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REVIEW 2 major objections 4 minor 32 references

Spin-orbit coupling joins structural and magnetic chirality into two distinct p-wave phases that longitudinal conductivity can tell apart.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-12 08:06 UTC pith:HLI4BSDY

load-bearing objection Clean relative-chirality classification of spin-orbital p-wave order with a conductivity probe; solid inside a minimal 1-D model whose transfer to real B20s is still untested. the 2 major comments →

arxiv 2607.02378 v2 pith:HLI4BSDY submitted 2026-07-02 cond-mat.mes-hall

Coupled Spin-Orbital p-Wave Magnetism via Structural and Magnetic Chirality

Tom G. Saunderson , B\"orge G\"obel , Ersoy \c{S}a\c{s}{\i}o\u{g}lu , Samir Lounis This is my paper
classification cond-mat.mes-hall
keywords p-wave magnetismstructural chiralitymagnetic chiralityspin-orbit couplingorbital Edelstein effecthomochiralheterochiralB20 helimagnets
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Helical spin textures already produce momentum-odd spin polarization—the defining signature of p-wave magnetism. Structurally chiral crystals, independently, produce the same odd-parity polarization but in the orbital channel. This paper shows that spin-orbit coupling lets those two microscopic chiralities interact: the crystal’s orbital texture contributes an extra piece to the p-wave spin splitting. The combined state is classified by a single relative-chirality index that labels two symmetry-distinct phases—homochiral when the handednesses match, heterochiral when they oppose. Because the phases rebuild the electronic structure differently, the ordinary longitudinal conductivity changes magnitude between them, giving a direct transport fingerprint. The result unifies orbitronics with unconventional magnetism and points to real platforms such as B20 helimagnets, where composition can reverse magnetic helicity while crystal chirality stays fixed.

Core claim

Spin-orbit coupling couples the momentum-odd orbital polarization of a structurally chiral crystal to the momentum-odd spin polarization of a helical magnet. The resulting spin-orbital p-wave state is classified by the relative chirality η = χ_c χ_m into two symmetry-distinct phases—homochiral (η = +1) and heterochiral (η = −1)—that possess distinct band structures and can be read out through the longitudinal conductivity.

What carries the argument

Relative chirality η = χ_c χ_m. It collapses the four combinations of structural and magnetic handedness into two sectors whose electronic reconstructions are inequivalent and whose longitudinal conductivities therefore differ in magnitude.

Load-bearing premise

The claim rests on a one-dimensional tight-binding helix with a single s-orbital per site and effective hoppings being enough to capture the essential spin-orbital physics of real three-dimensional chiral magnets.

What would settle it

Measure longitudinal conductivity versus Fermi energy or doping in a B20 helimagnet such as Mn1−xFexGe while chemically reversing magnetic helicity at fixed crystal chirality; if the conductivity magnitude does not change systematically between the two helicities, the claimed electronic reconstruction is absent.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Homochiral and heterochiral configurations produce different longitudinal-conductivity magnitudes at the same Fermi energy.
  • Reversing only structural chirality flips the orbital Edelstein response; reversing only magnetic chirality flips the spin Edelstein response; both remain independently observable.
  • In B20 alloys such as Mn1−xFexGe, composition-tuned reversal of magnetic helicity switches η between the two phases while crystal chirality stays fixed.
  • Structural chirality alone, via spin-orbit coupling, can induce spin p-wave splitting even on a collinear antiferromagnet.

Where Pith is reading between the lines

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

  • The same relative-chirality classification should apply to any chiral crystal hosting helical or non-collinear compensated order, not only one-dimensional helices.
  • Nanotube geometries that already host pure orbital or pure spin p-wave textures could be engineered to host the coupled phases by adding a controllable helical magnetization.
  • Mapping longitudinal conductivity across a magnetic-helicity reversal in a B20 compound would directly test the predicted electronic reconstruction.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript argues that structural chirality (producing momentum-odd orbital polarization) and magnetic chirality (producing momentum-odd spin polarization of helical order) are independent microscopic degrees of freedom. Spin-orbit coupling couples them, so that the resulting spin-orbital state is classified by the relative chirality η = χ_c χ_m into two symmetry-distinct p-wave phases (homochiral for η = +1, heterochiral for η = −1). Using an analytically solvable one-dimensional tight-binding helix with a single s orbital, geometry-encoded hoppings, a local exchange field, and effective spin-dependent hopping, the authors show that the orbital texture is transferred into the spin sector and either reinforces or opposes the magnetic p-wave contribution. The two phases exhibit distinct band structures (Fig. 3) and transport responses (Fig. 4); the longitudinal conductivity is proposed as a direct experimental probe that is insensitive to the individual chirality reversals but sensitive to their relative sign. B20 helimagnets are suggested as candidate materials in which chemical substitution can switch η.

