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Non-relativistic linear Edelstein effect in helical EuIn2As2

T0 review · 2 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Magnetic exchange alone, not spin-orbit coupling, generates the odd-parity spin texture behind a non-relativistic Edelstein effect in EuIn2As2, with a fivefold phase contrast.

desk verdict A careful spin-symmetry analysis of EuIn2As2 that makes a concrete phase-distinguishing Edelstein prediction, but the experimental relevance leans on an unquantified hole-doping shift. read the letter →

arxiv 2412.10984 v4 pith:2MN3LN5Q submitted 2024-12-14 cond-mat.str-el

Nayra A. Álvarez Pari , Rodrigo Jaeschke-Ubiergo , Atasi Chakraborty , Libor Šmejkal , Jairo Sinova This is my paper · ORCID
classification cond-mat.str-el
keywords EuIn2As2non-relativisticEdelsteineffectspinspacegroupspin-momentumlockingnon-collinearantiferromagnetismg-waveorderaxioninsulatorcurrent-induceddensity
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 argues that the magnetic exchange field of the non-collinear coplanar order in EuIn2As2, rather than spin-orbit coupling, is the source of a distinctive out-of-plane spin-momentum locking, and that this exchange-only physics produces a non-relativistic linear Edelstein effect: an electric current along the crystal c-axis induces an out-of-plane spin density. The helical and broken-helical phases share an odd-parity $S_z$ order with a single unpolarized nodal plane at $k_z=0$, while the broken-helical phase alone displays an in-plane $g$-wave order with four nodal planes. First-principles calculations predict that the current-induced out-of-plane spin density is about five times larger in the helical phase than in the broken-helical phase near $E_F \pm 0.3$ eV, making the effect a candidate transport fingerprint of the magnetic transition. The response is essentially non-relativistic; spin-orbit coupling adds only in-plane terms roughly an order of magnitude smaller.

What carries the argument

The central object is the spin space group, which treats rotations in spin space and real space as independent and therefore captures the exchange-dominated physics of non-collinear magnets that magnetic space groups miss. For coplanar order the spin-only group contains $[C_{2\perp}T\|T]$; the helical phase's nontrivial generators include $[C_{3z}\|E]$, which eliminates in-plane spin components, and $[C_{2z}\|C_{2z}]$, which together with $[C_{2\perp}T\|T]$ imposes $S_z(k_x,k_y,k_z)=-S_z(k_x,k_y,-k_z)$. The broken-helical phase replaces the threefold spin rotation by generators that include $[C_{2v}\|P]$, which selects an in-plane $S_v$ component with $g$-wave texture. These symmetries are encoded in the minimal Hamiltonians $h(\mathbf{k}) = A(k_x^2+k_y^2)+B k_z^2 + C k_z\sigma_z$ for the helical phase and the same expression plus $D k_y k_z ((\sqrt{3}k_x)^2 - k_y^2)\,\vec{\sigma}\cdot\hat{v}$ for the broken-helical phase; the $\chi_{ij}$ response tensors are evaluated in the Kubo formalism, with the intraband term proportional to $1/\Gamma$ and the interband term, and the tensors' symmetry-allowed shapes are listed for both phases with and without spin-orbit coupling.

What would settle it

Measure the current-induced out-of-plane spin density (for example by magneto-optical Kerr rotation) in hole-doped EuIn2As2 single crystals while cooling through the 16.2 K transition to the broken-helical phase. A disappearance of the signal or the absence of a roughly fivefold drop between the helical and broken-helical phases would contradict the central claim, as would spin-resolved photoemission showing no antisymmetric $S_z$ splitting at $k_z=0$ or no four g-wave nodal planes for the in-plane component.

Watch

Extended reading notes

Core claim

The paper's central claim is that magnetic exchange alone can produce the kind of antisymmetric spin-momentum locking and current-induced spin response usually associated with spin-orbit coupling. Concretely, the spin point group of the helical phase forbids in-plane spin polarization and forces $S_z$ to be odd in $k_z$, giving an odd-parity order with one nodal plane; the broken-helical phase keeps this $S_z$ odd-parity order and additionally develops a $g$-wave order for the in-plane $S_v$ component, with four nodal planes protected by transposing mirror symmetries. Because the two orders break inversion symmetry while remaining time-reversal-broken, the Kubo intraband response contains a non-relativistic $\chi_{zz}$: an electric field along $z$ creates a non-equilibrium out-of-plane spin density. The authors' DFT and Wannier-interpolated calculations show that this response dominates the spin-orbit-coupling contribution and differs by roughly a factor of five between the two phases near $E_F \pm 0.3$ eV, so measuring the current-induced spin density could distinguish the phases and rule out competing magnetic ground states.

