Anisotropic transport properties and topological Hall effect in the annealed kagome antiferromagnet FeGe

Chenchao Xu; Chenfei Shi; Hanjie Guo; Jiajun Ma; Jialu Wang; Jianhui Dai; Jiaxing Liao; Jin-Ke Bao; Shixun Cao; Wenhe Jiao

REVIEW 3 major objections 4 minor 61 references

Anisotropic transport properties and topological Hall effect in the annealed kagome antiferromagnet FeGe

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Annealed FeGe shows a field-induced topological Hall effect in its canted antiferromagnetic state.

desk verdict New transport data on annealed FeGe; the topological Hall claim needs a multiband check before it will persuade. read the letter →

arxiv 2412.18824 v1 pith:ATWXUJEC submitted 2024-12-25 cond-mat.str-el

Jiajun Ma , Chenfei Shi , Yantao Cao , YuWei Zhang , Yazhou Li , Jiaxing Liao , Jialu Wang , Wenhe Jiao

show 6 more authors

Hanjie Guo Chenchao Xu Shixun Cao Jianhui Dai Jin-Ke Bao Yuke Li

This is my paper · ORCID

classification cond-mat.str-el PACS 71.45.Lr73.43.–f73.23.–b75.50.Ee

keywords kagomemagnetFeGechargedensitywavetopologicalHalleffectspin-floptransitionanisotropictransportcantedantiferromagnetBerryphase

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 studies annealed single crystals of the kagome antiferromagnet FeGe, where a charge density wave (CDW) forms inside the A-type antiferromagnetic order. It reports that transport is strongly anisotropic: with current in the ab-plane, resistivity shows a first-order anomaly near the CDW transition at 108 K and is about three times larger than the c-axis resistivity. The central claim is that when the magnetic field is applied along the c-axis, a spin-flop transition around 6 T transforms the canted double-cone antiferromagnetic state into a noncollinear spin texture, and that this texture produces a large topological Hall effect below the CDW transition. The evidence is a broad hump in the Hall resistivity above the spin-flop field that does not track magnetization, reaches $0.2\,\mu\Omega\,\text{cm}$, and disappears when the field is rotated toward the ab-plane.

What carries the argument

The load-bearing object is the field-induced spin-flop transition in the canted double-cone antiferromagnetic state of FeGe. With field along the easy c-axis and current in the ab-plane, the spin flop rotates the magnetic moments, yielding the basal-plane moment component $M_{ij}=M_0\sin(-\mathbf{q}\cdot\mathbf{r}_i+\phi)$ and a noncollinear spin texture. The mechanism that converts this texture into a Hall voltage is the real-space Berry phase from finite scalar spin chirality $\chi_{ijk}=\mathbf{S}_i\cdot(\mathbf{S}_j\times\mathbf{S}_k)$; subtracting the normal and anomalous terms via $\rho_{yx}=R_0\mu_0 H+\rho^A_{yx}+\rho^T_{yx}$ isolates the topological contribution $\rho^T_{yx}$ as the hump in $\Delta\rho_{yx}$ above $H_{sf}$.

What would settle it

Measure Hall and longitudinal resistivity on the same annealed FeGe crystal using a six-contact geometry with the magnetic field rotated through the c-axis, and fit the full conductivity tensor with a two-band model that includes field-dependent mobilities and magnetoresistance. If the fitted ordinary terms alone reproduce the $0.2\,\mu\Omega\,\text{cm}$ hump above $H_{sf}$, the topological Hall assignment is falsified; if the hump persists only when the spin texture is noncollinear and vanishes when the field approaches the ab-plane, the Berry-phase reading survives.

Watch

Extended reading notes

Core claim

For $\mathbf{H}$ along the c-axis and current along the ab-plane, the Hall resistivity $\rho_{yx}(H)$ is linear at low fields, defining a normal Hall coefficient $R_0$ with carrier density near $6\times10^{22}\,\text{cm}^{-3}$. Above the spin-flop field $H_{sf}\sim 6\,\text{T}$ and below $T_{cdw}=108\,\text{K}$, the authors observe a broad hump in $\Delta\rho_{yx}=\rho_{yx}-R_0\mu_0 H$ that grows with decreasing temperature and reaches about $0.2\,\mu\Omega\,\text{cm}$. This hump is strongest in the canting antiferromagnetic phase below $T_{cant}=56\,\text{K}$, weakens between $T_{cant}$ and $T_{cdw}$, and is absent above $T_{cdw}$; the authors attribute it to the real-space Berry phase acquired by electrons moving through the field-induced noncollinear spin texture of the canted double-cone AFM state. In contrast, with current along the c-axis and field in the ab-plane, no spin-flop transition appears and the Hall resistivity bends at low fields but is discussed in terms of two-band or alternative mechanisms. The paper also constructs a magnetic phase diagram in which $H_{sf}$ jumps from about $6\,\text{T}$ to $9\,\text{T}$ across $T_{cdw}$, indicating that the CDW order stabilizes the low-field magnetic texture responsible for the effect.

