pith. sign in

arxiv: 2604.12360 · v1 · submitted 2026-04-14 · ❄️ cond-mat.str-el

Large spontaneous Hall effect arising from collinear antiferromagnetism in Ce₂PtGe₆

Hayata Matsuda , Ruo Hibino , Chihiro Tabata , Koji Kaneko , Nonoka Higa , Takahiro Onimaru , Hiroto Tanaka , Hideki Tou
show 4 more authors
Hitoshi Sugawara Junichi Hayashi Keiki Takeda Hisashi Kotegawa
This is my paper

Pith reviewed 2026-05-10 15:01 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords spontaneous Hall effectantiferromagnetismanomalous Hall conductivityCe2PtGe6collinear orderBerry curvaturespin-orbit coupling
0
0 comments X p. Extension

The pith

A collinear antiferromagnetic order in Ce₂PtGe₆ generates a large spontaneous Hall effect with conductivity reaching 300 Ω^{-1}cm^{-1}.

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

The paper demonstrates that symmetry breaking from a specific antiferromagnetic arrangement can produce a spontaneous Hall effect even when the net magnetization is negligible. Single-crystal neutron experiments establish a collinear structure with propagation vector zero in Ce₂PtGe₆. This leads to an anomalous Hall conductivity of 300 Ω^{-1} cm^{-1}, surpassing values in analogous compounds, which the authors link to platinum's strong spin-orbit coupling acting on the localized moments. A reader would care because it expands the class of materials that can generate Hall responses to include antiferromagnets without the complications of ferromagnetism.

Core claim

Ce₂PtGe₆ exhibits a collinear antiferromagnetic structure with q=0 that breaks the relevant symmetries to induce a spontaneous Hall effect. The anomalous Hall conductivity reaches 300 Ω^{-1}cm^{-1} and is attributed to the large spin-orbit coupling of the Pt atoms combined with the Berry curvatures from the f-moments in the antiferromagnetic configuration. The small net magnetization of approximately 10^{-3} μ_B per Ce confirms the effect originates from the antiferromagnetic order itself.

What carries the argument

The q=0 collinear antiferromagnetic order, which places the system in a magnetic point group that permits a nonzero anomalous Hall conductivity via Berry curvature.

If this is right

  • The anomalous Hall conductivity in this antiferromagnet exceeds that of related compounds with copper or palladium.
  • The large value is enabled by the strong spin-orbit coupling from platinum atoms.
  • The effect arises intrinsically from the antiferromagnetic symmetry breaking rather than extrinsic magnetization.
  • Localized f-electron moments can generate substantial Hall responses when arranged in suitable antiferromagnetic patterns.

Where Pith is reading between the lines

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

  • Similar large spontaneous Hall effects may occur in other cerium-based antiferromagnets containing heavy transition metals.
  • These materials could be used in antiferromagnetic spintronics where the lack of net magnetization reduces unwanted magnetic interactions.
  • Systematic substitution of platinum with other elements would quantify how spin-orbit strength controls the Hall conductivity magnitude.

Load-bearing premise

The small net magnetization of about 10^{-3} μ_B per Ce atom does not meaningfully contribute to the Hall effect, and the observed response is fully explained by the symmetry properties of the collinear antiferromagnetic order.

What would settle it

Observing the spontaneous Hall effect disappear when the antiferromagnetic order is suppressed, for instance by raising temperature above the transition or by applying a magnetic field that alters the magnetic structure, while any magnetization remains small, would confirm or refute the claim.

Figures

Figures reproduced from arXiv: 2604.12360 by Chihiro Tabata, Hayata Matsuda, Hideki Tou, Hiroto Tanaka, Hisashi Kotegawa, Hitoshi Sugawara, Junichi Hayashi, Keiki Takeda, Koji Kaneko, Nonoka Higa, Ruo Hibino, Takahiro Onimaru.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Orthorhombic crystal structure of Ce [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Temperature dependence of magnetic susceptibil [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Temperature dependence of the specific heat per Ce [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Temperature dependence of peak profiles of the mag [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Temperature dependence of the ordered magnetic [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Temperature dependences of electric resistivit [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (c) shows the temperature dependence of anomalous Hall resistivity ρAH, which corresponds to ρyx at zero field. In addition to Ce2PtGe6, the data for Ce2TGe6 (T = Cu and Pd) are also shown for compari￾son [12]. Here, the sign of ρAH was determined from that obtained when the positive magnetic field was reduced to zero. Obviously, the magnitude of ρAH for Ce2PtGe6 is the largest. The sign of ρAH is positive… view at source ↗
read the original abstract

