Unconventional anomalous Hall effect in hexagonal polar magnet Y_3Co_8Sn_4

Afsar Ahmed; Aftab Alam; Anis Biswas; Arnab Bhattacharya; I. Das; Jyoti Sharma; Tukai Singha; Yaroslav Mudryk

REVIEW 4 major objections 7 minor 68 references

Unconventional anomalous Hall effect in hexagonal polar magnet Y_3Co_8Sn_4

T0 review · 4 major / 7 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The hexagonal polar magnet Y3Co8Sn4 shows an unconventional anomalous Hall effect that switches from positive below its magnetic transition to negative above it, which the authors trace to Weyl points near the Fermi level.

desk verdict Interesting experimental finding undermined by a broken nonmagnetic-phase AHC calculation and an unvalidated scaling subtraction. read the letter →

arxiv 2502.03452 v1 pith:772WIYKH submitted 2025-02-05 cond-mat.mtrl-sci

Afsar Ahmed , Jyoti Sharma , Arnab Bhattacharya , Anis Biswas , Tukai Singha , Yaroslav Mudryk , Aftab Alam , I. Das This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords unconventionalanomalousHalleffectWeylpointsBerrycurvaturetopologicalspintexturepolarmagnetY3Co8Sn4conductivityferrimagnetism

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 reports that the noncentrosymmetric hexagonal magnet Y3Co8Sn4 shows an unconventional anomalous Hall effect (UAHE) whose sign is positive below the magnetic ordering temperature $T_C \approx 53$ K and negative above it. This two-stage, sign-changing behavior is rare, and the authors argue that it arises from intrinsic Berry curvature produced by Weyl points lying near the Fermi level in both the low-temperature ferrimagnetic phase and the high-temperature nonmagnetic phase, with an additional contribution from a topological magnetic spin texture below $T_C$. The claim matters because it identifies a single material in which momentum-space topology and real-space magnetism cooperate to produce a transport signature that can be switched by temperature, and it points to the $R_3$Co$_8$Sn$_4$ polar family as a promising setting for spintronic and topological-transport studies. The paper supports the claim with magnetization, resistivity, Hall, and ac-susceptibility measurements together with density-functional calculations of Weyl nodes and anomalous Hall conductivity.

What carries the argument

The argument is carried by the decomposition of the measured Hall resistivity into ordinary, conventional anomalous, and unconventional components, using the scaling form $\rho^{UA}_{xy} = \gamma \rho_{xx}^2 M$ for the unconventional part. The reciprocal-space machinery consists of Weyl points (band degeneracies near the Fermi level that act as sources and sinks of Berry curvature) identified by ab initio band-structure searches in both the FiM2 ferrimagnetic and nonmagnetic phases, with the intrinsic anomalous Hall conductivity computed by integrating Berry curvature over the Brillouin zone. The TYJ scaling analysis of the conventional anomalous Hall conductivity is used to establish that the intrinsic Karplus-Luttinger mechanism dominates, and the field dependence of ac susceptibility is used as evidence for the topological spin texture that contributes below $T_C$.

What would settle it

Measure the Hall resistivity of a single crystal of Y$_3$Co$_8$Sn$_4$ at temperatures above and below $T_C$ while tuning the field, and check whether the extracted $\rho^{UA}_{xy}$ follows $\gamma \rho_{xx}^2 M$ across a wider field range; in particular, if $\rho^{UA}_{xy}$ remains nonzero after full field polarization well beyond the critical field, the scaling assumption fails. Alternatively, perform Lorentz transmission electron microscopy or small-angle neutron scattering to see whether the topological spin texture presumed below $T_C$ actually exists and vanishes at the field where the anomaly disappears.

