Higher-order Weyl nodes driven by helical magnetic order in EuAgAs

Andrew T. Boothroyd; Anne Stunault; Daniil Yevtushynsky; Dharmalingam Prabhakaran; J. Alberto Rodr\'iguez-Velamaz\'an; Jian-Rui Soh; Louis Withers; Oscar Fabelo; Shengyuan A. Yang; Timur K. Kim

arxiv: 2605.19347 · v1 · pith:QW2723YRnew · submitted 2026-05-19 · ❄️ cond-mat.str-el

Higher-order Weyl nodes driven by helical magnetic order in EuAgAs

Jian-Rui Soh , Ziming Zhu , Louis Withers , J. Alberto Rodr\'iguez-Velamaz\'an , Timur K. Kim , Oscar Fabelo , Anne Stunault , Daniil Yevtushynsky

show 3 more authors

Dharmalingam Prabhakaran Shengyuan A. Yang Andrew T. Boothroyd

This is my paper

Pith reviewed 2026-05-20 04:46 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords EuAgAshelical magnetic orderhigher-order Weyl nodesband foldingtopological semimetalneutron diffractionfirst-principles calculations

0 comments

The pith

Helical magnetic order in EuAgAs folds electronic bands to create effective higher-order Weyl nodes.

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

The paper determines the magnetic ground state of EuAgAs through scattering experiments and then uses that structure as input for first-principles calculations. Those calculations show that the transverse helical order produces band folding and effective higher-order Weyl nodes near the computed Fermi energy. A reader would care because the work directly connects a specific long-range magnetic pattern to the generation of new topological quasiparticles in a real crystal. The predicted nodes sit above the Fermi level measured by photoemission and therefore remain unobserved in the present data.

Core claim

Neutron diffraction, resonant x-ray scattering, and spherical neutron polarimetry establish that EuAgAs undergoes two magnetic transitions at 12 K and 8 K into a transverse helical structure aligned along the c axis with a period roughly twice the lattice constant. When this helical configuration is supplied to density-functional calculations, the electronic bands undergo folding that produces effective higher-order Weyl nodes close to the calculated Fermi energy.

What carries the argument

The experimentally fixed transverse helical magnetic order, which supplies the periodic potential that folds the bands and generates the higher-order Weyl nodes in the first-principles electronic-structure calculation.

If this is right

The helical order with its two slightly different propagation vectors folds the bands and produces effective higher-order Weyl nodes.
These nodes appear near the Fermi energy obtained from the calculations performed on the helical phase.
The magnetic transitions at 12 K and 8 K each correspond to one of the two propagation vectors in the helical structure.
Because the calculated Fermi energy lies above the ARPES value, the nodes remain inaccessible to direct spectroscopic probe in the present study.

Where Pith is reading between the lines

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

Shifting the Fermi level by doping or gating could bring the predicted nodes into the experimentally accessible energy window.
The same helical-order mechanism might be tested in chemically related hexagonal pnictides that share the same crystal structure.
Calculations performed on the paramagnetic or other non-helical phases would isolate whether the magnetic periodicity is strictly required for the nodes to appear.

Load-bearing premise

The transverse helical magnetic structure measured by scattering is the correct periodic potential that must be used in the calculations to obtain the higher-order Weyl nodes.

What would settle it

Angle-resolved photoemission spectra taken at the calculated Fermi energy in the helical phase either show or fail to show the predicted band crossings that define the higher-order Weyl nodes.

Figures

Figures reproduced from arXiv: 2605.19347 by Andrew T. Boothroyd, Anne Stunault, Daniil Yevtushynsky, Dharmalingam Prabhakaran, J. Alberto Rodr\'iguez-Velamaz\'an, Jian-Rui Soh, Louis Withers, Oscar Fabelo, Shengyuan A. Yang, Timur K. Kim, Ziming Zhu.

**Figure 1.** Figure 1: a The hexagonal unit cell of EuAgAs can be described by the P63/mmc space group. b The magnetic susceptibility of EuAgAs with the magnetic field (H) along the crystal a axis displays two anomalies, at TN1=12 K and TN2 ≃ 8 K. arXiv:2605.19347v1 [cond-mat.str-el] 19 May 2026 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** Figure 2: Unravelling the magnetic order of EuAgAs with neutrons and x-rays. a Temperature dependence of the q1 peak intensity obtained with resonant elastic x-ray scattering (REXS) and neutron diffraction (ND). b. Intensity of the q2 magnetic reflection measured with ND. c Temperature evolution of the reciprocal space location of the q1 and q2 reflections. d–g Scans along the line (1, 1, L) in reciprocal space at T… view at source ↗

**Figure 4.** Figure 4: First and second harmonics of the q1 magnetic peak. The scans are along the (0, 0, L) direction in reciprocal space, and were measured with x-rays tuned to the Eu M5 absorption edge in the π → σ ′ polarization channel. a The q1 = (0, 0, 0.5 + δ1) magnetic peak. b Second harmonics of the q1 peak. absorbing samples that the magnetic structure is determined from ratios of spin-dependent scattering intensit… view at source ↗