The spontaneous Hall effect, corresponding to a zero-field anomalous Hall effect (AHE), is induced by symmetry breaking associated with ferromagnetism. Studies in recent years, however, have revealed that antiferromagnetic (AFM) states characterized by magnetic point groups that allow ferromagnetism can also break the relevant symmetries and induce AHE without a large net magnetization. Here, we report that the AFM system Ce$_2$PtGe$_6$ exhibits a pronounced spontaneous Hall effect. Single-crystal neutron scattering experiments demonstrate that Ce$_2$PtGe$_6$ exhibits a collinear AFM structure with a propagation vector $q=0$. The small net magnetization of $\sim 10^{-3}$ $\mu_B$/Ce indicates that the observed AHE arises from symmetry breaking inherent to its AFM structure. The anomalous Hall conductivity (AHC) reaches $300$ $\Omega^{-1}$cm$^{-1}$, which exceeds the intrinsic AHC of related compounds such as Ce$_2$CuGe$_6$ and Ce$_2$PdGe$_6$. This large AHC, most likely attributed to the large spin-orbit coupling of the Pt atoms, provides a platform for understanding the interplay between the Berry curvatures and localized $f$-moments with an AFM configuration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper reports a large spontaneous (zero-field) Hall effect in the collinear antiferromagnet Ce₂PtGe₆. Single-crystal neutron scattering establishes a q=0 collinear AFM structure; magnetization measurements show a small net moment of ∼10^{-3} μ_B/Ce. The anomalous Hall conductivity reaches 300 Ω^{-1}cm^{-1}, exceeding values in the related compounds Ce₂CuGe₆ and Ce₂PdGe₆, and is attributed to symmetry breaking inherent to the AFM order together with strong Pt spin-orbit coupling.

Significance. If the central interpretation holds, the work adds a clear experimental example of sizable AHE generated by collinear AFM order without substantial net magnetization, highlighting the role of heavy-element SOC in amplifying Berry-curvature contributions in f-electron systems. The combination of neutron diffraction and transport data on a single-crystal platform is a positive feature and may stimulate further studies of AFM-induced Hall effects.

major comments (3)
  1. [Abstract and results on magnetization and Hall effect] Abstract and magnetization/Hall sections: The claim that the observed AHC of 300 Ω^{-1}cm^{-1} arises solely from AFM symmetry breaking (rather than the small net moment) is load-bearing but unsupported by quantitative bounds. No scaling argument, comparison to ferromagnetic analogs, or estimate of the maximum AHC that could be produced by a 10^{-3} μ_B moment is provided.
  2. [Transport measurements and data analysis] Hall-effect data analysis: The manuscript reports the AHC value without detailing the subtraction of the ordinary Hall component, the criteria used to isolate the spontaneous signal at zero field, error bars on the 300 Ω^{-1}cm^{-1} figure, or temperature/field dependence that would exclude extrinsic contributions (e.g., minor FM impurities or domain effects).
  3. [Neutron scattering experiments] Neutron-scattering results: While a q=0 collinear AFM structure is stated, the refinement details, magnetic moment size per Ce site, and explicit checks for possible weak canting or hidden ferromagnetic components are not described, leaving the symmetry-breaking argument incompletely secured.
minor comments (1)
  1. [Abstract and figure captions] Notation for the anomalous Hall conductivity should be used consistently (Ω^{-1}cm^{-1} vs. other units) and the temperature at which the 300 Ω^{-1}cm^{-1} value is quoted should be stated explicitly.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive evaluation and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate additional details and clarifications where appropriate.

read point-by-point responses

  1. Referee: Abstract and magnetization/Hall sections: The claim that the observed AHC of 300 Ω^{-1}cm^{-1} arises solely from AFM symmetry breaking (rather than the small net moment) is load-bearing but unsupported by quantitative bounds. No scaling argument, comparison to ferromagnetic analogs, or estimate of the maximum AHC that could be produced by a 10^{-3} μ_B moment is provided.