Significance. If the classification and transport distinction survive beyond the minimal model, the work supplies a clean symmetry framework that unifies orbitronics with the emerging class of odd-parity (p-wave) magnets and identifies relative chirality as a new control parameter. The proposal that longitudinal conductivity isolates the coupled phase, while spin and orbital Edelstein responses track the individual channels, is experimentally actionable and falsifiable. The symmetry reduction of four microscopic configurations to two sectors labeled by η is transparent and does not rely on fitted parameters. These conceptual and predictive elements constitute a genuine contribution even if quantitative details remain model-dependent.

major comments (2)
  1. [Model paragraph preceding Fig. 1; Figs. 3–4] The entire quantitative demonstration (spin- and orbital-resolved bands of Fig. 3 and the normalized conductivities/susceptibilities of Fig. 4) rests on a one-dimensional tight-binding helix whose Hamiltonian is never written in the main text; only a reference to the Supplemental Material and to prior works [17,21] is given. Free parameters (hopping amplitudes, exchange strength, SOC strength) therefore cannot be inspected or varied by a reader. Because the claimed distinction between homochiral and heterochiral phases is quantitative (band-structure reconstruction and magnitude changes in σ_zz), the absence of the explicit model and parameter set is load-bearing: the robustness of the reported differences cannot be assessed independently. The Hamiltonian, the values used for all figures, and a brief parameter-sensitivity check should appear in the main text or a self-contained appendix.
  2. [Abstract; final two paragraphs (material realizations)] The abstract, introduction and final discussion present the relative-chirality classification and the longitudinal-conductivity probe as relevant to real three-dimensional chiral magnets (B20 helimagnets, Mn1-xFexGe, etc.). Yet every explicit result is obtained inside a single-s-orbital 1-D helix. No symmetry argument, multi-orbital calculation, or even a 3-D tight-binding estimate is supplied to show that the same η classification and the isolation of the coupling by σ_zz survive multi-orbital d bands, longer-range hoppings and three-dimensional Fermi surfaces. This transferability assumption is load-bearing for the experimental claims; either a supporting calculation (or symmetry analysis) for a more realistic setting must be added, or the claims must be explicitly delimited to the minimal model.
minor comments (4)
  1. [Text around Fig. 4; Fig. 4 caption] Inconsistent conductivity index: the text defines σ_zz while the caption of Fig. 4 writes σ_xx (and normalizes to σ_LH,LH_xx). Unify the notation.
  2. [Paragraph introducing transport responses] Typographical error: “longitudional” should be “longitudinal”.
  3. [References] Reference [17] is listed as “manuscript in preparation.” Either replace it with a publicly available preprint or remove the citation until the work is accessible.
  4. [Fig. 1 caption] Fig. 1 panels (c,d) are described as spin expectation values for opposite magnetic helices on a fixed structural helix, yet the color scale and axis labels are not defined in the caption. Add a brief legend.

Circularity Check

1 steps flagged

Mild self-citation of the authors’ own 1-D helix models supplies the Hamiltonian, but the relative-chirality classification and conductivity distinction are not forced by definition or fit.

specific steps
  1. self citation load bearing [Methods paragraph introducing the model (after Fig. 1 discussion)]
    "To isolate the minimal ingredients required for coupled spin-orbital p-wave order, we employ the analytically solvable tight-binding model [21] for structurally chiral one-dimensional helices. … Next we introduce a helical spin spiral by a local exchange field [17], while spin-orbit coupling is incorporated via an effective spin-dependent hopping following Ref. [21]."

