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REVIEW 3 major objections 4 minor 61 references

Spin-polarized injection into CrSb produces anomalous and nonlinear Hall effects that gold contacts do not.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.5

2026-07-10 19:21 UTC pith:GUD5YPWU

load-bearing objection Solid contact-controlled AHE/NLHE data on CrSb with a real orientation-dependent slope flip; the joint bulk+surface mechanism is plausible but still under-constrained by length-scale controls. the 3 major comments →

arxiv 2607.07334 v1 pith:GUD5YPWU submitted 2026-07-08 cond-mat.mes-hall

Spin-polarized electron transport for the altermagnet CrSb

V.D. Esin , D.Yu. Kazmin , A.V. Timonina , N.N. Kolesnikov , E.V. Deviatov This is my paper
classification cond-mat.mes-hall PACS 73.40.Qv71.30.+h
keywords altermagnetCrSbanomalous Hall effectnonlinear Hall effectspin injectiontopological surface statesBerry curvature dipolebow-tie hysteresis
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.

CrSb is a centrosymmetric altermagnet whose bulk spectrum has alternating spin splitting but zero net magnetization, and which is also reported to host topological surface states. Without spin-orbit coupling one would not expect a conventional anomalous Hall effect, and centrosymmetry forbids a Berry-curvature-dipole nonlinear Hall effect. The experiment shows that both effects appear clearly when charge current is injected from ferromagnetic nickel contacts into a single-crystal CrSb flake, and both are absent for non-magnetic gold contacts on otherwise identical samples. The anomalous Hall loops are bow-tie shaped and reverse slope when the Hall-bar orientation is rotated by 90 degrees on the same flake. The authors interpret the sign inversion and bow-tie shape as the joint action of bulk altermagnetic spin texture and spin-polarized surface states, and take the hysteretic nonlinear Hall signal as evidence of a finite Berry curvature dipole under spin injection. The result therefore supplies a transport signature of the dual altermagnetic-plus-topological character of CrSb that is visible only when the injected carriers are spin polarized.

Core claim

In single-crystal CrSb flakes, spin-polarized injection from nickel contacts produces a first-harmonic anomalous Hall voltage with bow-tie hysteresis and an orientation-dependent sign of the Hall slope, together with a second-harmonic nonlinear Hall voltage that is likewise hysteretic; both responses are absent for gold contacts. The authors attribute these signals to the interplay of alternating bulk altermagnetic spin splitting and spin-polarized topological surface states, implying a finite Berry curvature dipole under spin injection.

What carries the argument

Spin-polarized current injection from ferromagnetic Ni contacts into CrSb, which generates charge imbalance between counter-propagating topological surface states and couples them to the bulk altermagnetic spin texture, thereby activating both the anomalous Hall response and a Berry-curvature-dipole nonlinear Hall response.

Load-bearing premise

The macroscopic Hall voltages (measured across tens of micrometers) come from spin-polarized topological surface states of CrSb rather than from local remagnetization or spin accumulation confined near the nickel contacts.

What would settle it

A control experiment that maps the Hall voltage versus contact separation or that independently measures the spin-injection length in these flakes; if the anomalous and nonlinear signals collapse to the contact vicinity rather than remaining finite at 20–80 µm, the surface-state interpretation fails.

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

If this is right

  • Transport detection of altermagnetic and topological character in CrSb requires deliberate spin injection and cannot be read from ordinary gold-contact Hall measurements.
  • The sign of the anomalous Hall slope on a single crystal becomes a directional probe of the bulk altermagnetic spin texture once carriers are spin polarized.
  • A hysteretic second-harmonic Hall voltage under spin injection can be used as a practical indicator of Berry curvature dipole in centrosymmetric altermagnets.
  • Room-temperature Néel ordering of CrSb makes the same contact geometry a candidate platform for spintronic devices that exploit surface-bulk coupling.

Where Pith is reading between the lines

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

  • If the surface-state interpretation is correct, similar spin-injection Hall protocols should work on other altermagnetic candidates that host topological surface bands, providing a rapid screening tool before ARPES.
  • The orientation-dependent slope reversal suggests that patterned multi-terminal devices on a single flake could electrically map the crystallographic axes of the altermagnetic spin splitting.
  • Because the nonlinear Hall signal tracks nickel remagnetization, the same geometry may allow electrical readout of contact magnetization without an external magnetometer.