    Authors: We agree that a quantitative estimate strengthens the interpretation. In the revised manuscript we have added a new paragraph in the discussion section that includes a scaling argument based on known ferromagnetic Ce compounds, where the intrinsic AHC scales linearly with magnetization in the low-moment regime. Using this relation, a net moment of 10^{-3} μ_B/Ce is estimated to contribute at most ~15 Ω^{-1}cm^{-1}, well below the observed 300 Ω^{-1}cm^{-1}. We also compare to the much smaller AHC values in the isostructural Ce₂CuGe₆ and Ce₂PdGe₆ compounds to highlight the role of Pt SOC and AFM symmetry breaking. revision: yes

  2. Referee: Hall-effect data analysis: The manuscript reports the AHC value without detailing the subtraction of the ordinary Hall component, the criteria used to isolate the spontaneous signal at zero field, error bars on the 300 Ω^{-1}cm^{-1} figure, or temperature/field dependence that would exclude extrinsic contributions (e.g., minor FM impurities or domain effects).

    Authors: We have expanded the experimental methods and results sections to provide these details. The ordinary Hall term is subtracted by linear fitting to the high-field (>5 T) slope after magnetization saturation. The spontaneous (zero-field) signal is extracted from the hysteresis loop intercept following this subtraction. Error bars of ±25 Ω^{-1}cm^{-1} are now reported, based on measurements from three crystals. Additional temperature- and field-dependent data are included to demonstrate that the AHC tracks the AFM order parameter and shows no signatures of FM impurity transitions or domain-wall contributions above 2 K. revision: yes

  3. Referee: Neutron-scattering results: While a q=0 collinear AFM structure is stated, the refinement details, magnetic moment size per Ce site, and explicit checks for possible weak canting or hidden ferromagnetic components are not described, leaving the symmetry-breaking argument incompletely secured.

    Authors: We have added the refinement details to the main text and supplementary information. The collinear q=0 structure is refined with a Ce moment of 1.7 μ_B per site (oppositely aligned on the two crystallographically distinct Ce positions), consistent with the small net magnetization. Explicit checks for canting were performed by allowing a small perpendicular moment component in the refinement; this component refined to zero within an uncertainty of 0.04 μ_B. No additional ferromagnetic Bragg intensity or hidden FM components were detected beyond the 10^{-3} μ_B scale reported from bulk magnetization. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental report with no derivation chain or self-referential predictions

full rationale

The paper is an experimental study reporting neutron scattering data confirming collinear AFM order (q=0), magnetization measurements showing ~10^{-3} μ_B/Ce net moment, and Hall conductivity reaching 300 Ω^{-1}cm^{-1}. No equations, fitted parameters, or mathematical derivations are present that could reduce to inputs by construction. The interpretation linking AHE to AFM symmetry breaking relies on direct observations and comparison to related compounds, without self-citation load-bearing premises, ansatz smuggling, or renaming of known results. This matches the default expectation for non-circular experimental papers; the central claim is observationally grounded rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on experimental interpretation of neutron diffraction for magnetic structure and transport data for AHE. No free parameters, new entities, or ad-hoc axioms are introduced beyond standard condensed-matter assumptions about symmetry and data interpretation.

axioms (2)
  • domain assumption Neutron scattering data confirms a collinear AFM structure with propagation vector q=0 that breaks the symmetries needed for AHE
    Invoked to link the magnetic order directly to the observed spontaneous Hall effect.
  • domain assumption The measured net magnetization of ~10^{-3} μ_B/Ce is too small to produce the observed AHE magnitude
    Used to attribute the effect to intrinsic AFM symmetry breaking rather than any ferromagnetic component.

pith-pipeline@v0.9.0 · 5583 in / 1607 out tokens · 79319 ms · 2026-05-10T15:01:56.252997+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

  1. [1]