    The entire numerical demonstration that SOC produces two distinct electronic structures classified by η (and that longitudinal conductivity distinguishes them) is performed exclusively inside this self-cited model family; one reference is still a manuscript in preparation. The central claim therefore rests on the authors’ prior ansatz without an independent derivation or external benchmark, although the relative-chirality classification itself is not tautological.

full rationale

The paper’s derivation is a direct calculation inside an analytically solvable tight-binding helix: structural chirality produces odd-parity orbital polarization, magnetic chirality produces odd-parity spin polarization, and SOC projects the former onto the spin sector so that the two channels add or subtract according to the relative sign η = χ_c χ_m. The four handedness combinations therefore collapse into two sectors whose band structures and longitudinal conductivities differ (Figs. 3–4). This is not self-definitional (η is simply the product of two independently defined chiralities), nor a fitted parameter renamed as a prediction, nor a uniqueness theorem imported from prior work. The only circularity-adjacent feature is that the concrete Hamiltonian (geometry-encoded hoppings, local exchange field, effective spin-dependent hopping) is taken from the authors’ own Refs. [21] and [17] (the latter still “in preparation”), with details deferred to the Supplemental Material. That self-citation is load-bearing for the numerical demonstration, yet the new claim—that the relative sign defines two symmetry-distinct phases distinguishable by σ_zz—does not reduce to those earlier papers by construction. No external data are fitted, no ansatz is smuggled as a theorem, and no known empirical pattern is merely renamed. Score 2 therefore reflects ordinary self-citation of a model without elevating it to circularity of the central result.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 2 invented entities

The central claim rests on standard condensed-matter machinery (tight-binding, modern orbital magnetization, effective SOC) plus the authors’ own prior 1-D chiral-helix models. No free parameters are fitted to experimental data; model parameters remain unspecified in the main text. The only invented entities are the relative-chirality label and the two named phases, which are symmetry classifications rather than new microscopic degrees of freedom.

free parameters (1)
  • hopping amplitudes, exchange-field strength, SOC strength of the 1-D helix model
    These set the scale of the band splitting and transport responses; their numerical values are never stated in the main text and are therefore free choices that affect the quantitative curves in Figs. 3–4.
axioms (4)
  • domain assumption A helical magnetic texture produces a momentum-odd spin polarization ⟨S_z(k)⟩=−⟨S_z(−k)⟩ whose sign tracks magnetic chirality χ_m.
    Taken as established by Refs. [9,10,17]; used from the first paragraph onward.
  • domain assumption A structurally chiral lattice produces a momentum-odd orbital polarization ⟨L_z(k)⟩=−⟨L_z(−k)⟩ whose sign tracks structural chirality χ_c, even for s-orbitals.
    Taken from the modern theory of orbital magnetization and Ref. [21]; invoked for Fig. 1(b) and Fig. 2.
  • domain assumption An effective spin-dependent hopping term transfers orbital polarization into the spin sector without destroying the orbital texture.
    Standard SOC modeling choice; stated after the introduction of the Hamiltonian and illustrated in Fig. 2(c,d).
  • ad hoc to paper The four microscopic combinations of (χ_c,χ_m) collapse into two symmetry-distinct sectors labeled solely by the product η=χ_c χ_m.
    The paper’s central organizing claim; demonstrated by the band structures of Fig. 3.
invented entities (2)
  • relative chirality η=χ_c χ_m no independent evidence
    purpose: Single symmetry index that distinguishes the two coupled spin-orbital p-wave phases.
    Defined in Eq. (3); not present in the cited literature.
  • homochiral and heterochiral spin-orbital p-wave phases no independent evidence
    purpose: Name the two sectors that exhibit distinct electronic structures and longitudinal-conductivity magnitudes.
    Introduced after Eq. (3) and illustrated in Figs. 3–4; the transport distinction is the proposed experimental handle.

pith-pipeline@v1.1.0-grok45 · 12673 in / 2930 out tokens · 34331 ms · 2026-07-12T08:06:08.922335+00:00 · methodology

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read the original abstract

Helical spin textures represent the minimal realization of $p$-wave magnetism which is characterized by momentum-odd spin polarization. Independently, structurally chiral crystals exhibit momentum-odd orbital polarization arising from broken inversion symmetry. Here, we demonstrate that spin-orbit coupling couples these two independent microscopic chirality degrees of freedom, allowing the orbital polarization of a chiral crystal to generate an additional contribution to the $p$-wave spin splitting. The resulting spin-orbital state is naturally classified by the relative chirality $\eta=\chi_{\mathrm c}\chi_{\mathrm m}$, giving rise to two symmetry-distinct $p$-wave phases corresponding to homochiral and heterochiral configurations which can be directly probed by the longitudinal conductivity. These phases exhibit distinct transport signatures, establishing a unified framework linking orbitronics and unconventional magnetism through coupled spin-orbital $p$-wave order.