**Figure 5.** Figure 5: Comparison between the measured and calculated electronic band structure of EuAgAs. a-c Experimental dispersion along M−Γ−M at three temperatures (T = 17, 10 and 5.9 K). d, e Calculated dispersion along high symmetry lines in the paramagnetic and helical magnetic phase. An upward shift of 0.5 eV has been applied to the calculated bands shown in order to match the ARPES data. The folded bands near Γ at abou… view at source ↗

read the original abstract

Magnetic topological semimetals provide a fertile ground for exploring how long-range magnetic order can alter electronic band structures and generate novel quasiparticles such as Weyl fermions. Here, we investigate the coupled magnetic and electronic structure of single-crystalline EuAgAs, a hexagonal pnictide whose magnetic ground state has remained elusive. Using neutron diffraction and resonant elastic X-ray scattering, we identify an unusual magnetic ordering sequence with two successive phase transitions at $T_\mathrm{N1} = 12$ K and $T_\mathrm{N2} = 8$ K. We observe two slightly different magnetic propagation vectors, one associated with $T_\mathrm{N1}$ and the other with $T_\mathrm{N2}$. Spherical neutron polarimetry reveals that the magnetic structure is a transverse helix aligned along the $c$ axis with a period that is approximately twice the $c$ lattice parameter. First-principles calculations for the helical phase predict subtle band folding effects and the emergence of effective higher-order Weyl nodes. These topological features appear near the calculated Fermi energy $E_{\mathrm{F}}$ which, however, lies above the position of $E_{\mathrm{F}}$ obtained from angle-resolved photoemission spectroscopy so could not be probed in this study.

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.

Desk Editor's Note private letter to a colleague

EuAgAs has a two-transition helical magnetic order that calculations connect to higher-order Weyl nodes, but the nodes are above the ARPES Fermi level and the supercell may introduce artifacts.

read the letter

EuAgAs orders in two steps at 12 K and 8 K into a transverse helical magnetic structure along the c axis, according to neutron and X-ray measurements. Calculations on this structure then predict the appearance of effective higher-order Weyl nodes through band folding. The experimental mapping of the magnetic order is the clear strength here, while the link to topology has some limitations that are worth noting. The measurements combine neutron diffraction to find the propagation vectors, resonant elastic X-ray scattering for confirmation, and spherical neutron polarimetry to establish the helical character. This gives a detailed picture of the two slightly different vectors associated with each transition and the approximate doubling of the c period. It is a useful experimental result for the field of magnetic pnictides. The first-principles calculations take this helical order and show subtle folding effects leading to higher-order Weyl nodes near the calculated Fermi energy. The paper is upfront that this energy is higher than the Fermi level from ARPES, so the nodes are not observed in the experiment. A potential issue is the use of a commensurate supercell for what is described as an approximately incommensurate helix. Imposing exact periodicity in a minimal cell can generate artificial band crossings or nodes via zone folding that would be absent or modified in a truly incommensurate modulation. This is a standard concern with such approximations and seems relevant here. The paper is mainly for people studying topological features induced by magnetic order in semimetals. The experimental data provide a new example that could be cited in reviews of the area. It deserves peer review because the measurements are thorough and the calculations, while limited by the energy mismatch and possible artifact, still pose an interesting question for the community to evaluate.

Referee Report

2 major / 1 minor

Summary. The manuscript experimentally identifies a transverse helical magnetic structure in EuAgAs with successive transitions at TN1 = 12 K and TN2 = 8 K, using neutron diffraction, resonant elastic X-ray scattering, and spherical neutron polarimetry to determine two slightly different propagation vectors and a period approximately twice the c lattice parameter. First-principles calculations for this helical phase predict subtle band folding and the emergence of effective higher-order Weyl nodes near the calculated Fermi energy, although this EF lies above the position determined by ARPES.

Significance. If the predicted higher-order Weyl nodes prove robust, the work would advance understanding of how helical magnetic order induces novel topological quasiparticles in pnictide semimetals. The experimental magnetic structure determination is clearly presented and serves as direct input to the calculations, which are free of additional fitted parameters. However, the topological claim's relevance is limited by the EF mismatch with experiment.

major comments (2)

[First-principles calculations] First-principles calculations section: The helical order is modeled via a commensurate supercell with period approximately twice the c-axis. Given the propagation vectors are described as 'slightly different' and the period as 'approximately', this minimal supercell imposes artificial periodicity that can produce spurious Brillouin-zone folding and higher-order Weyl nodes absent in a truly incommensurate helix.
[ARPES and calculations comparison] ARPES comparison: The calculated EF lies above the ARPES-determined EF, so the predicted nodes lie outside the experimentally probed region. It is unclear whether these nodes remain or become gapped when the chemical potential is shifted to match the experimental EF.

minor comments (1)

[Abstract] Abstract: The term 'effective higher-order Weyl nodes' is used without a brief definition or reference; adding one sentence clarifying the meaning in this context would aid accessibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address the two major comments below regarding the first-principles calculations and the comparison with ARPES measurements. We have made revisions to clarify these aspects.

read point-by-point responses

Referee: First-principles calculations section: The helical order is modeled via a commensurate supercell with period approximately twice the c-axis. Given the propagation vectors are described as 'slightly different' and the period as 'approximately', this minimal supercell imposes artificial periodicity that can produce spurious Brillouin-zone folding and higher-order Weyl nodes absent in a truly incommensurate helix.