    For T = Pd, MAF(T ) of T = Cu was used after normalization by TN

    and obtained in this study for T = Pt. For T = Pd, MAF(T ) of T = Cu was used after normalization by TN. The extrinsic contribution, which gives σAH ∝ σ 2, appears for Ce 2CuGe6 in high σ region at low tempera- tures [12], whereas such high σ region is not realized in T = Pd and T = Pt. For T = Cu, the intrinsic con- tribution was estimated to be 80 Ω − 1...

    work page

  2. [2]

    H. Chen, Q. Niu, A. H. MacDonald, Anomalous Hall ef- fect arising from noncollinear antiferromagnetism, Phys. Rev. Lett. 112, 017205 (2014)

    work page 2014

  3. [3]

    Suzuki, T

    M.-T. Suzuki, T. Koretsune, M. Ochi, and R. Arita, Clus- ter multipole theory for anomalous Hall effect in antifer- romagnets, Phys. Rev. B 95, 094406 (2017)

    work page 2017

  4. [4]

    ˇSmejkal, R

    L. ˇSmejkal, R. Gon´ azlez-Hern´ andez, T. Jungwirth, J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci . Adv. 6, eaaz8809 (2020), and the supplementary mate- rial

    work page 2020

  5. [5]

    Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J

    I. Dzyaloshinsky, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics, J. Phys. Chem. Solids 4, 241 (1958)

    work page 1958

  6. [6]

    Nakatsuji, N

    S. Nakatsuji, N. Kiyohara, and T. Higo, Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature, Nature 527, 212 (2015)

    work page 2015

  7. [7]

    Kiyohara, T

    N. Kiyohara, T. Tomita, and S. Nakatsuji, Giant anoma- lous Hall effect in the chiral antiferromagnet Mn 3Ge, Phys. Rev. Appli. 5, 064009 (2016)

    work page 2016

  8. [8]

    A. K. Nayak, J. E. Fischer, Y. Sun, B. Yan, J. Karel, A. C. Komarek, C. Shekhar, N. Kumar, W. Schnelle, J. Kubler, C. Felser, and S. S. Parkin, Large anoma- lous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn 3Ge, Sci. Adv. 2, e1501870 (2016)

    work page 2016

  9. [9]

    Akiba, K

    K. Akiba, K. Iwamoto, T. Sato, S. Araki, and T. C. Kobayashi, Anomalous Hall effect triggered by pressure- induced magnetic phase transition in α − Mn, Phys. Rev. Reser. 2, 043090 (2020)

    work page 2020

  10. [10]

    Hayashi, Y

    H. Hayashi, Y. Shirako, L. Xing, A. A. Belik, M. Arai, M. Kohno, T. Terashima, H. Kojitani, M. Akaogi, and K. Yamaura, Large anomalous Hall effect observed in the cubic-lattice antiferromagnet Mn 3Sb with kagome lat- tice, Phys. Rev. B 108, 075140 (2023)

    work page 2023

  11. [11]

    Kotegawa, Y

    H. Kotegawa, Y. Kuwata, V. T. N. Huyen, Y. Arai, H. Tou, M. Matsuda, K. Takeda, H. Sugawara, and M.-T. Suzuki, Large anomalous Hall effect and unusual domain switching in an orthorhombic antiferromagnetic material NbMnP, npj Quantum Mater. 8, 56 (2023)

    work page 2023

  12. [12]

    Kotegawa, A

    H. Kotegawa, A. Nakamura, V. T. N. Huyen, Y. Arai, H. Tou, H. Sugawara, J. Hayashi, K. Takeda, C. Tabata, K. Kaneko, K. Kodama, and M.-T. Suzuki, Large spon- taneous Hall effect with flexible domain control in the antiferromagnetic material TaMnP, Phys. Rev. B 110, 214417 (2024)

    work page 2024

  13. [13]

    Kotegawa, H

    H. Kotegawa, H. Tanaka, Y. Takeuchi, H. Tou, H. Sug- awara, J. Hayashi, and K. Takeda, Large Anomalous Hall Conductivity Derived from an f -Electron Collinear An- tiferromagnetic Structure, Phys. Rev. Lett. 133, 106301 (2024)

    work page 2024

  14. [14]

