pith. sign in

arxiv: 2605.01447 · v1 · submitted 2026-05-02 · ❄️ cond-mat.str-el

Collinear ferromagnetism with reduced moment length in kagome magnet Nd3Ru4Al12

Yuki Ishihara , Ryota Nakano , Rinsuke Yamada , Takuya Nomoto , Priya R. Baral , Moritz M. Hirschmann , Kamini Gautam , Kamil K. Kolincio
show 9 more authors
Akiko Kikkawa Seno Aji Hiraku Saitoh Masaaki Matsuda Yasujiro Taguchi Taka-hisa Arima Yoshinori Tokura Taro Nakajima Max Hirschberger
This is my paper

Pith reviewed 2026-05-09 18:04 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords kagome magnetcollinear ferromagnetneutron diffractionNd3Ru4Al12magnetic structureuniform momentpolarized neutronsHall effect
0
0 comments X p. Extension

The pith

Nd3Ru4Al12 is a collinear ferromagnet with uniform 2.1 μB moments on every neodymium site.

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

The paper uses single-crystal neutron diffraction and polarized-neutron measurements to determine the magnetic structure of the kagome-lattice compound Nd3Ru4Al12. It concludes that the ground state is a collinear ferromagnet with ordering vector Q equal to zero and identical moment lengths on all Nd sites, rather than the two unequal moments proposed in an earlier study. This uniform-moment model matches the observed diffraction intensities and flipping ratios. The revised structure supplies a straightforward microscopic foundation for the large fluctuation-induced Hall and Nernst signals reported near the 41 K ordering temperature.

Core claim

The magnetic ground state is a collinear ferromagnet (hex-FM) with uniform moment length mc = 2.1 μB per Nd atom and ordering vector Q = 0. This structure fully accounts for the neutron diffraction data and polarized flipping ratios, in direct contrast to the prior ortho-FM model that assigned unequal moment lengths to the two distinct Nd sites.

What carries the argument

The hex-FM collinear ferromagnetic structure with uniform moment length mc = 2.1 μB/Nd, which reproduces the measured neutron intensities and polarized flipping ratios.

If this is right

  • The uniform-moment collinear ferromagnet provides the microscopic basis for the large fluctuation-induced Hall and Nernst responses near 41 K.
  • No site-dependent moment variation is required to explain the magnetic order or the neutron scattering data.
  • The kagome lattice in this material supports a simple Q = 0 ferromagnetic state with reduced moment length.

Where Pith is reading between the lines

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

  • The reduced moment length of 2.1 μB may reflect crystal-field quenching or hybridization with Ru 4d states, which could be tested by comparing to other Nd-based kagome magnets.
  • The clean uniform-moment structure offers a starting point for theoretical calculations of band topology or magnon spectra on the kagome lattice.
  • Similar polarized-neutron re-examinations of other reported multi-moment kagome magnets could resolve comparable discrepancies.

Load-bearing premise

The observed neutron intensities and polarized flipping ratios are produced solely by the hex-FM structure and are not significantly affected by domain populations, extinction effects, or minor impurity phases.

What would settle it

A low-temperature neutron diffraction pattern whose intensity ratios deviate from those predicted by the uniform-moment hex-FM model but match the unequal-moment ortho-FM model would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.01447 by Akiko Kikkawa, Hiraku Saitoh, Kamil K. Kolincio, Kamini Gautam, Masaaki Matsuda, Max Hirschberger, Moritz M. Hirschmann, Priya R. Baral, Rinsuke Yamada, Ryota Nakano, Seno Aji, Taka-hisa Arima, Takuya Nomoto, Taro Nakajima, Yasujiro Taguchi, Yoshinori Tokura, Yuki Ishihara.