Watch

Extended reading notes

Core claim

The central discovery is that Y$_3$Co$_8$Sn$_4$ exhibits an unconventional anomalous Hall resistivity component $\rho^{UA}_{xy}$ that is positive below $T_C$ and negative above $T_C$, with the magnitude evolving in opposite ways in the two temperature ranges. The authors attribute the effect to reciprocal-space topology: density-functional calculations find five pairs of Weyl points close to the Fermi level in the stable planar ferrimagnetic (FiM2) state below $T_C$ and four pairs in the nonmagnetic phase above $T_C$, and the computed anomalous Hall conductivities (about 168 S/cm and 154 S/cm respectively) agree with measured values. Field-dependent ac susceptibility shows peaks suggestive of topologically nontrivial spin textures, so a real-space contribution is also invoked. On the paper's account, this is the first observation of the two-stage sign-changing UAHE in a noncentrosymmetric magnet, and the mechanism differs between the magnetically ordered and nominally nonmagnetic regimes.

Load-bearing premise

The reported sign-changing unconventional Hall signal rests on assuming that the extra Hall term follows the magnetic-scattering form $\rho^{UA}_{xy} = \gamma \rho_{xx}^2 M$ and disappears above a critical field; if that form is wrong or the term persists, the sign change could be an artifact of the subtraction.

Editorial extensions

If this is right

Y$_3$Co$_8$Sn$_4$ is a rare single material whose unconventional Hall signal changes sign across its magnetic transition, implying that the dominant topological mechanism switches with temperature.
The computed Weyl points near the Fermi level in both phases make the polar magnet family $R_3$Co$_8$Sn$_4$ a platform for studying Weyl-mediated transport without requiring an applied field.
The intrinsic Berry-curvature contribution to the anomalous Hall effect is substantial even above $T_C$, where only short-range ferromagnetic correlations survive.
The sign and magnitude of the UAHE could serve as a sensitive probe of field-induced changes in magnetic topology in this compound.

Reading between the lines

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

If the Weyl-point energy positions control the sign of $\rho^{UA}_{xy}$, then chemical substitution or pressure that shifts the Fermi level should flip or tune the sign-change temperature; this is a testable consequence the paper does not pursue.
Direct imaging of the spin texture (for instance by Lorentz microscopy or small-angle neutron scattering) could separate the real-space and reciprocal-space contributions, since the momentum-space part should survive even where no texture is detected.
The resemblance to EuCd$_2$As$_2$'s two-stage UAHE suggests the sign-changing behavior may be a general property of polar magnets with Weyl nodes, not an accident of this one compound.
Because the extraction assumes $\rho^{UA}_{xy} = \gamma \rho_{xx}^2 M$ vanishes above a critical field, independent verification of that scaling on a single crystal would substantially strengthen the claim.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear colleague,

What you should know first: this paper is an honest experimental report with a load-bearing interpretation that doesn't hold together. The authors find a Hall resistivity component in Y3Co8Sn4 that changes sign from positive below TC to negative above TC, and they attribute it to Weyl nodes. The observation itself, if real, is a genuine new data point for the UAHE literature. The DFT work is thorough on the magnetic side: they converge to a planar ferrimagnetic ground state, find five pairs of Weyl points near EF, and compute an intrinsic AHC of ~168 S/cm that matches the low-T experimental value. That part is credible.

The soft spots are serious. First, the nonmagnetic-phase AHC calculation reports 154 S/cm at EF for a state with zero net moment. Under time-reversal symmetry, the intrinsic AHC must vanish. Either the calculation is actually spin-polarized (which would mean it is not the nonmagnetic phase) or there is a numerical error. The authors use this number to claim agreement with the 60 K data, so this is not peripheral.

Second, the explanation for the negative UAHE above TC is internally inconsistent. The text says random FM domains produce Weyl nodes with opposite chiralities in different domains, and that positive and negative contributions cancel, explaining the lack of spontaneous UAHE. But they claim to observe a field-induced negative UAHE in exactly that temperature range. How the field breaks the cancellation is never explained.

Third, the extraction of ρUA_xy is a scaling subtraction: they fit (ρxy/H) vs (ρxx^2 M/H) above some Hc, assume the unconventional term vanishes there, and treat the residual as UAHE. This is a standard recipe, but here the fit is done where M is small and nearly linear, so the fitted coefficients are very sensitive to noise and to the choice of Hc. No error bars and no independent check of the assumption are given. The sign-changing signal could be an artifact.

So: worth a serious referee because the experimental phenomenon, if confirmed, is interesting and the DFT has solid parts. As written, the mechanism is not established and the nonmagnetic AHC result looks wrong. I would send it to review rather than desk-reject, with clear instructions to address the TRS issue and to validate the subtraction. My own verdict is skeptical until those are fixed.