Figures

Figures reproduced from arXiv: 2607.02378 by B\"orge G\"obel, Ersoy \c{S}a\c{s}{\i}o\u{g}lu, Samir Lounis, Tom G. Saunderson.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Reference graph

Works this paper leans on

32 extracted references · 11 linked inside Pith

  1. [1]

    Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism,

    Rafael Gonz´ alez-Hern´ andez, Libor ˇSmejkal, Karel V´ yborn´ y, Yuta Yahagi, Jairo Sinova, Tom´ aˇ s Jungwirth, and Jakub ˇZelezn´ y, “Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism,” Phys. Rev. Lett.126, 127701 (2021), arXiv:2002.07073

    Pith/arXiv arXiv 2021

  2. [2]

    Be- yond Conventional Ferromagnetism and Antiferromag- netism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry,

    Libor ˇSmejkal, Jairo Sinova, and Tomas Jungwirth, “Be- yond Conventional Ferromagnetism and Antiferromag- netism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry,” Phys. Rev. X12, 031042 (2022)

    2022

  3. [3]

    Emerging Research Landscape of Altermagnetism,

    Libor ˇSmejkal, Jairo Sinova, and Tomas Jungwirth, “Emerging Research Landscape of Altermagnetism,” Phys. Rev. X12, 040501 (2022), arXiv:2204.10844

    Pith/arXiv arXiv 2022

  4. [4]

    Altermagnetism Then and Now,

    I I Mazin, “Altermagnetism Then and Now,” Phys. Rev. X (2024)

    2024

  5. [5]

    Nanoscale imaging and control of alter- magnetism in MnTe,

    O. J. Amin, A. Dal Din, E. Golias, Y. Niu, A. Za- kharov, S. C. Fromage, C. J. B. Fields, S. L. Heywood, R. B. Cousins, F. Maccherozzi, J. Krempask´ y, J. H. Dil, D. Kriegner, B. Kiraly, R. P. Campion, A. W. Rushforth, K. W. Edmonds, S. S. Dhesi, L. ˇSmejkal, T. Jungwirth, and P. Wadley, “Nanoscale imaging and control of alter- magnetism in MnTe,” Nature6...

    2024

  6. [6]

    Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2,

    Olena Fedchenko, Jan Min´ ar, Akashdeep Akashdeep, Sunil Wilfred D’Souza, Dmitry Vasilyev, Olena Tkach, Lukas Odenbreit, Quynh Nguyen, Dmytro Kutnyakhov, Nils Wind, Lukas Wenthaus, Markus Scholz, Kai Ross- nagel, Moritz Hoesch, Martin Aeschlimann, Benjamin Stadtm¨ uller, Mathias Kl¨ aui, Gerd Sch¨ onhense, Tomas Jungwirth, Anna Birk Hellenes, Gerhard Jako...

    Pith/arXiv arXiv 2024

  7. [7]

    All-electrically controlled spintronics in altermagnetic heterostructures,

    Pei Hao Fu, Qianqian Lv, Yong Xu, Jorge Cayao, Jun Feng Liu, and Xiang Long Yu, “All-electrically controlled spintronics in altermagnetic heterostructures,” npj Quantum Mater. 2025 10110, 111– (2025), arXiv:2506.05504

    arXiv 2025

  8. [8]

    Chiral-Angle- Controlled Altermagnetic Spin Splitting in Nanotubes,

    Ersoy S S ¸a¸ sıo˘ glu, Tom G Saunderson, B¨ orge G¨ obel, Ingrid Mertig, and Samir Lounis, “Chiral-Angle- Controlled Altermagnetic Spin Splitting in Nanotubes,” (2026), arXiv:2606.08757

    Pith/arXiv arXiv 2026

  9. [9]

    P-wave magnets,

    Anna Birk Hellenes, Tom´ aˇ s Jungwirth, Rodrigo Jaeschke-Ubiergo, Atasi Chakraborty, Jairo Sinova, and Libor ˇSmejkal, “P-wave magnets,” arXiv2309.01607 (2023), arXiv:2309.01607 [cond-mat.mtrl-sci]