Load-bearing premise

The paper treats the low-field linear slope of the Hall resistivity as a field-independent normal Hall coefficient $R_0$, so every deviation above the spin-flop field is assigned to anomalous or topological terms; if ordinary magnetoresistance or multiband conduction also bends $\rho_{yx}(H)$ in the same way, the topological Hall effect claim collapses.

Editorial extensions

If this is right

If the topological Hall interpretation is correct, the observed hump is a direct electrical signature of a field-induced noncollinear magnetic state, so Hall measurements can be used to track the spin-flop reconstruction in FeGe.
The phase diagram shows $H_{sf}$ jumps from about $6\,\text{T}$ below $T_{cdw}$ to about $9\,\text{T}$ above it, implying the CDW order pins or stabilizes the low-field magnetic texture; tuning $T_{cdw}$ should tune the field range of the topological Hall effect.
The angle-dependent data, where $\rho_{yx}$ vanishes once $\mathbf{H}$ is rotated more than roughly $60^\circ$ from the c-axis, give a practical geometric criterion for when the chiral texture contributes; the same criterion can be tested in other canted antiferromagnets.
Because the effect only appears below $T_{cant}$, where the cone half-angle of the canted double-cone structure grows, the magnitude of the topological Hall signal should correlate with the cone angle across the magnetic phase diagram.

Reading between the lines

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

A sharp test follows from the Berry-phase picture: the topological Hall resistivity should be proportional to the sample-averaged scalar spin chirality, so a combined neutron-diffraction and Hall measurement sweeping through the spin-flop region could confirm the mechanism or force a multiband explanation.
The same subtraction logic, applied to the c-axis current data, classifies the low-field bending in $\rho_{zx}$ as non-topological; if the two-band fit fails at 5 K because of strong scattering, a Corbino or six-terminal geometry could separate the intrinsic Hall term from contact and magnetoresistance artifacts.
The authors leave open why $\rho_{zx}(T)$ changes sign below $T_{cant}$; an editorial guess is that the sign reversal marks a crossover from CDW-dominated to spin-texture-dominated transport, which could be tested by doping or pressure that suppresses $T_{cdw}$ without fully killing the canting.

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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,

The one line you need: this is a solid new dataset on annealed FeGe, but the topological Hall effect claim is not yet backed by the analysis. The paper is worth engaging with, not because the THE is established, but because the anisotropic transport and phase diagram are new and the interpretation exposes a common methodological problem.

What's actually new: this is the first transport work on annealed FeGe crystals. The authors see anisotropic resistivity (ρ_ab roughly 3× ρ_c), a resistivity loop at the CDW transition that is a good sign of first-order character, a spin-flop transition that shifts with temperature but leaves T_cdw alone, and angle-dependent Hall data that kill the THE when H is rotated away from c. Those results look internally consistent and should survive contact with experiment.

The soft spot is exactly where the stress-test puts it. The THE is defined as the residual after subtracting R0 μ0 H, with R0 from the low-field slope of the same curve. That is only legitimate if R0 is field-independent. Here, ρ_ab shows 43% MR at 14 T and 2 K, which suggests the carriers' mobility or density may well be field dependent. The authors' own two-band fit for the perpendicular geometry fails to explain both MR and Hall simultaneously, and the conclusion explicitly says the phenomenon 'remains unclear' and could be explained by two-band effects, loop currents, or Dirac points. That sentence alone should temper the abstract's claim. I don't think the stress-test is overstating; if anything, it is generous—the in-plane geometry gets no multiband check at all. So the THE hump may just be a multiband artifact.

Minor things: no error bars on transport, no data release, and the paper uses 'topological Hall' in the abstract while the conclusion hedges to near-falsification.

This is for a serious referee, but the referee should treat the THE as an interpretation to be tested, not a result. I would accept it for peer review, because the material and data are timely and the field can use a clear example of why baseline subtraction alone is not enough. I would not cite it as evidence for THE in its current form.

Referee Report

3 major / 4 minor

Summary. The manuscript reports anisotropic resistivity, magnetization, and Hall-effect measurements on annealed FeGe single crystals, with current along the ab-plane and c-axis and magnetic fields in both orientations. The authors observe a first-order resistivity loop at the CDW transition T_cdw ≈ 108 K, a field-induced spin-flop transition near H_sf ≈ 6 T for H ∥ c, and a broad hump in the Hall resistivity at high fields in the canted antiferromagnetic phase below T_cant. This hump is interpreted as a topological Hall effect arising from noncollinear spin textures during the spin-flop process. The paper also reports a strongly nonlinear Hall resistivity for the perpendicular configuration (I ∥ c, H ∥ ab) and a magnetic field–temperature phase diagram.