Referee Report

4 major / 7 minor

Summary. This manuscript reports a combined transport, magnetization, ac-susceptibility, and density-functional-theory study of the hexagonal polar magnet Y3Co8Sn4 (space group P63mc). The authors claim an unconventional anomalous Hall effect (UAHE) whose sign is positive below the magnetic transition (TC ≈ 53 K) and negative above it, which they attribute to Weyl-point Berry curvature in the ferrimagnetic ground state and in the high-temperature nonmagnetic phase, with a possible contribution from topological spin textures inferred from field-dependent ac susceptibility. The DFT study identifies a planar ferrimagnetic (FiM2) ground state with 3.3 µB/f.u. and five pairs of near-Fermi Weyl points, giving an intrinsic anomalous Hall conductivity (AHC) of about 168 S/cm, compared with a measured value of about 160 S/cm at 30 K. The authors also report four Weyl pairs in a nonmagnetic calculation and an AHC of 154 S/cm, which they compare with the 60 K experimental value of 136 S/cm.

Significance. If the sign-changing dual UAHE were established experimentally, Y3Co8Sn4 would be a notable addition to the small family of compounds showing two-stage unconventional Hall behavior in a noncentrosymmetric magnet, with plausible relevance to spintronics. The DFT portion is a genuine strength: Table I documents relative energies and moments for all tested collinear configurations, Table II lists coordinates, types, energies, and chiralities of the Weyl points, and the computed intrinsic AHC (168 S/cm) and planar FiM2 ground state are consistent with the low-temperature magnetization data; these are concrete, falsifiable, first-principles predictions with no fitting to the transport data. However, the central transport claim is built entirely on an unvalidated subtraction residual, the nonmagnetic-phase AHC claim violates time-reversal symmetry, and the proposed high-temperature mechanism contradicts the reported observation; these problems are load-bearing and cannot be fixed by local revision. The transport analysis also contains no error bars anywhere.

major comments (4)

[Results and Discussions, Fig. 2(c)–(f)] The extraction of ρUAxy is self-referential: the linear fit of (ρxy/H) versus (ρxx²M/H) is restricted to fields above a critical field Hc, where ρUAxy is assumed to vanish, and the resulting R0 and γ are then subtracted from the full field range to define ρUAxy as a residual. The manuscript never states the values of Hc, the fitting windows, the number of points per fit, or any measure of fit quality, and no error bars are propagated into ρUAxy or the derived AHC. Above TC, M(H) is small and nearly linear, so ρxx²M/H is almost field-independent; in that regime the slope γ is ill-conditioned, and the reported negative peak in Fig. 2(f) is consistent with a subtraction artifact (for example, slight curvature in M(H) or magnetoresistance anisotropy). Because the dual positive-to-negative UAHE is the central claim and exists only as this residual, the claim is not established without independent validation (e.g., Hc determined from dM/dH or χ′(H), stability of the fit over varied windows, and a full-range global fit that includes a parameterized ρUAxy term).
[Results and Discussions, Figs. 1(e)–(f) and 2(f)] The field range of the reported ρUAxy humps below 14 K coincides with the two anomalies in dM/dH at 60 mT and 0.3 T and with the peak/hump structure in χ′(H). Because the intrinsic AHE depends on the magnetization direction, a field-induced spin reorientation changes ρCAxy in a way that the smooth γρxx²M form cannot represent; the paper does not test whether the extracted ρUAxy is simply the deviation of the intrinsic AHE from linearity in M through these reorientations. This is a concrete, unaddressed alternative explanation for the low-temperature signal.
[Results and Discussions, nonmagnetic-phase DFT paragraph and Fig. S7] The calculated AHC of 154 S/cm at EF for the nonmagnetic phase is incompatible with time-reversal symmetry. In a spin-unpolarized, T-symmetric band structure, Ωn(−k) = −Ωn(k) and the occupation factor is even in k, so the Brillouin-zone integral defining σxy vanishes identically; the equal +/− chirality balance of the reported Weyl pairs, which the authors themselves connect to the Nielsen–Ninomiya theorem, likewise forces the net Berry-curvature contribution to zero. The claimed agreement between the computed NM AHC (154 S/cm) and the measured 60 K value (136 S/cm) therefore cannot be a physical comparison; either the NM calculation is not actually spin-unpolarized, or the reported AHC is a numerical artifact. The measured above-TC AHC is a field-induced quantity (time reversal broken by the applied field), so a zero-field T-symmetric calculation is not an appropriate reference in any case. This undermines the headline claim of a reasonably large AHC in both phases.
[Results and Discussions, paragraph beginning 'Such observation in the nonmagnetic phase can be understood'] The proposed explanation of the high-temperature behavior is internally inconsistent with the reported observation. The text states that within randomly oriented short-range ferromagnetic domains the positive and negative chirality contributions cancel, 'explaining the lack of spontaneous component of UAHE in NM phase.' A cancellation mechanism predicts a vanishing net UAHE, yet Fig. 2(f) reports a prominent negative ρUAxy peak at 60, 70, and 100 K; the offered mechanism cannot produce the sign-changing behavior it is invoked to explain.