    Pith/arXiv arXiv 2023

  10. [10]

    Minimal Mod- els and Transport Properties of Unconventionalp-Wave Magnets,

    Bjørnulf Brekke, Pavlo Sukhachov, Hans Hans Gl¨ ockner Giil, Arne Brataas, and Jacob Linder, “Minimal Mod- els and Transport Properties of Unconventionalp-Wave Magnets,” Phys. Rev. Lett.133, 236703 (2024)

    2024

  11. [11]

    Emergence ofp-wave collinear magnetism in antiferromagnets with reflection- asymmetric magnetic motifs,

    Reynel C´ ardenas, Valeria Quintana, Lin-Ding Yuan, and Carlos Mera Acosta, “Emergence ofp-wave collinear magnetism in antiferromagnets with reflection- asymmetric magnetic motifs,” Phys. Rev. B113, 94431 (2026)

    2026

  12. [12]

    Electrical switching of a p-wave magnet,

    Qian Song, Srdjan Stavri´ c, Riccardo Comin, and Others, “Electrical switching of a p-wave magnet,” Nature642, 349–355 (2025)

    2025

  13. [13]

    Highly efficient non- relativistic Edelstein effect in nodal p-wave magnets,

    Atasi Chakraborty, Anna Birk Hellenes, Libor ˇSmejkal, Jairo Sinova, and Others, “Highly efficient non- relativistic Edelstein effect in nodal p-wave magnets,” Nat. Commun.16(2025), 10.1038/s41467-025-62516-0

    doi:10.1038/s41467-025-62516-0 2025

  14. [14]

    P-wave magnetism in a metal,

    Daniel McNally, “P-wave magnetism in a metal,” Nat. Mater.25, 16 (2026)

    2026

  15. [15]

    Floquet Odd-Parity Collinear Mag- nets,

    Tongshuai Zhu, Di Zhou, Huaiqiang Wang, Su Huai Wei, and Jiawei Ruan, “Floquet Odd-Parity Collinear Mag- nets,” Phys. Rev. Lett.136, 126704 (2026)

    2026

  16. [16]

    Rolling Two-Dimensional Collinear Magnets into Chiral Nanotubes withp-Wave Magnetism,

    Zhejunyu Jin, Robin R. Neumann, Rodrigo Jaeschke- Ubiergo, Jairo Sinova, and Alexander Mook, “Rolling Two-Dimensional Collinear Magnets into Chiral Nanotubes withp-Wave Magnetism,” (2026), arXiv:2606.30214

    Pith/arXiv arXiv 2026

  17. [17]

    Chirality-dependentp-wave anti-altermagnetism and edelstein effect in analytically solvable spin-spiral model,

    B¨ orge G¨ obel, Tom G. Saunderson, Lennart Schimpf, Freia Opfermann, Ersoy S ¸a¸ sıo˘ glu, and Samir Lou- nis, “Chirality-dependentp-wave anti-altermagnetism and edelstein effect in analytically solvable spin-spiral model,” (2026), manuscript in preparation

    2026

  18. [18]

    Orbital Topology of Chiral Crystals for Orbitronics,

    Kenta Hagiwara, Ying Jiun Chen, Dongwook Go, Xin Liang Tan, Sergii Grytsiuk, Kui Hon Ou Yang, Guo Jiun Shu, Jing Chien, Yi Hsin Shen, Xiang Lin Huang, Iulia Cojocariu, Vitaliy Feyer, Minn Tsong Lin, Stefan Bl¨ ugel, Claus Michael Schneider, Yuriy Mokrousov, and Christian Tusche, “Orbital Topology of Chiral Crystals for Orbitronics,” Adv. Mater.37, 2418040...