Load-bearing premise

Real EuIn2As2 crystals must be hole-doped so that the Fermi level sits in the energy window where the calculated $\chi_{zz}$ is large; at the stoichiometric Fermi level the predicted spin density is exactly zero.

Editorial extensions

If this is right

  • An electric field along the c-axis should produce an out-of-plane spin density in both phases, with the helical response roughly five times larger near $E_F \pm 0.3$ eV; this ratio gives a transport signature of the helical-to-broken-helical transition.
  • The dominant response is non-relativistic, so it should survive even where spin-orbit coupling is weak; SOC contributes only in-plane components about an order of magnitude smaller than the out-of-plane signal.
  • The broken-helical phase's in-plane $g$-wave order, with its four nodal planes, is unique to that phase and should be observable in spin-resolved photoemission or Kerr rotation.
  • A null current-induced spin density would exclude the proposed amplitude-modulated A1 and A2 phases, which the paper shows are $P$-symmetric and $PT$-symmetric and therefore Edelstein-inactive.
  • The vanishing at the stoichiometric Fermi level is not fatal, because the material is known to be hole-doped; the predicted signal lives in the doped energy window.

Reading between the lines

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

  • The authors do not develop this, but the coexistence of odd-parity $S_z$ order and even-parity $g$-wave order in the broken-helical phase could couple to the axion-insulator topology in ways that modify surface-state or magnetoelectric behavior.
  • Because the intraband response scales as $1/\Gamma$, the disorder-independent ratio $\chi_{zz}/S_{zz}$ reported in the appendix is a more robust experimental target than the raw spin density; measuring it as a function of doping would test the prediction without knowing the scattering rate.
  • The same spin-space-group analysis could be applied to other Eu-based 122 compounds with coplanar non-collinear order; it may predict exchange-dominated Edelstein responses in materials previously assumed to require strong spin-orbit coupling.
  • If the non-relativistic origin is correct, the effect should scale with magnetic exchange strength rather than atomic number, suggesting that lighter-element magnets with similar spin symmetries could show comparable current-induced spin densities.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper studies two non-collinear coplanar magnetic phases of EuIn2As2—the helical and broken-helical phases—using spin-space-group symmetry analysis, non-relativistic DFT+U calculations, and Wannier-interpolated Kubo linear-response computations. The authors show that magnetic exchange alone produces an out-of-plane odd-parity spin polarization with a single nodal plane in both phases, while an in-plane g-wave spin texture appears only in the broken-helical phase. They further compute the current-induced spin-density (Edelstein) response and find a dominant out-of-plane component of non-relativistic origin, with a helical-to-broken-helical contrast of roughly a factor of five near E_F ± 0.3 eV. The paper proposes this response as a transport signature to distinguish the two magnetic phases and to discriminate against other proposed ground states.

Significance. If the quantitative predictions hold, the paper offers a symmetry-principled explanation of exchange-driven spin textures in a candidate axion insulator and identifies a concrete experimental observable, the current-induced out-of-plane spin density, that could distinguish between competing magnetic orders. The work is rigorous in construction: the symmetry analysis is internally consistent, the DFT spin textures match the symmetry-imposed shapes, and the Edelstein tensor magnitudes come from independent Wannier-interpolated Kubo calculations rather than from fits to the symmetry model. The use of the spinspg package and the Wannier90/WannierBerri pipeline also makes the computational workflow reproducible. The main gap is that the proposed experimental signature relies on an unquantified hole-doping shift of the Fermi level, and the quantitative claims are made at a single Hubbard U and spectral broadening.

major comments (2)
  1. [Sec. IV, Fig. 4] This is load-bearing because the abstract and conclusion propose the Edelstein contrast as a means to identify the magnetic transition.
  2. [Appendix A, Fig. 4] This is a load-bearing issue because the paper's headline is the phase contrast and the non-relativistic dominance, not merely the existence of an allowed tensor component.
minor comments (4)
  1. [Sec. III, Eq. (5)]
  2. [Appendix A]
  3. [Sec. II and III]
  4. [Sec. IV]

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the computed Edelstein magnitudes are independent outputs of DFT-based Kubo calculations, not re-imported symmetry-model inputs.