Significance. If the topological Hall interpretation were established, the paper would provide a interesting platform for studying the interplay of charge order, magnetism, and topology in a kagome antiferromagnet. The raw transport and magnetization data appear internally consistent, and the observation of a first-order CDW signature in resistivity, a field-induced spin-flop transition, and strong transport anisotropy is a useful experimental contribution. The symmetrized Hall measurements and the comparison of in-plane and out-of-plane configurations are well conceived, and the phase diagram in Fig. 5 is a useful summary. The central claim, however, rests on a subtraction procedure whose assumptions are not validated for the key configuration, and the authors themselves list alternative explanations in the conclusion. The strength of the paper therefore depends on whether the topological Hall effect claim can be either supported by additional analysis or appropriately weakened.

major comments (3)

[Section III, Fig. 3(c)-(d)] The topological Hall effect extraction is not robust. The residual is defined as Δρ_yx = ρ_yx − R0 μ0 H, where R0 is obtained from a low-field linear fit to the same ρ_yx(H) curves. This assumes a field-independent normal Hall coefficient and no anomalous or magnetoresistance-induced nonlinearity. The paper's own data show a 43% in-plane magnetoresistance at 14 T and 2 K (Fig. 2(b)), so a field-dependent multi-band normal Hall contribution can mimic the observed hump. No two-band or multiband analysis is presented for the H ∥ c, I ∥ ab configuration that is the basis of the central claim, in contrast to the analysis for the perpendicular geometry in Fig. 4(c). To support the topological Hall claim, the authors should either provide an independently determined baseline (for example, a two-band fit constrained by the measured magnetoresistance, or a high-field slope check) or reframe the finding as a nonlinear Hall effect of unresolved origin.
[Section IV (Conclusion)] The conclusion explicitly states that the phenomenon 'remains unclear, which may be explained by various models including the two-band modal, the charge order with a chiral loop-current effect or the topological Dirac points.' This statement undercuts the abstract's unqualified claim of having 'discovered' a topological Hall effect. The situation is made more serious by Fig. 4(c), where the authors show that a two-band model fails for the perpendicular geometry and invoke skew/side-jump scattering or charge-order-induced unconventional Hall effects as alternatives. A falsifiable distinction between the topological spin-texture mechanism and these alternatives is needed, or the central claim must be revised to a more cautious statement about a field-induced nonlinear Hall effect with several candidate mechanisms.
[Section III, Fig. 3(e)] Plotting Δρ_yx as a function of magnetization Mc does not by itself establish a topological origin. Since Mc is nearly linear above H_sf (Fig. 1(g)), a field-dependent normal Hall contribution or a multiband effect will also produce a nonlinear Δρ_yx(Mc) trace. A quantitative comparison with the scalar spin chirality expected from the canted double-cone structure, or an independent probe of the spin texture (for example, field-dependent neutron scattering or a control measurement on a non-canted sample), would be required to distinguish the topological mechanism from the alternatives the authors themselves list.

minor comments (4)

[Captions of Figs. 3(a) and 3(e)] The caption of Fig. 3(a) refers to magnetization data plotted in 'figure 4(a)', and the caption of Fig. 3(e) refers to 'figure 2f'; these should be corrected to the actual magnetization panels in Fig. 1.
[Section I (Introduction)] The phrase 'anomalous/topopolocal Hall effect/Nernst effect' contains a typo; 'topopolocal' should be 'topological'.
[Throughout] The term 'two-band modal' appears twice (Section III and Section IV) and should be 'two-band model'.
[Section II (Experimental Details)] The description of the two rectangular pieces could be clarified by stating which piece was used for the in-plane and which for the out-of-plane transport measurements, and by giving the contact geometry for the Hall measurements.

Circularity Check

1 steps flagged · score 3.0 of 10

The topological Hall signal is obtained by subtracting a linear baseline fitted to the same Hall curves, so the 'discovery' is the residual of that fit; the topological attribution is not independently derived.

fitted input called prediction [Section III, Figs. 3(a)-3(d); equation ρ_yx = R0 μ0 H + ρ^A_yx + ρ^T_yx]
"at a low temperature of 2 K, ρyx(H) follows nearly a linear field-dependent at low fields, denoting Hall coefficient R0 ... We thus can obtain THE and AHE by subtracting the normal Hall effect at low fields using the formula: ρyx = R0µ0H + ρA yx + ρT yx. The obtained ∆ρyx = ρyx−R0µ0H (Fig. 3(c) and 3(d)) shows a broad hump at high fields, reaching a maximum of 0.2 µΩ cm."