    Pith/arXiv arXiv 2025

  19. [19]

    Intrinsic Spin and Orbital Hall Ef- fects from Orbital Texture,

    Dongwook Go, Daegeun Jo, Changyoung Kim, and Hyun Woo Lee, “Intrinsic Spin and Orbital Hall Ef- fects from Orbital Texture,” Phys. Rev. Lett.121, 86602 (2018), arXiv:1804.02118

    Pith/arXiv arXiv 2018

  20. [20]

    Orbitronics: Orbital currents in solids,

    Dongwook Go, Daegeun Jo, Hyun Woo Lee, Mathias Kl¨ aui, and Yuriy Mokrousov, “Orbitronics: Orbital currents in solids,” Europhys. Lett.135, 37001 (2021), arXiv:2107.08478

    Pith/arXiv arXiv 2021

  21. [21]

    Chirality-induced Orbital Edelstein Effect in an Analyt- ically Solvable Model,

    B¨ orge G¨ obel, Lennart Schimpf, and Ingrid Mertig, “Chirality-induced Orbital Edelstein Effect in an Analyt- ically Solvable Model,” Phys. Rev. Res.7, 33180 (2025)

    2025

  22. [22]

    Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and met- als,

    Davide Ceresoli, T Thonhauser, David Vanderbilt, and Raffaele Resta, “Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and met- als,” Phys. Rev. B74, 24408 (2006)

    2006

  23. [23]

    Berry phase effects on electronic properties,

    Di Xiao, Ming Che Chang, and Qian Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys.82, 1959–2007 (2010), arXiv:0907.2021

    Pith/arXiv arXiv 1959

  24. [24]

    Quan- 6 tum Theory of Orbital Magnetization and Its Generaliza- tion to Interacting Systems,

    Junren Shi, G. Vignale, Di Xiao, and Qian Niu, “Quan- 6 tum Theory of Orbital Magnetization and Its Generaliza- tion to Interacting Systems,” Phys. Rev. Lett.99, 197202 (2007), arXiv:0704.3824

    Pith/arXiv arXiv 2007

  25. [25]

    Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure,

    Taiki Yoda, Takehito Yokoyama, and Shuichi Murakami, “Current-induced Orbital and Spin Magnetizations in Crystals with Helical Structure,” Sci. Rep.5, 12024– (2015)

    2015

  26. [26]

    Chirality-induced selectivity of angular momentum by orbital Edelstein effect in carbon nanotubes,

    B¨ orge G¨ obel, Ingrid Mertig, and Samir Lounis, “Chirality-induced selectivity of angular momentum by orbital Edelstein effect in carbon nanotubes,” Commun. Phys.8, 395– (2025), arXiv:2504.07665

    arXiv 2025

  27. [27]

    See Supplemental Material

  28. [28]

    Controlling the helicity of magnetic skyrmions in aβ-Mn-type high-temperature chiral mag- net,

    K Karube, K Shibata, J S White, T Koretsune, X Z Yu, Y Tokunaga, H M Rønnow, R Arita, T Arima, Y Tokura, and Y Taguchi, “Controlling the helicity of magnetic skyrmions in aβ-Mn-type high-temperature chiral mag- net,” Phys. Rev. B98, 155120 (2018)

    2018

  29. [29]

    A new class of chiral materials hosting magnetic skyrmions beyond room temperature,

    Y Tokunaga, X Z Yu, J S White, H M Rønnow, D Morikawa, Y Taguchi, and Y Tokura, “A new class of chiral materials hosting magnetic skyrmions beyond room temperature,” Nat. Commun.6, 7638 (2015)

    2015

  30. [30]

    Chiral Properties of Structure and Magnetism in Mn 1−xFexGe Compounds: When the Left and the Right are Fighting, Who Wins?

    S V Grigoriev, N M Potapova, S.-A. Siegfried, V A Dyad- kin, E V Moskvin, V Dmitriev, D Menzel, C D De- whurst, D Chernyshov, R A Sadykov, L N Fomicheva, and A V Tsvyashchenko, “Chiral Properties of Structure and Magnetism in Mn 1−xFexGe Compounds: When the Left and the Right are Fighting, Who Wins?” Phys. Rev. Lett.110, 207201 (2013)

    2013

  31. [31]

    Control of Dzyaloshinskii-Moriya Interaction in Mn1−xFexGe: A First-Principles Study,

    Takashi Koretsune, Naoto Nagaosa, and Ryotaro Arita, “Control of Dzyaloshinskii-Moriya Interaction in Mn1−xFexGe: A First-Principles Study,” Sci. Rep.5, 13302 (2015)

    2015

  32. [32]

    Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling,

    K. Shibata, X. Z. Yu, T. Hara, D. Morikawa, N. Kanazawa, K. Kimoto, S. Ishiwata, Y. Matsui, and Y. Tokura, “Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling,” Nat. Nanotechnol.8, 723–728 (2013)

    2013