full rationale

The paper's derivation chain cleanly separates symmetry analysis from ab initio calculation. The spin-texture shapes in Secs. II and III are derived from spin point group generators and captured in the minimal Hamiltonians (Eqs. 2 and 5), but the central quantitative claims — the out-of-plane non-relativistic Edelstein response and the approximate factor of five between helical and broken-helical phases — come from the Kubo formulas (Eqs. 6 and 7) evaluated on Wannier-interpolated DFT band structures via the Wannierberri package, as described in Appendix A. No parameter is fitted to the target quantity, and the minimal Hamiltonians are not used to generate the response tensors; the symmetry-constrained tensor shapes in Table I are independently confirmed by the DFT/Wannier calculations. The magnetic structures themselves are taken from the external MAGNDATA database, not from the authors' prior work. Self-citations to the same group's p-wave-magnet and spin-space-group papers appear, but they are used for context and terminology (e.g., the distinction from Ref. [24] and the statement that non-relativistic Edelstein effects have been demonstrated in Refs. [30, 31]), and the present claim does not reduce to those citations. The acknowledged limitation that the spin density vanishes at the stoichiometric Fermi level, with experimental relevance resting on the assumption of hole doping (Sec. IV), is an operating-point assumption with external experimental references, not a circular input-output equivalence. I therefore find no circular step.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The analysis relies on two experimentally reported magnetic structures plus standard DFT and Kubo approximations; the only hand-chosen numerical inputs are U and Γ.

free parameters (2)
  • Hubbard U = 5 eV
    Chosen to localize Eu 4f states; shifts band energies and therefore the energy profile of χzz; no sensitivity scan is presented.
  • Spectral broadening Γ = 0.01 eV
    Chosen for the Kubo formulas; the absolute spin density scales as 1/Γ, but the phase-contrast ratio is Γ-independent and also given.
assumptions (4)
  • domain assumption The helical and broken-helical coplanar structures (with tripled unit cell) are the relevant magnetic ground states for the comparison.
    Sec. I and App. A use MAGNDATA entries #1.0.31 and #1.0.32; alternate incommensurate and amplitude-modulated structures (Refs. 15-17) are explicitly not analyzed but are part of the experimental debate.
  • standard math The non-relativistic spin-space-group classification with the coplanar spin-only group applies to the exchange-dominated regime.
    Sec. II invokes the Litvin-Opechowski spin-group formalism, an accepted framework in this field.
  • domain assumption PBE+U DFT with U=5 eV and constrained moments accurately describes the relevant bands and Fermi surface.
    App. A; one functional choice is used, without convergence or sensitivity checks.
  • domain assumption Kubo linear response with constant broadening describes the current-induced spin density.
    Sec. IV; standard response theory, but Γ is an external parameter and the absolute response scales as 1/Γ.

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Cite this review

Pith. "Pith review of Non-relativistic linear Edelstein effect in helical EuIn2As2." pith.science (2026). https://pith.science/paper/2MN3LN5Q

@misc{pith2026241210984,
  author       = {Pith},
  title        = {Pith review of: Non-relativistic linear Edelstein effect in helical EuIn2As2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2MN3LN5Q}},
  note         = {Machine review of arXiv:2412.10984}
}
read the original abstract

Motivated by the ongoing interest in understanding the actual magnetic ground state of the promising axion insulator candidate EuIn2As2, we present here a spin symmetry analysis and ab-initio calculations, aiming to identify specific exchange-dominated physics that could offer insights into the current debate. We investigate two non-collinear coplanar magnetic orders reported in this compound: the helical and broken helical phases. Our symmetry analysis shows that magnetic-exchange alone results in the formation of an out-of-plane odd-wave order in momentum space with a single un-polarized nodal plane in both phases. Additionally, we identified an in-plane g-wave order that emerges exclusively in the broken helical phase, providing a distinguishing feature for this phase. Furthermore, we report a non-relativistic Edelstein effect with a distinct out-of-plane polarized spin density that dominates over spin-orbit coupling effects. Our ab-initio calculations reveal a significant contrast in the magnitude of this effect between both phases, which could serve as a means to identify the magnetic transition and distinguish them from other magnetic ground states proposed for this compound.

Figures

Figures reproduced from arXiv: 2412.10984 by the authors.

Figure 1
Figure 1. FIG. 1. Non-collinear coplanar magnetic textures of EuIn [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Electronic band structures and momentum-space energy iso-surfaces without SOC of the non-collinear helical EuIn [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Electronic band structure and energy iso-surfaces without SOC for the non-collinear broken-helical EuIn [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Computed intraband out-of-plane response tensor [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Six in-plane axes, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Electronic band structure of the collinear EuIn [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. In-plane spin polarized energy bands of the helical phase [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Momentum-space [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Intraband response tensor [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 10
Figure 10. Figure 10: FIG. 10. (a-b)Momentum-space [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 12
Figure 12. Figure 12: (a), we show the longitudinal conductivity Szz, featuring values within the typical range of conductivities observed in semiconductors. Finally, in [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]

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Reviewed August 11, 2026 · model on record in the stance chip above.