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REVIEW 4 major objections 6 minor 54 references

In the altermagnet CrSb, the intrinsic anomalous Hall conductivity does not depend linearly on net magnetization, so nonlinear Hall signals are not proof of a topological Hall effect.

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2026-08-03 02:39 UTC pith:UJD2FQZ6

load-bearing objection A useful new data point for CrSb, but the central nonlinearity claim is undersupported and the 'field simulation' framing overreaches until the authors connect their constrained configurations to an actual field path. the 4 major comments →

arxiv 2607.29646 v1 pith:UJD2FQZ6 submitted 2026-07-31 cond-mat.str-el cond-mat.mtrl-sci

Study of the Anomalous Hall effect by tuning the spin orientation in the Altermagnetic material CrSb

Sreedevi Chintalapudi , Upasana Agrawal , Suvadip Das This is my paper
classification cond-mat.str-el cond-mat.mtrl-sci PACS 72.15.Gd71.15.Mb
keywords anomalous Hall effectaltermagnetismCrSbBerry curvaturespin orientationtopological Hall effectfirst-principles DFTWannier interpolation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper targets a common experimental assumption: that the anomalous Hall conductivity (AHC) scales linearly with net magnetization, so any deviation from linearity is attributed to an exotic topological Hall effect. By computing the intrinsic AHC of the altermagnet CrSb for several constrained spin orientations—coplanar, canted at 45 and 135 degrees, and collinear—the authors find a clearly nonlinear AHC-versus-magnetization relation. They also find nonzero AHC in two of three zero-net-moment configurations. The intended takeaway is that altermagnets can violate the linear rule through their band structure alone, without invoking topological spin textures. If correct, this challenges the routine interpretation of nonlinear Hall signals in compensated magnets.

Core claim

The central assertion is that in CrSb, a compensated altermagnet, the intrinsic anomalous Hall conductivity does not vary linearly with net magnetization. The support comes from first-principles calculations of the Berry-curvature contribution to AHC for four nonzero-moment configurations (coplanar, 45-degree canted, 135-degree canted, and collinear) and three zero-moment configurations (antiparallel spins along a, b, and c). The computed AHC values plotted against magnetization fall on a curve that is not a straight line, and two of the three antiferromagnetic configurations give nonzero AHC. The paper concludes that the linear AHC-M relation, while valid for single-domain ferromagnets, can

What carries the argument

The central object is the intrinsic anomalous Hall conductivity, obtained from the Berry curvature via the Kubo formula. The tuning mechanism is the constrained spin orientation of the Cr sublattices: the paper fixes the moment directions in DFT calculations without an explicit Zeeman term, then constructs maximally localized Wannier functions and integrates the Berry curvature over a dense 200x200x200 k-mesh to extract the intrinsic AHC for each configuration. This machinery isolates the band-geometric contribution to the Hall response as a function of spin orientation and net moment.

Load-bearing premise

The calculated spin configurations fix the Cr moments' directions and magnitudes without including a Zeeman coupling to a real external field, so these constrained states may not match the field-tuned states an experiment actually measures.

What would settle it

Measure the anomalous Hall resistivity as a function of magnetization in a single-domain CrSb crystal; if the data fall on a straight line through the origin, the claimed nonlinearity is not realized in practice. Alternatively, a first-principles calculation that includes an explicit Zeeman field and finds a linear AHC-M relation would undermine the claim.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Experimental reports of a topological Hall effect in CrSb or similar altermagnets must be re-examined, because the band structure alone can produce nonlinear Hall signals.
  • The linear AHC-magnetization scaling assumed for ferromagnets is not transferable to compensated magnetic classes such as altermagnets.
  • Nonzero AHC at zero net magnetization means altermagnets can generate Hall voltages without an applied field, a useful property for spintronics.
  • The orientation-dependent AHC (antiparallel along a, b, or c) suggests that the direction of the staggered magnetic moment could be read out electrically.
  • All computed nonlinearity comes from the intrinsic Berry-curvature contribution, so extrinsic scattering mechanisms need not be invoked to explain the deviation.

