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Three-dimensional nature of anomalous Hall conductivity in YMn6Sn6-xGax, x ~ 0.55

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper establishes that the intrinsic anomalous Hall conductivity in YMn6Sn5.45Ga0.55 is fully three-dimensional and comparable to TbMn6Sn6, ruling out 2D Chern gaps as its origin in the RMn6Sn6 family.

desk verdict The experimental case against 2D Chern-gap AHE in this kagome family is strong; the quantitative in-plane intrinsic value is weakened by an unvalidated fit and a large DFT mismatch. read the letter →

arxiv 2411.12134 v1 pith:BBZIOMCD submitted 2024-11-19 cond-mat.mtrl-sci

Hari Bhandari , Zhenhua Ning , Po-Hao Chang , Peter E. Siegfried , Resham B. Regmi , Mohamed El. Gazzah , Albert V. Davydov , Allen G. Oliver
show 3 more authors
Liqin Ke Igor I. Mazin Nirmal J. Ghimire
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords kagomelatticeanomalousHalleffectYMn6Sn6CherngapspinfluctuationsBerrycurvatureferrimagnetempiricalscalingrelation
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

This paper sets out to settle where the anomalous Hall effect comes from in the RMn6Sn6 kagome metals, using Ga-doped YMn6Sn6 as a testbed. It argues that the intrinsic anomalous Hall conductivity is comparable to that of TbMn6Sn6 (fitted 121 S/cm out-of-plane versus 140 S/cm) yet persists with larger magnitude (310 S/cm) when the magnetic field lies in the kagome plane, where a 2D Chern gap cannot contribute. A sympathetic reader would take this as experimental evidence that the intrinsic Hall response is a three-dimensional property of the ferrimagnetic band structure rather than a topological 2D gap feature. The paper also reads its three-term scaling law as confirmed, since the fitted spin-fluctuation term remains nonzero in a compound that contains no Tb, implying fluctuating Mn moments are sufficient to generate it.

What carries the argument

The central device is the empirical scaling law $\sigma_{xy}=a\sigma_{xx}^2+d/\sigma_{xx}+c$, which extends the standard Berry-phase-plus-impurity scaling by adding a term that grows when $\sigma_{xx}$ is small, i.e., at high temperature. Fitting the measured Hall conductivity to this law partitions it into impurity scattering ($a\sigma_{xx}^2$), spin-fluctuation scattering ($d/\sigma_{xx}$), and an intrinsic part $c$ identified with the Berry-curvature integral. The second device is geometric: comparing the $B\parallel[001]$ configuration, in which a 2D Chern gap would contribute, with the $B\parallel[120]$ configuration, in which it cannot, converts the scaling fit into a dimensional test of the intrinsic AHC.

What would settle it

A first-principles calculation that includes explicit Ga disorder at the experimental composition and still predicts the in-plane intrinsic AHC far below the fitted 310 S/cm — the paper's own rigid-band estimate is 36.76 S/cm — would undercut the claim that the fitted in-plane value is intrinsic; if the discrepancy persists with disorder properly treated, the three-dimensionality conclusion is not supported by the data.

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Extended reading notes

Core claim

The central claim is that, in YMn6Sn5.45Ga0.55, the intrinsic (Berry-curvature) contribution to the anomalous Hall conductivity is fully three-dimensional. Fitting the Hall conductivity over 1.8–300 K to $\sigma_{xy}=a\sigma_{xx}^2+d/\sigma_{xx}+c$ gives $c=121$ S/cm for $B\parallel[001]$, comparable to the TbMn6Sn6 value of 140 S/cm, and $c=310$ S/cm for $B\parallel[120]$. Because a 2D Chern gap, an energy gap in a two-dimensional band with a nonzero Chern number, would contribute only in the out-of-plane geometry, the large in-plane value shows that the Hall conductivity does not originate from those gaps. The nonzero fitted $d$ in a Tb-free compound is presented as confirmation that the extra $d/\sigma_{xx}$ term is a spin-fluctuation contribution universal to the RMn6Sn6 family.