minor comments (7)

[Text near Fig. 2(c)] The sentence 'the intercept of the linearly fitted (ρxy/H) vs (ρ2xxM/H) curves above the critical field (Hc) is nothing but γ' is incorrect as stated: the intercept of that plot is R0 and the slope is γ.
[Table I caption] The caption contains a typo: 'in-pane' should read 'in-plane'.
[Reference [23]] Reference [23] has a garbled author list; it should be formatted as 'M. Hirschberger, S. Kushwaha, Z. Wang, Q. Zhang, S. Liang, C. A. Belvin, B. A. Bernevig, R. J. Cava, N. P. Ong, Nat. Mater. 15, 1161 (2016)'.
[Supplementary Material notice] The Supplementary Material is not posted, yet key validation content (Fig. S3 for the TYJ/power-law analysis, Figs. S6–S7 for the nonmagnetic phase, and Tables ST1–ST2) is essential for checking the claims; the placeholder 'Supplementary URL to be added by journal (2025)' should be replaced before any further review.
[Abstract] The abstract attributes the UAHE partly to topological magnetic texture 'as inferred from the measured field-dependent ac susceptibility,' but the χ′(H) features vanish by 16 K (Fig. 1(f)) while the claimed UAHE persists to 100 K; the manuscript itself states that the mechanism above 14 K is different, so the abstract overstates the texture contribution.
[General transport analysis] No error bars or measurement uncertainties are given for ρxy, ρUAxy, σCAxy, R0, γ, or the TYJ parameters; for a quantity defined as a subtraction residual this is not merely cosmetic and should be addressed in any revision.
[Fig. 2(c) and Fig. 2(f)] Quantitative reading of the key figures is difficult: the vertical offsets in Fig. 2(c) and the tiny insets (i)–(ii) of Fig. 2(f) make the temperature evolution of the anomaly hard to verify; enlarging the inset panels and labeling the offset values would help.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the UAHE is extracted via a model-dependent residual subtraction, and the DFT AHC calculation is independent of the transport data.

full rationale

The central observational claim is the two-stage unconventional anomalous Hall effect, obtained by writing rho_xy = R0*H + gamma*rho_xx^2*M + rho_UA_xy, fitting gamma above Hc where rho_UA_xy is assumed to vanish, and then defining rho_UA_xy as the residual. This is a model-dependent extraction rather than a circular derivation: the sign-changing part of the residual is not assumed in the fit, and the paper does not use the residual to set any parameter in the first-principles calculation. The DFT searches for Weyl points and computes the AHC (about 168 S/cm below T_C and about 154 S/cm above) independently of the transport data; the experimental AHC values are compared with these results, not fitted to them, so the first-principles claim is self-contained. The inference of topological magnetic texture from ac-susceptibility anomalies and the comparison with EuCd2As2 are analogical interpretations, not circular reductions. The only same-group citation, Ref. [24], appears in a general introductory sentence and is not load-bearing. The main weakness identified by the skeptic is the untested assumption that rho_UA_xy vanishes above Hc; if that assumption fails, the reported residual can be an artifact. That is a validity and reliability concern about the subtraction, not an equivalence of input and output, so it does not constitute circularity. The placeholder supplementary-material reference is a completeness issue, not a circularity issue.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central results rest on standard DFT approximations and on two phenomenological scaling decompositions whose regimes of validity are not independently established. The nonmagnetic-phase AHC comparison introduces a symmetry inconsistency. No new particles, fields, or conserved quantities are introduced.