Where Pith is reading between the lines

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

  • A direct experimental test could settle the claim: measure the anomalous Hall resistivity versus magnetization in a single-domain CrSb crystal; a strictly linear scaling would contradict the constrained-moment result.
  • The constrained-moment approach neglects field-induced changes in the magnitude of the Cr moments and any Zeeman-induced band changes; a full field-dependent calculation may restore a different scaling in the regime accessed by experiments.
  • The same methodology could be applied to other altermagnetic candidates (e.g., MnTe, RuO2) to assess whether nonlinear AHC-M is a generic altermagnetic feature or specific to CrSb.
  • If the conclusion is right, existing topological Hall effect assignments in compensated magnets may need to be revisited, as the residual term could be an intrinsic band-geometric effect rather than a signature of real-space topology.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper reports a comprehensive first-principles DFT plus Wannier-interpolation study of the altermagnetic compound CrSb, covering spin- and orbital-resolved band structures, phonon dispersions with participation-ratio decomposition, Berry curvature and Fermi-surface maps, slab surface states, and anomalous Hall conductivity (AHC) for several constrained noncollinear and collinear magnetic configurations. The central scientific claim is that the AHC of CrSb does not depend linearly on the net magnetization, based on a four-point plot (Fig. 8) of AHC versus magnetization for coplanar, 45°-canted, 135°-canted, and collinear parallel configurations, together with three zero-net-moment configurations (Fig. 7). The authors argue that this nonlinearity means deviations from linear Hall scaling in altermagnets should not be automatically interpreted as a topological Hall effect. The abstract and conclusion further state that these constrained calculations 'simulate the effect of external fields.'

Significance. If quantitatively established, the claim would be a useful caution for magnetotransport analyses in altermagnets and similar compensated magnets, where deviations from a linear AHC-versus-magnetization relation are often attributed to topological Hall physics. The paper uses standard, non-empirical methodology: PBE DFT, maximally localized Wannier functions, WannierBerri with a dense 200×200×200 mesh for Berry curvature, and WannierTools for surface states; this is a strength. The phonon and electronic-structure characterization of CrSb is a useful reference dataset. However, the central evidence is presented only as a schematic four-point plot with no numerical AHC values, no convergence tests, and no field-realistic treatment, so the main conclusion is not yet established to the standard expected for a journal publication.

major comments (4)
  1. [Section III, final paragraph and Fig. 8] The central claim—that AHC does not depend linearly on magnetization—rests entirely on Fig. 8, which is a four-point plot with no numerical values, no error bars, and no stated convergence data. The reader cannot verify the magnitude of the nonlinearity, the sign of the AHC, or the sensitivity to technical choices (Wannier disentanglement window, k-mesh density, smearing). A table listing σ_xy for each constrained configuration, the corresponding net moment, and the Wannier/k-mesh parameters is required, together with at least one convergence check. As written, the manuscript's own phrase 'suggestive' is an accurate but insufficient endorsement of the headline conclusion.
  2. [Section III, paragraph beginning 'In the final part' and Abstract] The abstract states that the constrained calculations 'simulate the effect of external fields,' but no Zeeman term or external-field Hamiltonian is introduced. The spin directions are imposed by constraint with fixed moment magnitudes; therefore the four configurations in Fig. 6 and the three in Fig. 7 are not connected by a physical field-driven path. In a real field sweep, the canting angle is determined by exchange/anisotropy versus Zeeman energy, and the local moment magnitude can also change; both can modify the Berry curvature and AHC. The computed AHC-versus-M curve is thus not the experimental field response. The claim should either be restated as 'for hypothetical constrained spin configurations' or the calculations must include an explicit Zeeman term and a field-continuous sequence of states.
  3. [Section III, Fig. 7 and surrounding text] The three zero-net-moment configurations (spins antiparallel along a, b, and c) are potentially the strongest evidence for nonlinearity, because two of them yield nonzero AHC at M=0. But no AHC values, no symmetry analysis of why the a and b axes give different results from the c axis, and no comparison with the ground-state spin axis are provided. Without these details, the reader cannot determine whether the nonzero zero-M AHC is a robust intrinsic property or an artifact of constraining spins along high-symmetry directions that may not correspond to stable or field-addressable states.
  4. [Section III, Eq. (9) and definition of 'linear'] The manuscript does not operationally define the 'linear dependence' it claims to disprove. If the benchmark is σ_xy = c M (zero intercept), then nonzero AHC at M=0 already disproves it; but experimental Hall analysis often allows an intercept or uses a field-dependent M(H) path. If the benchmark is a general linear relation σ_xy = c M + d, the four-point Fig. 8 cannot rule out linearity with d≠0, and the text conflates 'proportional to M' with 'linear in M.' The target hypothesis should be stated precisely, and the AHC-M data should be tested against the relevant functional forms.
minor comments (6)
  1. [Section IV] The text says 'Section III details the findings ... whereas in Section III, we delineate the conclusions'; the conclusions are in Section IV.
  2. [Section III, final paragraph] The cross-reference 'from the four configurations in Fig. 5 have been displayed in Figure 7' is wrong: the configurations are in Fig. 6 and the AHC-versus-M plot is in Fig. 8.
  3. [Fig. 5 caption] The caption lists (a) S_x, (b) S_x, (c) S_x, but the text says the panels show S_x, S_y, and S_z. The caption should be corrected.
  4. [Section II, Eq. (9)] In the Kubo expression for σ_xy, the matrix elements contain v_x in both positions; one should be v_y. This is likely a typo since the formula is not subsequently evaluated.
  5. [Section III, Wannier interpolation paragraph] The text reports a 200×200×200 mesh but gives no information on the Wannier frozen/fitting energy windows, the number of Wannier functions and projectors, or the interpolation quality; these are standard details needed for reproducing the AHC.
  6. [Section V and various] Minor typos include 'ellmann–Feynman' (Hellmann–Feynman), 'aotoms' in Fig. 7 caption, 'WannierBeeri' for WannierBerri, and 'eprformance' in Section IV.

