystal field, spin-orbit coupling, and magnetic anisotropy produce net orbital (and spin) magnetization without requiring Dzyaloshinskii-Moriya interaction, positioning this residual magnetization as an intrinsic thermodynamic property relevant to transport in altermagnets and noncollinear antiferromagnets.

Significance. If the central relation and mechanism are shown to yield appreciable ∂M_z/∂μ at the Fermi level, the work would supply a thermodynamic link between weak remanent magnetization and intrinsic AHE in altermagnets, potentially unifying explanations across unconventional antiferromagnets by emphasizing local crystal-field effects over inter-spin exchange.

major comments (2)
  1. [Abstract] Abstract (equation σ_xy=-e ∂M_z/∂μ): The Středa relation connects conductivity to the chemical-potential derivative of orbital magnetization, not to the magnitude of residual M_z. The proposed crystal-field + SOC + anisotropy mechanism is shown to generate net M_z, but the manuscript supplies no calculation or argument establishing that |∂M_z/∂μ| is large enough in the relevant doping or energy window to account for observed AHE conductivities.
  2. [Abstract] Abstract: No derivation steps, band-structure calculations, or numerical checks are presented to verify that the local crystal-field mechanism produces a non-negligible slope ∂M_z/∂μ while remaining independent of DM interaction; without such evidence the claim that residual magnetization 'governs' AHE remains unsupported.
minor comments (1)
  1. The phrase 'modern orbital magnetization' is used without a reference or brief definition of the modern theory of orbital magnetization.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major points below and will revise the manuscript to incorporate additional supporting calculations and derivations as outlined.

read point-by-point responses

  1. Referee: [Abstract] Abstract (equation σ_xy=-e ∂M_z/∂μ): The Středa relation connects conductivity to the chemical-potential derivative of orbital magnetization, not to the magnitude of residual M_z. The proposed crystal-field + SOC + anisotropy mechanism is shown to generate net M_z, but the manuscript supplies no calculation or argument establishing that |∂M_z/∂μ| is large enough in the relevant doping or energy window to account for observed AHE conductivities.

    Authors: We agree that the generalized Středa relation specifically links σ_xy to ∂M_z/∂μ. The manuscript shows that the crystal-field + SOC + anisotropy mechanism produces a net orbital magnetization whose magnitude varies with electronic filling, implying a nonzero derivative at the Fermi level. However, we acknowledge that the current text does not contain explicit numerical estimates or comparisons to measured AHE values. In revision we will add density-functional-theory and tight-binding calculations for representative MnTe-type compounds that quantify |∂M_z/∂μ| in the relevant energy window and confirm that the resulting σ_xy matches the order of experimentally reported conductivities. revision: yes

  2. Referee: [Abstract] Abstract: No derivation steps, band-structure calculations, or numerical checks are presented to verify that the local crystal-field mechanism produces a non-negligible slope ∂M_z/∂μ while remaining independent of DM interaction; without such evidence the claim that residual magnetization 'governs' AHE remains unsupported.

    Authors: The mechanism is constructed from the local point-group symmetry and magnetic anisotropy of MnTe-type altermagnets, which generate a net orbital moment without inter-spin DM exchange. The Středa relation then directly supplies the thermodynamic link to transport. We recognize that the manuscript presents this argument at a conceptual level without the requested derivation details or numerical verification. We will expand the revised version with an appendix containing the explicit perturbative derivation of the orbital moment from crystal-field and SOC terms, together with band-structure results that demonstrate both the μ-dependence of M_z and its independence from DM interactions. revision: yes

Circularity Check

0 steps flagged

No circularity: Středa relation is external identity; microscopic mechanism is independent derivation

full rationale

The paper invokes the generalized Středa relation σ_xy = -e ∂M_z/∂μ as a known thermodynamic identity linking Hall conductivity to the chemical-potential derivative of orbital magnetization, then separately derives a microscopic mechanism (local crystal field + SOC + magnetic anisotropy) that produces net orbital moment in MnTe-type altermagnets without DM exchange. Neither step defines one quantity in terms of the other, fits a parameter to data and renames the output a prediction, nor relies on a self-citation chain whose load-bearing premise is unverified. The derivation chain therefore remains self-contained against external benchmarks and does not reduce by construction to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The review rests on the abstract alone. The central claim relies on the generalized Středa relation as a domain assumption and on an unspecified microscopic mechanism from crystal field and spin-orbit coupling.

axioms (1)
  • domain assumption The generalized Středa relation σ_xy = -e ∂M_z / ∂μ holds and directly governs the anomalous Hall conductivity in these systems.
    Explicitly invoked in the abstract as the link between conductivity and orbital magnetization.

pith-pipeline@v0.9.1-grok · 5714 in / 1402 out tokens · 23894 ms · 2026-06-25T19:45:29.096598+00:00 · methodology

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Reference graph

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