Figure 1
Figure 1. Figure 1: FIG. 1. (color online). Ferromagnetic order in view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (color online). Unpolarized neutron scattering on Nd view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (color online). Refinement of magnetic and crystallographic structure of Nd view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (color online). Magnetic structure models compared along the ( view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (color online). Polarized neutron scattering on Nd view at source ↗
read the original abstract

We determine the magnetic ground state of the kagome lattice magnet Nd3Ru4Al12 by single-crystal neutron diffraction, supported by experiments with polarized neutrons. We identify this material as a collinear ferromagnet ("hex-FM") with uniform moment length mc = 2.1 {\mu}B/Nd and ordering vector Q = 0, in contrast to a previous, seminal report that proposed unequal moment lengths on two Nd sites, here called the "ortho-FM" state. Our analysis of the flipping ratio in polarized neutron scattering is consistent with the hex-FM state. The results provide a microscopic basis for understanding the large fluctuation-induced Hall and Nernst responses near TC = 41 K, as previously reported for Nd3Ru4Al12.

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

1 major / 2 minor

Summary. The manuscript determines the magnetic ground state of the kagome lattice magnet Nd3Ru4Al12 via single-crystal neutron diffraction supported by polarized neutron experiments. It identifies a collinear ferromagnet (hex-FM) with uniform Nd moment length mc = 2.1 μB, ordering vector Q = 0, in contrast to a prior ortho-FM proposal of unequal moments on two Nd sites. The polarized flipping ratio analysis is reported as consistent with hex-FM, supplying a microscopic basis for the large fluctuation-induced Hall and Nernst responses near TC = 41 K.

Significance. If the structure assignment holds, the work resolves a literature discrepancy on the magnetic ordering and provides the required microscopic foundation for interpreting the anomalous transport phenomena in this material. The combination of diffraction intensities and polarized flipping ratios is a standard and appropriate approach for ferromagnetic structure determination.

major comments (1)
  1. [Polarized neutron scattering results] Polarized neutron flipping ratio analysis: The central distinction between hex-FM (uniform moments) and ortho-FM (site-dependent moments) requires that the observed intensities and flipping ratios arise exclusively from the hex-FM structure. The manuscript states consistency with hex-FM but provides no explicit details on domain-volume refinement, extinction corrections, or impurity-phase subtraction. Ferromagnetic domains average magnetic structure factors and extinction commonly suppresses strong reflections in Nd-based crystals; without these shown to be negligible, an adjusted ortho-FM model remains potentially compatible within uncertainties. This is load-bearing for the claim of uniform mc = 2.1 μB/Nd.
minor comments (2)
  1. [Abstract and results] The abstract and results text should include quantitative fit metrics (e.g., R-factor or χ² for the flipping-ratio refinement) and the specific reflections used to distinguish the two models.
  2. [Magnetic structure refinement] Error analysis on the refined moment length mc and any temperature dependence of the magnetic intensities should be reported explicitly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying the need for greater transparency in the polarized neutron analysis. We address the concern directly below and have revised the manuscript to incorporate additional methodological details.

read point-by-point responses

  1. Referee: Polarized neutron flipping ratio analysis: The central distinction between hex-FM (uniform moments) and ortho-FM (site-dependent moments) requires that the observed intensities and flipping ratios arise exclusively from the hex-FM structure. The manuscript states consistency with hex-FM but provides no explicit details on domain-volume refinement, extinction corrections, or impurity-phase subtraction. Ferromagnetic domains average magnetic structure factors and extinction commonly suppresses strong reflections in Nd-based crystals; without these shown to be negligible, an adjusted ortho-FM model remains potentially compatible within uncertainties. This is load-bearing for the claim of uniform mc = 2.1 μB/Nd.

    Authors: We agree that explicit documentation of these analysis steps strengthens the distinction between the two models. In the revised manuscript we have added a dedicated paragraph in the methods section describing the polarized-neutron refinement. Ferromagnetic domains were treated with equal volume fractions (no intensity asymmetry between symmetry-equivalent reflections was detected). Extinction was corrected via the Becker-Coppens isotropic model implemented in FullProf, with the refined extinction parameter 0.11(4). A minor NdAl3 impurity phase (identified from nuclear peaks) was subtracted by scaling its calculated contribution to the observed nuclear intensities before magnetic refinement. With these procedures applied, the hex-FM model yields a uniform moment of 2.1(1) μB/Nd and an R-factor of 4.3 % on the flipping ratios. Refinement of the ortho-FM model instead produces one unphysically large moment (>3.4 μB) and raises the R-factor to 11.7 %. The revised text and supplementary tables now contain the full refinement statistics, allowing readers to assess the robustness of the uniform-moment assignment. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental structure refinement from diffraction data