Authors: We appreciate the referee's concern about the use of a commensurate supercell for modeling the helical magnetic order. The experimental propagation vectors are slightly different, leading to an approximate doubling of the c-axis period. The minimal supercell was chosen to enable computationally tractable first-principles calculations while capturing the primary effects of the magnetic ordering on the electronic structure. This is a standard approach for systems with long-period magnetic structures. The emergence of effective higher-order Weyl nodes results from the band folding due to the broken translational symmetry imposed by the helix. Although a fully incommensurate helix would not have a simple periodic supercell, the topological features associated with the approximate periodicity are expected to be robust. In the revised manuscript, we have included an additional discussion on the limitations of the commensurate approximation and why we believe the predicted nodes are not spurious. revision: partial
Referee: ARPES comparison: The calculated EF lies above the ARPES-determined EF, so the predicted nodes lie outside the experimentally probed region. It is unclear whether these nodes remain or become gapped when the chemical potential is shifted to match the experimental EF.

Authors: We acknowledge the discrepancy between the calculated and experimental Fermi levels, which is already stated in the abstract and main text. The higher-order Weyl nodes are predicted near the calculated EF in the helical phase. Since these nodes originate from the specific band folding induced by the helical magnetic order, they are topologically protected features of the electronic structure. Shifting the chemical potential to the experimental value (e.g., via rigid band approximation) would reposition the Fermi level but would not gap out the nodes, as their existence is determined by the symmetries of the magnetic structure rather than the exact position of EF. We have revised the manuscript to elaborate on this point and to clarify that while the nodes are not at the experimental EF, their prediction highlights the potential of helical order to generate such quasiparticles. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental magnetic structure drives independent first-principles prediction

full rationale

The paper first determines the transverse helical magnetic structure and propagation vectors experimentally using neutron diffraction, resonant elastic X-ray scattering, and spherical neutron polarimetry. These measured quantities are then supplied as fixed input to first-principles calculations that compute the electronic band structure, band folding, and effective higher-order Weyl nodes. This workflow is a standard separation of experimental characterization from theoretical computation; the predicted topological features are not obtained by fitting parameters to the target observables, by self-definition, or by any self-citation chain that would render the result tautological. No load-bearing step reduces the output to the input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on standard assumptions in neutron scattering analysis and density functional theory for band structure, with no free parameters or new entities explicitly introduced in the abstract.

axioms (1)

standard math Standard assumptions in density functional theory calculations for electronic bands in the presence of magnetic order.
Invoked for the first-principles predictions of band folding and Weyl nodes.

pith-pipeline@v0.9.0 · 5807 in / 1292 out tokens · 41189 ms · 2026-05-20T04:46:00.504528+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

First-principles calculations for the helical phase predict subtle band folding effects and the emergence of effective higher-order Weyl nodes.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

Orbital Selective Dirac-like States in EuAgAs Revealed by Polarization Dependent ARPES and DFT
cond-mat.mes-hall 2026-05 unverdicted novelty 4.0

Polarization-dependent ARPES combined with DFT reveals orbital-selective Dirac-like states in EuAgAs that show little change between 9 K and 30 K.

Reference graph

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N. P. Armitage, Mele E. J., and A. Vishwanath. Weyl and Dirac semimetals in three-dimensional solids.Rev. Mod. Phys., 90:015001, 2018

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Yahui Jin, Xu-Tao Zeng, Xiaolong Feng, Xin Du, Weikang Wu, Xian-Lei Sheng, Zhi-Ming Yu, Ziming Zhu, and Shengyuan A. Yang. Multiple magnetism-controlled topo- logical states in EuAgAs.Phys. Rev. B, 104:165424, 2021

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Coupled magnetic and structural tran- sition in topological antiferromagnet EuAgAs under high pressure.Materials T oday Physics, 38:101228, 2023

Zhuyi Zhang, Xuliang Chen, Chao An, Shuyang Wang, Lili Zhang, Yonghui Zhou, Min Zhang, Jian Zhou, and Zhaorong Yang. Coupled magnetic and structural tran- sition in topological antiferromagnet EuAgAs under high pressure.Materials T oday Physics, 38:101228, 2023

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Oppeneer, and Jian-Qiao Meng

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