R0 is read off from the low-field slope of the very same ρyx(H) curves that are then converted into Δρyx. By construction Δρyx is the nonlinear residual after a linear baseline, so the broad hump is not an independent prediction but the complement of the fitted term.

full rationale

The paper contains no self-citation chain: the sample-growth citation [34] is methodological, and the physical inputs (CDW transition, canted AFM structure) come from external prior work. The only step with a self-referential construction is the THE extraction: R0 is fitted to the low-field portion of the same Hall curves that are then transformed into Δρ_yx, so the reported hump is the residual of that fit. This is a mild form of fitted-input-called-prediction, because the hump's existence is empirical and its temperature and angular dependence provide independent content, but the assignment of the residual specifically to a topological Hall effect is an assumption not excluded by the paper's own two-band analysis. This warrants a low-intermediate circularity score rather than a finding of no circularity.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim of a topological Hall effect depends on a fitted normal Hall baseline and on prior structural and magnetic characterizations. No new particles or mediators are introduced. The materials preparation follows previously reported methods from the same group. The key unverified assumptions are the persistence of the canted double-cone state under field and the dominance of real-space Berry-phase contributions over ordinary multiband magnetotransport.

free parameters (2)

Normal Hall coefficient R0(T) = Not tabulated; inferred from low-field slope, approximately 1e-10 m3/C at 2 K
Used in the equation rho_yx = R0*mu0*H + rho_A_yx + rho_T_yx to subtract the normal Hall contribution. It is fitted from the low-field part of the same rho_yx(H) curves, so the extracted topological Hall signal depends directly on this fit.
Two-band model parameters (carrier densities and mobilities) = Not specified in the text
Used to fit the out-of-plane Hall conductivity in Fig. 4(c). The authors report that the fit seriously violates the data at 5 K, indicating that these parameters are not sufficient to describe the full field range.

assumptions (3)

domain assumption The canted double-cone antiferromagnetic structure with a basal-plane moment component Mij = M0 sin(-q dot ri + phi) persists under applied fields and is the source of noncollinear spin texture.
The topological Hall interpretation relies on this magnetic structure, which is taken from prior neutron diffraction studies (Refs. [7] and [20]). It is not re-measured in this work.
domain assumption A scalar spin chirality produces a real-space Berry phase that dominates the nonlinear Hall signal after subtracting a linear normal Hall term.
This is the standard theory of the topological Hall effect, assumed without direct measurement of spin chirality or Berry curvature in this material.
domain assumption The low-field Hall slope is purely from a single-band normal Hall effect.
The determination of R0 from the low-field linear region assumes no anomalous or multiband contribution at those fields, which is not independently verified.

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Cite this review

Pith. "Pith review of Anisotropic transport properties and topological Hall effect in the annealed kagome antiferromagnet FeGe." pith.science (2026). https://pith.science/paper/ATWXUJEC

@misc{pith2026241218824,
  author       = {Pith},
  title        = {Pith review of: Anisotropic transport properties and topological Hall effect in the annealed kagome antiferromagnet FeGe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ATWXUJEC}},
  note         = {Machine review of arXiv:2412.18824}
}

abstract

Electron correlation often gives birth to various orders in quantum materials. Recently, a strongly correlated kagome antiferromagnet FeGe is discovered to undergo a charge density wave transition inside the A-type antiferromagnetic state, providing an opportunity to explore the interplay between charge order and magnetism. Here, we reported the observation of anisotropic resistivity and Hall effect, along with a topological Hall effect, in the annealed FeGe crystals. As the current flows along the \emph{ab}-plane, the temperature dependence of $\rho_{ab}$ exhibits a distinct resistivity loop related to a first-order transition at $T_{cdw}$. The applied magnetic fields do not alter $T_{cdw}$ but can induce a spin-flop transition at $H_{sf}$. Consequently, a field-induced large topological Hall effect is observed in the canting antiferromagnetic (CAFM) state below $T_{cant}$, which is possibly attributed to the non-trivial spin texture during the spin-flop process. Whereas, as current is parallel to \emph{c}-axis, both the field-induced transitions in $\rho_{c}$ and $\chi_{c}$ disappear. Instead, the Hall resistivity in the annealed FeGe significantly exhibits a deviation from the linear field-dependent. These findings provide valuable insight into revealing the interplay among magnetism, charge order and topology in the kagome magnets.

Figures

Figures reproduced from arXiv: 2412.18824 by the authors.

**Figure 1.** (d)-1(e). In other words, CDW in FeGe is robust against magnetic fields but the canting magnetic order can be tuned by fields. Such large divergency in ρab and ρc suggests the different scattering mechanism for in-plane and out-of-plane transports. The anisotropic behaviors of transports are also observed in the magnetization data in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** FIG. 2. (a)Resistivity [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. For [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. The Hall resistivity [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Magnetic Phase diagram of FeGe and contour plot [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

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