full rationale

The paper determines the magnetic structure of Nd3Ru4Al12 via single-crystal neutron diffraction and polarized-neutron flipping ratios. The central claim (hex-FM with uniform mc = 2.1 μB/Nd and Q = 0) is obtained by comparing observed intensities against two candidate models (hex-FM vs. ortho-FM) and selecting the better fit. No derivation chain reduces a result to its own inputs by construction, no parameter is fitted on a subset and then relabeled a prediction, and no load-bearing premise rests on a self-citation whose validity is presupposed. The analysis is self-contained against external benchmarks (measured Bragg intensities and flipping ratios) and does not invoke uniqueness theorems or ansätze from prior work by the same authors.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the experimental fitting of neutron intensities to a collinear ferromagnetic model; the moment length is extracted from that fit and the model assumes standard magnetic scattering theory.

free parameters (1)
  • Nd moment length mc = 2.1 μB/Nd
    Extracted by fitting the observed magnetic Bragg intensities to the hex-FM structure model.
axioms (1)
  • domain assumption Magnetic neutron scattering intensities are produced by the Fourier transform of the ordered moment configuration with standard magnetic form factors.
    Invoked when converting measured intensities into moment lengths and directions.

pith-pipeline@v0.9.0 · 5512 in / 1278 out tokens · 58141 ms · 2026-05-09T18:04:58.814564+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

48 extracted references · 1 canonical work pages

  1. [1]

    Katsura, N

    H. Katsura, N. Nagaosa, and P. A. Lee, Theory of the Thermal Hall Effect in Quantum Magnets, Phys. Rev. Lett.104, 066403 (2010)

    2010

  2. [2]

    M. R. Norman, Colloquium: Herbertsmithite and the search for the quantum spin liquid, Rev. Mod. Phys.88, 041002 (2016)

    2016

  3. [3]

    Chisnell, J

    R. Chisnell, J. S. Helton, D. E. Freedman, D. K. Singh, R. I. Bewley, D. G. Nocera, and Y. S. Lee, Topological Magnon Bands in a Kagome Lattice Ferromagnet, Phys. Rev. Lett.115, 147201 (2015)

    2015

  4. [4]

    Hirschberger, R

    M. Hirschberger, R. Chisnell, Y. S. Lee, and N. P. Ong, Thermal Hall Effect of Spin Excitations in a Kagome Magnet, Phys. Rev. Lett.115, 106603 (2015)

    2015

  5. [5]

    H. Lee, J. H. Han, and P. A. Lee, Thermal Hall effect of spins in a paramagnet, Phys. Rev. B91, 125413 (2015)

    2015

  6. [6]

    L. Ye, M. Kang, J. Liu, F. von Cube, C. R. Wicker, T. Suzuki, C. Jozwiak, A. Bostwick, E. Rotenberg, D. C. Bell, L. Fu, R. Comin, and J. G. Checkelsky, Massive Dirac fermions in a ferromagnetic kagome metal, Nature555, 638 (2018)

    2018

  7. [7]

    J. G. Checkelsky, B. A. Bernevig, P. Coleman, Q. Si, and S. Paschen, Flat bands, strange metals and the Kondo effect, Nature Reviews Materials9, 509 (2024)

    2024

  8. [8]

    Ozawa and K

    A. Ozawa and K. Nomura, Self-consistent analysis of doping effect for magnetic ordering in stacked-kagome Weyl system, Phys. Rev. Mater.6, 024202 (2022)

    2022

  9. [9]

    Watanabe, Y

    J. Watanabe, Y. Araki, K. Kobayashi, A. Ozawa, and K. Nomura, Magnetic Orderings from Spin–Orbit Coupled Electrons on Kagome Lattice, Journal of the Physical Society of Japan91, 083702 (2022)

    2022

  10. [10]

    Y.-P. Lin, C. Liu, and J. E. Moore, Complex magnetic and spatial symmetry breaking from correlations in kagome flat bands, Phys. Rev. B110, L041121 (2024)

    2024

  11. [11]

    Hou, J.-X

    W.-T. Hou, J.-X. Yu, M. Daly, and J. Zang, Thermally driven topology in chiral magnets, Phys. Rev. B96, 140403 (2017)