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

3 major / 4 minor

Summary. The manuscript reports first-harmonic anomalous Hall effect (AHE) and second-harmonic nonlinear Hall effect (NLHE) in thick single-crystal CrSb flakes contacted by ferromagnetic Ni leads. AHE appears as bow-tie hysteresis loops of width ~0.3 T whose slope reverses sign when the Hall-bar current orientation is rotated by 90° on the same flake; both AHE and NLHE are absent in otherwise identical devices with non-magnetic Au contacts. The authors attribute the orientation-dependent AHE and the field-hysteretic NLHE to the joint action of k-dependent bulk altermagnetic spin splitting and spin-polarized topological surface states that become charge-imbalanced under spin injection, thereby generating a finite Berry curvature dipole.

Significance. Observation of spin-injection-activated AHE and NLHE in the centrosymmetric, low-SOC altermagnet candidate CrSb would be a useful experimental benchmark for the interplay between altermagnetic bulk bands and topological surface states. The work supplies several clean experimental controls: null results with Au contacts, two orthogonal Hall geometries on the identical flake, V2ω_xy ≫ V2ω_xx, quadratic current dependence of the second harmonic, and comparable hysteresis widths for first and second harmonics. These elements make the raw transport phenomenology worth reporting even if the microscopic assignment remains provisional.

major comments (3)
  1. Discussion §IV asserts that the observed AHE (and by extension NLHE) is macroscopic (20–80 µm probe spacing) because topological surface states are protected, while canted-Néel AHE is dismissed as confined to a bulk spin-relaxation length near the Ni contacts. No independent measurement of spin-injection efficiency, spin-diffusion length, or surface-state contribution is provided for these flakes. Given that the Hall resistivity is only ~0.5 µΩ·cm, the hysteresis width matches typical Ni remagnetization, and both signals vanish for Au contacts, a local interface or contact-region origin remains equally consistent with the data. A length-scale control (e.g., variable probe spacing or thickness series) is required before the joint bulk-surface interpretation can be regarded as established.
  2. Fig. 2 and accompanying text claim that the sign inversion of the AHE slope between the two orthogonal current orientations on the same flake is diagnostic of k-dependent bulk altermagnetic magnetization. In a conventional Hall geometry the Lorentz (or anomalous) slope is fixed by carrier sign and B direction and should be independent of in-plane current rotation; the observed inversion is therefore interesting. However, the manuscript does not quantify possible geometric admixture, current-path asymmetry, or contact-resistance anisotropy that can appear when the current line is rotated 90° on a thick, irregularly shaped flake. Without such a control or a quantitative estimate of the expected altermagnetic anisotropy, the sign inversion cannot yet be taken as direct evidence of alternating bulk spin splitting.
  3. The absolute scale of the first-harmonic signal (maximum Hall resistance ~5 mΩ, voltages of order 10 nV after multi-curve averaging) is extremely small. While the Au-contact nulls and the reproducibility across samples are reassuring, the paper should explicitly address whether residual thermoelectric, inductive, or capacitive pick-up could survive the lock-in and averaging procedures at this level, especially given that the second-harmonic voltages are three orders of magnitude larger under mA excitation.
minor comments (4)
  1. Fig. 1(b) caption and main text should state the precise crystallographic orientation of the flake relative to the two Hall-bar axes; without it the claimed link to altermagnetic k-space anisotropy remains schematic.
  2. The longitudinal resistance is quoted as ~0.5 Ω but no corresponding Rxx(B) or magnetoresistance data are shown; a brief panel would help the reader judge homogeneity and possible current-path effects.
  3. Several sentences in the Introduction and Discussion contain awkward phrasing or missing articles (e.g., “the principle origin”, “we corfirm”); a careful language edit would improve readability.
  4. References to the group’s own prior transport papers on related materials are numerous; a few additional independent ARPES or theoretical citations on CrSb surface states would strengthen the topological claim.

Circularity Check

1 steps flagged

Experimental Hall signals are independent measurements; only the interpretive link of orientation-dependent AHE slope sign inversion to bulk altermagnetic magnetization rests on a same-group self-citation.

specific steps
  1. self citation load bearing [Section IV (Discussion), paragraph on AHE sign inversion]
    "For other directions, AHE is affected by periodic bulk altermagnetic magnetization 58, which leads to the direction-dependent sign of the AHE slope in Fig. 2. In this case, the bow-tie hysteresis loops in Fig. 2 is the result of interaction 55,56 between the bulk alternating spin splitting and the surface spin polarization from the topological surface states 43,44."