Load-bearing premise

Everything rests on the empirically fitted three-term formula $\sigma_{xy}=a\sigma_{xx}^2+d/\sigma_{xx}+c$ being the true decomposition of the measured Hall conductivity; the 'intrinsic' values are fitted coefficients $c$, not directly measured quantities, and the paper gives no microscopic derivation of the $d$ term. If that decomposition is wrong, the comparison with TbMn6Sn6 and the 3D claim lose their quantitative footing.

Editorial extensions

If this is right

  • If the decomposition is correct, the 2D Chern gap near 130 meV above the Fermi energy cannot be the source of the measured AHC, because the in-plane geometry does not couple to it yet gives a comparable or larger intrinsic value.
  • The three-term scaling law should replace the two-term law when extracting intrinsic AHC from spin-fluctuating magnets; the two-term law would misattribute the high-temperature $d/\sigma_{xx}$ contribution.
  • The nonzero fitted $d$ in YMn6Sn5.45Ga0.55, a compound without Tb, means the spin-fluctuation term is not tied to a specific rare earth and is expected throughout the RMn6Sn6 ferrimagnets.
  • Ga substitution is a practical route to a saturable kagome ferromagnet whose in-plane and out-of-plane AHC can both be measured in a 9 T laboratory magnet, as opposed to TbMn6Sn6 whose in-plane saturation would require much higher fields.
  • First-principles calculations for YMn6Sn6 reproduce the same 3D pattern—appreciable $\sigma_{xy}$ for out-of-plane magnetization and appreciable $\sigma_{yz}/\sigma_{zx}$ for in-plane magnetization—consistent with the experimental conclusion.

Reading between the lines

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

  • Editorial inference: if the fitted $c$ values are true Berry-curvature contributions, the larger in-plane value (310 vs 121 S/cm) implies the dominant Berry-curvature hot spots are most active when the moment lies in the kagome planes; this could be checked with momentum-resolved Berry-curvature maps for in-plane magnetization.
  • Editorial inference: the $d/\sigma_{xx}$ term is empirical and not microscopically derived here; a controlled test would tune the Mn moment fluctuation amplitude (by pressure, doping, or field) and check that the fitted $|d|$ tracks the fluctuation strength rather than the residual resistivity.
  • Editorial inference: the same two-geometry protocol applied to a compound whose Fermi level genuinely sits in a 2D Chern gap should show a strong out-of-plane intrinsic AHC and a near-zero in-plane one; finding such a compound would sharpen the contrast the paper draws.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This manuscript reports a combined experimental and first-principles study of the ferromagnetic kagome compound YMn6Sn5.45Ga0.55. Single crystals are characterized by X-ray diffraction, magnetization, resistivity, angular magnetoresistance, and Hall-effect measurements in two field geometries (B||[001] and B||[120]). The anomalous Hall conductivity (AHC) is fitted to the empirical scaling law σxy = aσxx^2 + d/σxx + c, yielding intrinsic AHC values c = 121 S/cm (out-of-plane) and c = 310 S/cm (in-plane). DFT Berry-curvature calculations give σxy = 77.62 S/cm and σzx = 36.76 S/cm for the assumed hole doping. The authors conclude that the intrinsic AHC is three-dimensional and comparable in magnitude to TbMn6Sn6, and that the d/σxx term reflects spin fluctuations.