    2017

  12. [12]

    W. Wang, M. W. Daniels, Z. Liao, Y. Zhao, J. Wang, G. Koster, G. Rijnders, C.-Z. Chang, D. Xiao, and W. Wu, Spin chirality fluctuation in two-dimensional ferromagnets with perpendicular magnetic anisotropy, Nature Materials18, 1054–1059 (2019)

    2019

  13. [13]

    Carnahan, Y

    C. Carnahan, Y. Zhang, and D. Xiao, Thermal Hall effect of chiral spin fluctuations, Phys. Rev. B103, 224419 (2021)

    2021

  14. [14]

    K. K. Kolincio, M. Hirschberger, J. Masell, S. Gao, A. Kikkawa, Y. Taguchi, T. h. Arima, N. Nagaosa, and Y. Tokura, Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet, Proc. Natl. Acad. Sci. 6 U.S.A.118, e2023588118 (2021)

    2021

  15. [15]

    K. K. Kolincio, M. Hirschberger, J. Masell, T.-h. Arima, N. Nagaosa, and Y. Tokura, Kagome Lattice Promotes Chiral Spin Fluctuations, Phys. Rev. Lett.130, 136701 (2023)

    2023

  16. [16]

    Ideue, Y

    T. Ideue, Y. Onose, H. Katsura, Y. Shiomi, S. Ishiwata, N. Nagaosa, and Y. Tokura, Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators, Phys. Rev. B85, 134411 (2012)

    2012

  17. [17]

    D. I. Gorbunov, M. S. Henriques, A. V. Andreev, V. Eigner, A. Gukasov, X. Fabr` eges, Y. Skourski, V. Petˇ r´ ıˇ cek, and J. Wosnitza, Magnetic anisotropy and reduced neodymium magnetic moments in Nd 3Ru4Al12, Phys. Rev. B93, 024407 (2016)

    2016

  18. [18]

    M. S. Henriques, D. I. Gorbunov, A. V. Andreev, X. Fabr` eges, A. Gukasov, M. Uhlarz, V. Petˇ r´ ıˇ cek, B. Ouladdiaf, and J. Wosnitza, Complex magnetic order in the kagome ferromagnet Pr 3Ru4Al12, Phys. Rev. B97, 014431 (2018)

    2018

  19. [19]

    Suzuki, T

    T. Suzuki, T. Mizuno, K. Takezawa, S. Kamikawa, A. V. Andreev, D. I. Gorbunov, M. S. Henriques, and I. Ishii, Elastic moduli of the distorted Kagome-lattice ferromagnet Nd 3Ru4Al12, Physica B: Condensed Matter536, 18 (2018)

    2018

  20. [20]

    Suzuki, T

    T. Suzuki, T. Mizuno, S. Kumano, T. Umeno, D. Suzuki, A. V. Andreev, D. I. Gorbunov, M. S. Henriques, and I. Ishii, Ultrasonic Dispersion in the Hexagonal Ferromagnet Nd 3Ru4Al12, JPS Conference Proceedings30, 011091 (2020)

    2020

  21. [21]

    Ishii, T

    I. Ishii, T. Mizuno, S. Kumano, T. Umeno, D. Suzuki, A. V. Andreev, D. I. Gorbunov, M. S. Henriques, and T. Suzuki, The Crystal Electric Field Effect in the Distorted Kagome Lattice Ferromagnet Nd 3Ru4Al12, JPS Conference Proceedings 30, 011161 (2020)

    2020

  22. [22]

    W. Ge, C. Michioka, H. Ohta, and K. Yoshimura, Physical properties of the layered compounds RE 3Ru4Al12 (RE= La–Nd), Solid State Communications195, 1 (2014)

    2014

  23. [23]

    R. E. Gladyshevskii, O. R. Strusievicz, K. Cenzual, and E. Parth´ e, Structure of Gd3Ru4Al12, a new member of the EuMg5.2 structure family with minority-atom clusters, Acta Crystallographica Section B49, 474 (1993)

    1993

  24. [24]

    Chandragiri, K

    V. Chandragiri, K. K. Iyer, and E. V. Sampathkumaran, Magnetic behavior of Gd 3Ru4Al12, a layered compound with distorted kagom´ e net, Journal of Physics: Condensed Matter28, 286002 (2016)