    The central interpretive claim that the observed Hall-slope sign inversion (same flake, same B) arises from k-dependent bulk altermagnetic spin polarization is justified solely by citation 58, an arXiv preprint by the same authors. No independent measurement of that bulk magnetization texture is supplied in the present work; the citation therefore functions as an unverified premise that converts the raw sign-change observation into the “joint-effect” conclusion.

full rationale

The paper is an experimental transport study. The primary results (first-harmonic AHE with bow-tie hysteresis and slope sign change upon 90° Hall-bar rotation, second-harmonic NLHE quadratic in current and hysteretic in field, both present only with Ni contacts and absent with Au) are direct lock-in voltage measurements on the same flakes; they do not arise from any fitted parameter, self-defined quantity, or uniqueness theorem. No equation equates a claimed prediction to an input by construction. The sole mild circularity is interpretive: the Discussion attributes the unexpected sign inversion of the AHE slope (same carriers, same B direction) to “periodic bulk altermagnetic magnetization” via citation 58 (arXiv:2512.11344 by the identical author group). That citation is not independently re-verified here and is load-bearing for the “joint-effect” narrative, yet the raw observations remain self-contained against the Au-contact controls. Technique self-cites (contact fabrication, thermoelectric-exclusion geometry) are ordinary and non-load-bearing. Overall circularity is therefore low.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The central claim rests on domain assumptions imported from prior ARPES/theory (CrSb is centrosymmetric altermagnet with negligible SOC, hosts Weyl/topological surface states) and on experimental premises about spin injection from Ni versus Au. No free parameters are fitted to produce the Hall curves. No new particles or forces are invented; the ‘joint bulk+surface’ mechanism is an interpretive construct, not a new entity with independent mass or charge.

axioms (5)
  • domain assumption CrSb is a centrosymmetric altermagnet (P6₃/mmc) with alternating bulk spin splitting and negligible spin-orbit coupling, so ordinary bulk AHE and NLHE are symmetry-forbidden without spin injection.
    Stated in Introduction and Discussion; grounded in cited ARPES (Reimers et al., Yang et al.) and theory, not re-derived here.
  • domain assumption CrSb hosts spin-polarized topological (Weyl) surface states that can carry dissipationless or protected surface transport over macroscopic contact separations.
    Invoked in Discussion to explain why AHE appears over 20–80 µm; based on cited works (Li et al. 2025, Lu et al. 2025), not measured on these flakes.
  • domain assumption Ferromagnetic Ni contacts inject spin-polarized carriers into CrSb while Au contacts do not, and the observed hysteresis width tracks Ni remagnetization.
    Core experimental premise for attributing both AHE and NLHE to spin injection; supported by Au null controls but not by independent spin-polarization measurement at the interface.
  • domain assumption The chosen Hall-bar contact geometry excludes thermoelectric admixture in second-harmonic measurements.
    Stated in Samples and Technique with reference to prior group work (Shvetsov et al. 2019); not re-validated with new control data in this manuscript.
  • ad hoc to paper Sign inversion of the Hall slope between two orthogonal current orientations on the same flake reflects k-dependent bulk altermagnetic magnetization rather than geometry or carrier-type change.
    Central interpretive step in Discussion; no quantitative band-structure calculation for the measured flake orientations is provided.

pith-pipeline@v1.1.0-grok45 · 17838 in / 3275 out tokens · 45506 ms · 2026-07-10T19:21:07.499446+00:00 · methodology

0 comments
read the original abstract

We experimentally investigate spin-polarized electron transport for the centrosymmetric altermagnet CrSb, which is known to reveal both altermagnetic and topological features. We demonstrate pronounced first-harmonic anomalous and second-harmonic non-linear Hall effects for a single-crystal CrSb flake with ferromagnetic nickel contacts, while both effects can not be seen for the reference samples with non-magnetic gold ones. For the anomalous Hall effect, we demonstrate bow-tie hysteresis loop in Hall voltage, which is usually ascribed to surface spin textures in magnetic materials. The slope of the Hall curve changes a sign for two orientations of the Hall-bar contact configuration for the same sample, i.e. for the same sign of the charge carriers. We interpret the observed sign inversion and bow-tie hysteresis as the joint effect of the alternating bulk spin splitting and spin-polarized topological surface states in CrSb. The pronounced non-linear Hall effect with hysteresis in magnetic field confirms finite Berry curvature dipole under injection of spin-polarized electrons, i.e. the topological features for the altermagnetic candidate CrSb.

Figures

Figures reproduced from arXiv: 2607.07334 by A.V. Timonina, D.Yu. Kazmin, E.V. Deviatov, N.N. Kolesnikov, V.D. Esin.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color online) (a) The X-ray powder diffraction pat [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (Color online) Anomalous Hall effect for the CrSb [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: In principle, CrSb exhibits low magnetocrys [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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