Significance. The paper addresses a topical debate: whether the anomalous Hall effect in RMn6Sn6 kagome magnets arises from 2D Chern gaps or from a bulk 3D Berry-curvature distribution. The experimental observation of a large in-plane AHC in a Tb-free compound is a direct and convincing falsification of a purely 2D Chern-gap origin, independent of any scaling analysis. The DFT AHC calculation is a state-of-the-art parameter-free integration of Berry curvature over a dense k mesh using Wannier interpolation, with Ueff fixed from earlier work. The paper also provides an independent test of the scaling law proposed in Ref. [12]. However, the quantitative intrinsic AHC values, especially the in-plane value, rest on an empirical three-parameter decomposition that is not yet adequately justified.

major comments (3)
  1. [III.E, Table III, Eq. (2)] The central quantitative claim in the abstract—that the intrinsic AHC in YMn6Sn5.45Ga0.55 is comparable in magnitude to TbMn6Sn6 and is fully three-dimensional—relies on the fitted coefficient c in Eq. (2): c = 121 S/cm for B||[001] and c = 310 S/cm for B||[120] (Table III). No uncertainty estimates for a, d, or c are provided, and no alternative decomposition forms are tested. The in-plane fitted value is nearly an order of magnitude larger than the authors' own DFT value σzx = 36.76 S/cm (Sec. III.F, Fig. 8), and the brief caveat about rigid-band shifts does not quantify whether this discrepancy is consistent with the experimental c. Because this discrepancy directly affects the comparison to TbMn6Sn6 (140 S/cm), the manuscript needs either a robust statistical and systematic error analysis of the fit, or a reformulation of the quantitative claims.
  2. [III.E, Eq. (2)] The three-term scaling relation σxy = aσxx^2 + d/σxx + c is introduced as an empirical formula from Ref. [12]; the d/σxx term is attributed to spin fluctuations, but no microscopic derivation or independent verification is given in the present manuscript. The nonzero d observed in the Tb-free Y166-Ga is suggestive, but the manuscript does not analyze whether the magnitude and temperature dependence of d correlate with any spin-fluctuation measure, nor does it report goodness-of-fit statistics. Since this empirical relation is the only basis for extracting the intrinsic c values, its lack of a derivation or falsifiable test is a load-bearing assumption for the paper's quantitative conclusions.
  3. [III.D, III.E] The scaling law in Eq. (2) is written for a single longitudinal conductivity σxx, but the material is strongly anisotropic in transport: σ[001]/σ[100] > 2 over the whole temperature range (Sec. III.D, Fig. 3(b)). For the in-plane Hall geometry (B||[120], I||[100]), the Hall resistivity is converted to conductivity using σzx = -ρzx/(ρxxρzz), and the scaling plot in Fig. 6(c) uses the same σxx = 1/ρxx as in the out-of-plane case. The manuscript does not justify that the isotropic form of Eq. (2) remains valid for an anisotropic conductor, or that the appropriate longitudinal conductivity for the in-plane geometry is σxx rather than some combination of σxx and σzz. Without such a justification, the in-plane fitted c = 310 S/cm is not a reliable intrinsic AHC.
minor comments (5)
  1. [Section I] The text gives the composition as 'YMn6Sn6.45Ga0.55' in the sentence 'selected one particular composition YMn6Sn6.45Ga0.55 for the study'; this should be 'YMn6Sn5.45Ga0.55' to match the abstract and the rest of the paper.
  2. [Section III.E and Fig. 6] The Hall conductivity component is denoted inconsistently; the text defines σzx (and Table III uses |σxz|), while the caption of Fig. 6 labels it |σA_xz|. Please use a single convention throughout.
  3. [Section III.E] The statement 'σxx = 1/ρxx' is imprecise; in the in-plane geometry the longitudinal resistivity is ρxx but the Hall-conductivity conversion uses both ρxx and ρzz, so the notation should distinguish the tensor components.
  4. [Fig. 4 caption] The calculation is described as performed for 'YMn6Sn5Ga', but the experimental composition is YMn6Sn5.45Ga0.55; please clarify whether the calculation uses an ordered x=1 model and whether this is intended.
  5. [Section IV] The conclusion contains a duplicated word: 'may be important for not only for the large family' should read 'for not only the large family'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the scaling relation is tested on new data, and the 3D claim is independently supported by direct in-plane Hall measurements and first-principles Berry-curvature calculations.