Circularity Check

0 steps flagged

No circularity found: the AHC-vs-M nonlinearity is a direct first-principles output, not a fitted or self-referential result.

full rationale

The derivation chain is self-contained. The central claim that AHC does not depend linearly on magnetization is obtained from first-principles DFT plus Wannier interpolation: the Kubo/Berry-curvature expressions in Eqs. (9)-(12) define sigma_xy, and Figs. 6-8 report sigma_xy at the Fermi level for distinct constrained spin configurations. No parameter is fitted to the target quantity, and no equation is defined in terms of the outcome being predicted. The nonlinearity is a computed consequence of the band structure rather than an input assumption. The constrained-spin methodology (without an explicit Zeeman term) raises a physical-validity question about whether these configurations represent a real field sweep, but that is not circularity: the calculation would be circular only if the AHC values or the nonlinear relation were inserted by hand, which they are not. The cited ZrZn2 work [55] is acknowledged as a similar study, but it is not by the present authors and is not used as the proof of the CrSb result; the CrSb claim rests on the authors' own calculations. No load-bearing self-citation, uniqueness-import, or ansatz-smuggling step can be identified. Therefore the appropriate finding is no significant circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The central claim rests on the validity of DFT-PBE and the Berry-curvature treatment of AHC, plus the key modeling assumption that fixing spin directions is equivalent to field-tuning. No new particles, forces, or conserved quantities are introduced. The only user-chosen computational knob reported indirectly is the Wannier construction window, whose value is not disclosed.

free parameters (1)
  • Wannier disentanglement window (frozen/fitting window)
    The paper states that convergence of the Wannier function minimum spread is crucial (Section III) but does not report the disentanglement window or the number/character of the Wannier orbitals used. The AHC values and thus the nonlinearity conclusion depend on this choice.
axioms (5)
  • domain assumption Kohn-Sham DFT with the PBE exchange-correlation functional accurately describes the electronic structure and magnetic properties of CrSb.
    All electronic-structure and AHC results rely on PBE (Section III); no Hubbard U or hybrid corrections are applied, and the paper does not test sensitivity to the functional.
  • domain assumption The intrinsic anomalous Hall conductivity is fully captured by the Berry-curvature expression, and extrinsic contributions (skew scattering, side jump) are negligible.
    Section II derives the intrinsic AHC via Kubo/Berry curvature and omits dissipative terms. For a metallic altermagnet, extrinsic contributions may be non-negligible, but the paper does not estimate them.
  • domain assumption Constrained spin configurations with fixed moment magnitudes represent the states realized when an external field tunes the magnetization.
    Section III describes constraining spin moments along specific directions without including a Zeeman term. The AHC-vs-M relation is computed for these artificial configurations, not for a Hamiltonian with an actual magnetic field.
  • standard math The Kubo/Berry-phase formula is the correct quantum-mechanical description of the anomalous Hall effect.
    Eqs. (9)-(12) of Section II restate the standard Kubo-Greenwood and Berry-curvature formulas used throughout the field.
  • domain assumption CrSb crystallizes in the P6_3/mmc space group with the altermagnetic spin symmetry [E||H] + [C2||AH].
    The paper adopts this structure and symmetry from prior literature (Refs. [30-34]) without re-deriving it.

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read the original abstract

Recent development in the field of altermagnetism, and increased demand for the search of applications of anomalous hall effect have ushered in a new era for novel quantum phases in materials. Quantum materials previously anticipated to be scientifically predictable have unfolded novel properties that brought them into the spotlight. These manifestations have led us to rethink our understanding of existing classification of magnetic materials and preexisting notions about anomalous hall effect in the light of topologically nontrivial phases of matter. One such recent de- velopment lies in the novel class of alter-magnetic materials with prospect for quantum computing. In this article, we delineate the spin and orbital resolved electronic spectrum, mode-decomposed phonon dispersion relations, geometrical berry curvature and topological surface states and their implications on anomalous Hall conductivity in the promising altermagnetic compound CrSb. We further utilize first principles calculations coupled with computationally efficient maximally localized wannier states of numerous magnetic configurations of the altermagnet to simulate the effect of external fields and elucidate the fact that the linear behaviour of anomalous hall conductivity with magnetization does not necessarily hold true for all magnetic classes, such as altermagnets.

Figures

Figures reproduced from arXiv: 2607.29646 by Sreedevi Chintalapudi, Suvadip Das, Upasana Agrawal.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

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Reference graph

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