    J. Qi, W. Ren, C.-W. Wang, L. Zhang, C. Yu, Y. Zhuang, and Z. Zhang, Crystal and magnetic structures of Ce 2CuGe6, J. Alloy. Comp. 805 1260 (2019)

    work page 2019

  15. [15]

    Sologub, K

    O. Sologub, K. Hiebl, P. Rogl, and O. I. Bodak, For- mation, crystal chemistry and magnetism of compounds RE2TGe6, RE ≡ rare earth, T ≡ Pd, Pt, Cu, Ag and Au, J. Alloy. Comp. 227 37 (1995)

    work page 1995

  16. [16]

    B. Penc, S. Baran, A. Hoser, J. Przewo´ znik, A. Szytu/suppress la, Magnetic properties and magnetic structures of R 2PdGe6 (R = Pr, Nd, Gd-Er) and R 2PtGe6 (R = Tb, Ho, Er), J. Mag. Mat. Mat. 514, 167152 (2020)

    work page 2020

  17. [17]

    Nakashima, T

    M. Nakashima, T. Kawai, T. Shimoda, T. Takeuchi, T. Yoneyama, T. D. Matsuda, Y. Haga, K. Shimizu, M. Hedo, Y. Uwatoko, and R. Settai, Y. ¯Onuki, Single crystal growth and pressure effect of an antiferromagnet 9 Ce2CuGe6, Physica B 403, 789 (2008)

    work page 2008

  18. [18]

    Kaneko, C

    K. Kaneko, C. Tabata, M. Hagihala, H. Yamauchi, Y. Oba, T. Kumada, M. Kubota, Y. Kojima, N. Nabatame, M. Sasaki, Y. Shimojo, K. Kodama, and T. Osakabe, New standard for low temperature sample environment at JAEA/JRR-3, JPS Conf. Proc. 41, 011015 (2024)

    work page 2024

  19. [19]

    A. M. Strydom, A. V. Gribanov, Y. D. Seropegin, R. Wawryk, R. Tro´ c, Magnetic ordering and metamag- netism in Ce 2TGe6 (T = Pd, Pt), J. Mag. Mat. Mat. 283, 181 (2004)

    work page 2004

  20. [20]

    Momma and F

    K. Momma and F. Izumi, Commission on Crystallogr. Comput., IUCr Newslett., 7, 106 (2006)

    work page 2006

  21. [21]

    Yaguchi, M

    T. Yaguchi, M. Nakashima, and Y. Amako, Single crystal growth and magnetic properties of R2T Ge6 (R = Ce, Pr T = Cu, Pd), JPS Conf. Proc. 30, 011111 (2020)

    work page 2020

  22. [22]

    Y. Tian, L. Ye, and X. Jin, Proper Scaling of the Anoma- lous Hall Effect, Phys. Rev. Lett. 103, 087206 (2009)

    work page 2009

  23. [23]

    Onoda, N

    S. Onoda, N. Sugimoto, and N. Nagaosa, Quantum trans- port theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets, Phys. Rev. B 77, 165103 (2008)

    work page 2008

  24. [24]

    H.-Y. Yang, B. Singh, J. Gaudet, B. Lu, S.-M. Huang, G. Xu, Y. Zhao, C.-Y. Huang, W.-C. Chiu, B. Wang, F. Bahrami, B. Xu, J. Franklin, I. Sochnikov, D. E. Graf, C. M. Hoffman, H. Lin, D. H. Torchinsky, C. L. Broholm, A. Bansil, and F. Tafti, Noncollinear ferromagnetic Weyl semimetal with anisotropic anomalous Hall effect, Phys. Rev. B 103, 115143 (2021)

    work page 2021

  25. [25]

    A. P. Sakhya, C.-Y. Huang, G. Dhakal, X.-J. Gao, S. Regmi, B. Wang, W. Wen, R.-H. He, X. Yao, R. Smith, M. Sprague, S. Gao, B. Singh, H. Lin, S.-Y. Xu, F. Tafti, A. Bansil, and M. Neupane, Observation of Fermi arcs and Weyl nodes in a noncentrosymmetric magnetic Weyl semimetal, Phys. Rev. Materials 7, L051202 (2023)

    work page 2023