full rationale

The paper's central claims are not circular. Equation (2), sigma_xy = a sigma_xx^2 + d/sigma_xx + c, was proposed in the authors' prior work [12], but here it is applied to a new compound, YMn6Sn5.45Ga0.55, with independently measured transport data. Fitting this equation to new data and finding that it works is an external test of the phenomenological form, not a self-citation bootstrap. The fitted coefficient c is labeled the intrinsic AHC, but that identification follows from the prior Crépieux-Bruno framework and is not defined in terms of the conclusion being drawn. The 'fully three-dimensional' claim rests on direct observation of a large anomalous Hall signal in the in-plane geometry (Fig. 6) and on DFT calculations that yield nonzero in-plane AHC components by integrating Berry curvature (Eq. 4, Fig. 8); the DFT and experiment are independent lines of evidence. The quantitative discrepancy for sigma_zx (36.76 S/cm calculated vs. 310 S/cm fitted) is acknowledged, which shows the comparison is not forced. The only hand-set parameter, U_eff = 0.6, was fixed in earlier work on YMn6Sn6, not fitted to the target AHC values. No equation in the paper reduces to another by construction, no fitted parameter is renamed as an independent prediction, and no load-bearing conclusion is imported solely from a self-citation. The paper is self-contained against external structural, magnetic, transport, and DFT benchmarks; the scaling-law concern is a question of model validity, not circularity.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claim rests on an empirical three-term fit (with coefficients c, a, d as fitted parameters), a rigid-band shift for doping, and standard DFT assumptions. No new physical entities are introduced. The fitting parameters and U_eff are the main ingredients the reader pays for that are not derived from first principles.

free parameters (7)
  • intrinsic AHC c (out-of-plane B) = 121 S/cm
    Extracted from a three-parameter fit to Eq. 2 of measured |sigma_A_yx| versus sigma_xx. This is the central claimed intrinsic value.
  • intrinsic AHC c (in-plane B) = 310 S/cm
    Extracted from a three-parameter fit to Eq. 2 of measured |sigma_A_zx| versus sigma_xx. Used to claim 3D nature.
  • impurity-scattering coefficient a = 3.25e-8 S/cm (out-of-plane), 1.89e-7 S/cm (in-plane)
    Fitted coefficient in Eq. 2, interpreted as defect scattering.
  • spin-fluctuation coefficient d = -1.75e5 S^2/cm^2 (out-of-plane), -5.41e5 S^2/cm^2 (in-plane)
    Fitted coefficient in Eq. 2, interpreted as the spin-fluctuation contribution.
  • U_eff for DFT = 0, 0.6, and 2 eV
    Chosen by hand. U_eff = 0.6 was carried over from prior work on YMn6Sn6 because it best reproduces the magnetic states; the AHC depends on this choice.
  • Fermi-energy shift for Ga doping = -0.037 eV
    Estimated from 0.09 h/Mn hole doping using a rigid-band shift. Used to read theoretical AHC from Fig. 8. The paper cautions that random substitution may invalidate this shift.
  • Exchange couplings J1, J2, J3 = e.g., J1 = -11.9 meV, J2 = -10.6 meV, J3 = 1.5 meV for U_eff = 0.6
    Obtained by least-squares fitting the spin model Eq. 3 to DFT total energies. Used to explain the magnetic transition, not the central AHC claim.
assumptions (5)
  • ad hoc to paper The empirical scaling relation Eq. 2 (sigma_xy = a sigma_xx^2 + d/sigma_xx + c) is the correct decomposition of the measured anomalous Hall conductivity.
    Proposed by the authors in Ref. [12] and applied here without a microscopic derivation; the intrinsic value c and the spin-fluctuation term d are defined by this equation.
  • domain assumption The measured transverse resistivity rho_zx in the in-plane geometry is an intrinsic anomalous Hall response and is adequately described by sigma_zx = -rho_zx/(rho_xx rho_zz).
    The paper assumes the antisymmetrized rho_zx is a genuine Hall component from Berry curvature, not a planar-Hall or other artifact; the formula is stated in Sec. III E.
  • domain assumption Kohn-Sham DFT with PBE+U and the Wannier-interpolated tight-binding Hamiltonian accurately describes the electronic structure and Berry curvature of these compounds.
    Standard method, but U_eff is not determined from first principles.
  • domain assumption The J1-J3 spin Hamiltonian Eq. 3 with exchange couplings fitted to DFT total energies captures the magnetic ground states.
    Used to explain the ferromagnetic stabilization; based on the phase diagram in Ref. [44].
  • domain assumption Rigid-band approximation: Ga substitution only shifts the Fermi energy by -0.037 eV without changing the band structure.
    Used to compare DFT AHC with experiment; the paper explicitly cautions this may be invalid for random substitution.