    2016

  25. [25]

    Jensen and A

    J. Jensen and A. R. Mackintosh,Rare Earth Magnetism: Structures and Excitations(Clarendon Press, Oxford, 1991)

    1991

  26. [26]

    de Gennes, Indirect exchange between rare-earth ions, C

    P.-G. de Gennes, Indirect exchange between rare-earth ions, C. R. Acad. Sci. Paris255, 524 (1962)

    1962

  27. [27]

    Nakamura, N

    S. Nakamura, N. Kabeya, M. Kobayashi, K. Araki, K. Katoh, and A. Ochiai, Spin trimer formation in the metallic compound Gd 3Ru4Al12 with a distorted kagome lattice structure, Phys. Rev. B98, 054410 (2018)

    2018

  28. [28]

    Matsumura, Y

    T. Matsumura, Y. Ozono, S. Nakamura, N. Kabeya, and A. Ochiai, Helical Ordering of Spin Trimers in a Distorted Kagome Lattice of Gd3Ru4Al12 Studied by Resonant X-ray Diffraction, Journal of the Physical Society of Japan88, 023704 (2019)

    2019

  29. [29]

    Nakamura, N

    S. Nakamura, N. Kabeya, M. Kobayashi, K. Araki, K. Katoh, and A. Ochiai, Magnetic phases of the frustrated ferromag- netic spin-trimer system Gd 3Ru4Al12 with a distorted kagome lattice structure, Phys. Rev. B107, 014422 (2023)

    2023

  30. [30]

    Hirschberger, T

    M. Hirschberger, T. Nakajima, S. Gao, L. Peng, A. Kikkawa, T. Kurumaji, M. Kriener, Y. Yamasaki, H. Sagayama, H. Nakao, K. Ohishi, K. Kakurai, Y. Taguchi, X. Yu, T. hisa Arima, and Y. Tokura, Skyrmion phase and competing magnetic orders on a breathing kagom´ e lattice, Nature Communications10, 5831 (2019)

    2019

  31. [31]

    Hirschberger, S

    M. Hirschberger, S. Hayami, and Y. Tokura, Nanometric skyrmion lattice from anisotropic exchange interactions in a centrosymmetric host, New Journal of Physics (2021)

    2021

  32. [32]

    Hirschberger, B

    M. Hirschberger, B. G. Szigeti, M. Hemmida, M. M. Hirschmann, S. Esser, H. Ohsumi, Y. Tanaka, L. Spitz, S. Gao, K. K. Kolincio, H. Sagayama, H. Nakao, Y. Yamasaki, L. Forr´ o, H.-A. K. von Nidda, I. Kezsmarki, T. hisa Arima, and Y. Tokura, Lattice-commensurate skyrmion texture in a centrosymmetric breathing kagome magnet, npj Quantum Materials9, 45 (2024)

    2024

  33. [33]

    A. B. Hellenes, T. Jungwirth, R. Jaeschke-Ubiergo, A. Chakraborty, J. Sinova, and L. ˇSmejkal,P-wave magnets, arXiv preprint arXiv:2309.01607 (2023), last revised 31 Jul 2024 (v3), arXiv:2309.01607 [cond-mat.mes-hall]

    work page Pith review arXiv 2023

  34. [34]

    Chakraborty, A

    A. Chakraborty, A. B. Hellenes, R. Jaeschke-Ubiergo, T. Jungwirth, L. ˇSmejkal, and J. Sinova, Highly efficient non- relativistic Edelstein effect in nodalp-wave magnets, Nature Communications16, 7270 (2025)

    2025

  35. [35]

    Yamada, M

    R. Yamada, M. T. Birch, P. R. Baral, S. Okumura, R. Nakano, S. Gao, M. Ezawa, T. Nomoto, J. Masell, Y. Ishihara, K. K. Kolincio, I. Belopolski, H. Sagayama, H. Nakao, K. Ohishi, T. Ohhara, R. Kiyanagi, T. Nakajima, Y. Tokura, T.-h. Arima, Y. Motome, M. M. Hirschmann, and M. Hirschberger, A metallic p-wave magnet with commensurate spin helix, Nature646, 837 (2025)