free parameters (4)

γ (RS skew-scattering coefficient) = not quoted numerically
Obtained from the intercept of a linear fit of (ρxy/H) versus (ρxx^2 M/H) above the critical field Hc; the value is not stated in the text.
a and b (TYJ scaling parameters) = b ∼ 160 S/cm
Linear fit of σCA_xy versus σxx^2; b is the extracted intrinsic-plus-side-jump AHC, compared to DFT.
Critical field Hc = not explicitly defined
The field above which the unconventional Hall term is assumed to vanish; the choice affects the extracted ρUA_xy.
Carrier density n0 = ~10^22 cm^-3
From the slope of ρxy(H) at low field; used to separate the ordinary Hall term.

assumptions (4)

domain assumption Kohn-Sham DFT with the PBE exchange-correlation functional correctly describes the electronic structure and magnetism of Y3Co8Sn4.
Used for all band structures and AHC calculations; no Hubbard U or hybrid functional is tested, and the approximate nature of PBE is not discussed.
domain assumption The scaling relations ρUA_xy = γρxx^2 M (RS) and the TYJ decomposition σCA_xy = -aσxx0^-1 σxx^2 - b apply to this material.
These forms are taken from earlier literature and are assumed valid for the polycrystalline sample without independent justification.
ad hoc to paper The field-polarized state above Hc has no unconventional Hall contribution, so the linear fit isolates ordinary and conventional AHE.
The paper assumes the topological contribution vanishes above Hc, but provides no independent check of this assumption.
ad hoc to paper The nonmagnetic DFT calculation represents the paramagnetic phase above TC and its zero-field AHC can be compared to field-induced experimental AHC.
A nonmagnetic calculation preserves time-reversal symmetry, which should make AHC vanish; the comparison to finite-field data is questionable.

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Cite this review

Pith. "Pith review of Unconventional anomalous Hall effect in hexagonal polar magnet Y_3Co_8Sn_4." pith.science (2026). https://pith.science/paper/772WIYKH

@misc{pith2026250203452,
  author       = {Pith},
  title        = {Pith review of: Unconventional anomalous Hall effect in hexagonal polar magnet Y_3Co_8Sn_4},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/772WIYKH}},
  note         = {Machine review of arXiv:2502.03452}
}

read the original abstract

We report a rare realization of unconventional anomalous Hall effect (UAHE) both below and above the magnetic transition temperature (T_C) in a hexagonal noncentrosymmetric magnet Y_3Co_8Sn_4, using a combined experimental and ab-initio calculations. Occurrence of such UAHE is mainly attributed to the reciprocal (KS) topology (i.e. the presence of topological Weyl points at/near the Fermi level), along with some contribution from the topological magnetic texture, as inferred from the measured field-dependent ac susceptibility. The effect of UAHE on the measured transport behavior however evolves differently with temperature above and below T_C, suggesting different physical mechanism responsible in the two phases. A unique planar ferrimagnetic ordering is found to be the most stable state with ab-plane as the easy plane below TC, as observed experimentally. The simulated net magnetization and the moment per Co atom agrees fairly well with the measured values. A reasonably large AHC is also observed in both the phases (above and below and T_C) of the present compound, which is again not so ubiquitous. Our results underscore the family of R_3Co_8Sn_4 (R= rare earth) polar magnets as a compelling backdrop for exploring the synergy of topological magnetism and non-trivial electronic bands, pivotal for spintronic applications.

Figures

Figures reproduced from arXiv: 2502.03452 by the authors.

**Figure 2.** FIG. 2. For Y [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** (a) shows the schematic of unit cell with lowest energy planar FiM2 magnetic ordering (only Co-atoms are displayed for clarity) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Pith tools

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