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Cite this review

Pith. "Pith review of Three-dimensional nature of anomalous Hall conductivity in YMn6Sn6-xGax, x ~ 0.55." pith.science (2026). https://pith.science/paper/BBZIOMCD

@misc{pith2026241112134,
  author       = {Pith},
  title        = {Pith review of: Three-dimensional nature of anomalous Hall conductivity in YMn6Sn6-xGax, x ~ 0.55},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BBZIOMCD}},
  note         = {Machine review of arXiv:2411.12134}
}
abstract

The unique connectivity of kagome lattices gives rise to topological properties, such as flat bands and Dirac cones. When combined with ferromagnetism and a chemical potential near the 2D Dirac points, this structure offers the potential to realize the highly sought-after topological Chern magnetotransport. Recently, there was considerable excitement surrounding this possibility in the ferrimagnetic kagome metal TbMn$_\mathbf{6}$Sn$_\mathbf{6}$. However, density functional theory (DFT) calculations reveal that the 2D Chern gap lies well above the Fermi energy, challenging its relevance in the observed anomalous Hall conductivity. Here, we investigate YMn$_\mathbf{6}$Sn$_\mathbf{5.45}$Ga$_\mathbf{0.55}$, a compound with similar crystallographic, magnetic, and electronic properties to TbMn$_\mathbf{6}$Sn$_\mathbf{6}$. Our findings show that the intrinsic anomalous Hall conductivity in this material, while comparable in magnitude to that in TbMn$_\mathbf{6}$Sn$_\mathbf{6}$, is fully three-dimensional, thus providing experimental evidence that Hall conductivity in this class of materials does not originate from 2D Chern gaps. Additionally, we confirm that the newly proposed empirical scaling relation for extrinsic Hall conductivity is universally governed by spin fluctuations.

Figures

Figures reproduced from arXiv: 2411.12134 by the authors.

Figure 1
Figure 1. FIG. 1 : Crystal structure [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 : Magnetic properties of YMn [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 : Electrical transport properties of YMn [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4 : Calculated angular magnetoresistance. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 : Anomalous Hall effect of YMn [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 : Anomalous Hall effect of YMn [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 : Primitive unit cell used in AHC calculations. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 : Calculated intrinsic anomalous Hall con [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Room temperature quantum metric effect in TbMn6Sn6

    cond-mat.mtrl-sci 2024-11 conditional novelty 7.0 of 10

    TbMn6Sn6 shows strong, field-tunable second-harmonic transport at room temperature, attributed to the quantum metric dipole and Berry curvature dipole.

  2. Giant coercivity and enhanced intrinsic anomalous Hall effect at vanishing magnetization in a compensated kagome ferrimagnet

    cond-mat.str-el 2025-02 conditional novelty 6.0 of 10

    Adding chromium to TbMn6Sn6 produces a near-zero net moment, a coercive field above 14 T, and an increased intrinsic anomalous Hall effect tied to a Fermi-level shift.

  3. Doping-induced Spin Reorientation in Kagome Magnet TmMn6Sn6

    cond-mat.mtrl-sci 2025-05 conditional novelty 5.0 of 10

    Gallium doping gradually reorients magnetism in TmMn6Sn6 from easy-plane to easy-axis, with the reorientation temperature rising until it merges with the magnetic ordering temperature near x=2.

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