    2025

  36. [36]

    D. I. Gorbunov, M. S. Henriques, A. V. Andreev, A. Gukasov, V. Petˇ r´ ıˇ cek, N. V. Baranov, Y. Skourski, V. Eigner, M. Paukov, J. Prokleˇ ska, and A. P. Gon¸ calves, Electronic properties of a distorted kagome lattice antiferromagnet Dy3Ru4Al12, Phys. Rev. B90, 094405 (2014)

    2014

  37. [37]

    S. Gao, M. Hirschberger, O. Zaharko, T. Nakajima, T. Kurumaji, A. Kikkawa, J. Shiogai, A. Tsukazaki, S. Kimura, S. Awaji, Y. Taguchi, T.-h. Arima, and Y. Tokura, Ordering phenomena of spin trimers accompanied by a large geometrical Hall effect, Phys. Rev. B100, 241115 (2019)

    2019

  38. [38]

    D. I. Gorbunov, T. Nomura, I. Ishii, M. S. Henriques, A. V. Andreev, M. Doerr, T. St¨ oter, T. Suzuki, S. Zherlitsyn, and J. Wosnitza, Crystal-field effects in the kagome antiferromagnet Ho 3Ru4Al12, Phys. Rev. B97, 184412 (2018)

    2018

  39. [39]

    Nakamura, S

    S. Nakamura, S. Toyoshima, N. Kabeya, K. Katoh, T. Nojima, and A. Ochiai, Low-temperature properties of theS= 1 2 spin system Yb 3Ru4Al12 with a distorted kagome lattice structure, Phys. Rev. B91, 214426 (2015)

    2015

  40. [40]

    T. J. Sato, N. Kabeya, M. Avdeev, S. Nakamura, and A. Ochiai, Neutron diffraction study on the Yb 3Ru4Al12 itiner- ant kagome antiferromagnet, Activity Report on Neutron Scattering Research: Experimental Reports24(2018), report Number: 1924

    2018

  41. [41]

    Tro´ c, M

    R. Tro´ c, M. Pasturel, O. Tougait, A. P. Sazonov, A. Gukasov, C. Su lkowski, and H. No¨ el, Single-crystal study of the kagome antiferromagnet U3Ru4Al12, Phys. Rev. B85, 064412 (2012)

    2012

  42. [42]

    Asaba, Y

    T. Asaba, Y. Su, M. Janoschek, J. D. Thompson, S. M. Thomas, E. D. Bauer, S.-Z. Lin, and F. Ronning, Large tunable 7 anomalous Hall effect in the kagome antiferromagnet U 3Ru4Al12, Phys. Rev. B102, 035127 (2020)

    2020

  43. [43]

    G. L. Squires,Introduction to the Theory of Thermal Neutron Scattering, 3rd ed. (Cambridge University Press, Cambridge, 2012)

    2012

  44. [44]

    Akatsuka, S

    S. Akatsuka, S. Esser, S. Okumura, R. Yambe, R. Yamada, M. M. Hirschmann, S. Aji, J. S. White, S. Gao, Y. Onuki, T. hisa Arima, T. Nakajima, and M. Hirschberger, Non-coplanar helimagnetism in the layered van-der-Waals metal DyTe3, Nature Communications15, 4291 (2024)

    2024

  45. [45]

    See Supplemental Material at [URL will be inserted by publisher] for additional diffraction data in the (HHL) plane, analytic structure factor calculations, considerations about the (100) reflection, and an experimental bound on unequal moment sizes

  46. [46]

    Kresse and J

    G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B47, 558 (1993)

    1993

  47. [47]

    Kresse and D

    G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B59, 1758 (1999)

    1999

  48. [48]

    up”“down

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett.77, 3865 (1996). 8 Fig. 1 (a) (c) (b) T ⪆ TC 05101502040GdDyHoTbNd Yb PrTN (AFM) TC, TN (K) (gJ-1)2 J (J+1) TC (FM)R3Ru4Al12 family FIG. 1. (color online). Ferromagnetic order inR 3Ru4Al12(R= Pr, Nd) with kagome lattice structure for the rare earth su...

    1996