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Highly Efficient Non-relativistic Edelstein effect in p-wave magnets

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Pith's one-line read Coplanar p-wave magnets convert charge to spin up to 25 times more efficiently than the best spin-orbit-based materials, without needing heavy elements.

desk verdict A solid symmetry-based prediction of a non-relativistic Edelstein effect in p-wave magnets, with a concrete material proposal that needs a sharper check on the experimental magnetic order and the quasiparticle broadening. read the letter →

arxiv 2411.16378 v1 pith:QPFI4VPN submitted 2024-11-25 cond-mat.mes-hall cond-mat.mtrl-sci

Atasi Chakraborty , Anna Birk Hellenes , Rodrigo Jaeschke-Ubiergo , Tomas Jungwirth , Libor Šmejkal , Jairo Sinova This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords Edelsteineffectnon-relativisticp-wavemagnetsspin-chargeconversionCeNiAsOcoplanarnon-collinearmagnetismKubolinearresponsespin-orbit-freespintronics
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

Spin-charge conversion, the Edelstein effect, has generally been thought to require spin-orbit coupling and therefore heavy elements in non-centrosymmetric crystals. This paper argues that coplanar p-wave magnets, whose non-collinear magnetic order combines a 180-degree spin rotation with a lattice translation, produce a purely exchange-driven Edelstein effect with no spin-orbit coupling at all. The response is strongly anisotropic, with spin polarization pointing out of the plane of the magnetic order, and in the candidate material CeNiAsO it reaches about 13 $\hbar$ Å/V, roughly 25 times the best reported relativistic Rashba value and the non-relativistic value in LuFeO$_3$. If correct, this would make light-element magnets viable for efficient charge-to-spin conversion in spintronic devices.

What carries the argument

The carrier of the argument is the spin-space-group symmetry $[C_{2\perp}\|\mathbf{t}]$: a 180-degree rotation of spin space about an axis perpendicular to the plane of the coplanar spins combined with a translation by half a lattice vector. In a p-wave magnet this symmetry survives while inversion is broken, forcing the spin-polarization direction in the band structure to be perpendicular to the spin plane and producing the odd-parity p-wave spin splitting. The response is then calculated with Kubo linear response; the dominant term is the intra-band Fermi-surface contribution, which is even under time reversal, while the inter-band Berry-curvature-like term is forbidden because p-wave magnets preserve time-reversal symmetry in momentum space through the $\mathcal{T}\mathbf{t}$ operation. Exchange-driven hopping $t_J$ rather than spin-orbit coupling controls the magnitude, which is why light-element candidates can compete.

What would settle it

A spin-torque ferromagnetic resonance or magneto-optical Kerr measurement of current-induced spin density in CeNiAsO would settle it: if the out-of-plane susceptibility $\chi^{zx}$ comes out near the relativistic baseline (about 0.5 $\hbar$ Å/V) rather than the predicted 13 $\hbar$ Å/V, or if the dominant spin polarization is in-plane rather than out-of-plane, the central claim would be contradicted.

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Extended reading notes

Core claim

The paper's central claim is that the non-relativistic Edelstein effect (NREE) exists in p-wave magnets: magnets with coplanar non-collinear order whose spin-space group contains the element $[C_{2\perp}\|\mathbf{t}]$—a 180° spin rotation about an axis perpendicular to the spin plane followed by a translation. This symmetry forces the band structure to split into opposite out-of-plane spin polarizations with odd-parity p-wave character, while the combined time-reversal-and-translation symmetry $\mathcal{T}\mathbf{t}$ keeps time-reversal symmetry in momentum space and zero net magnetization. Under an applied electric field, the intra-band Fermi-surface term of the Kubo response produces an out-of-plane spin accumulation with only $\chi^{zx}$ and $\chi^{zz}$ components finite; the inter-band T-odd term vanishes. In density-functional-theory calculations on CeNiAsO with spin-orbit coupling switched off, the integrated $\chi^{zx}$ susceptibility is about 13 $\hbar$ Å/V, 25 times larger than the best reported relativistic Rashba value and the NREE of LuFeO$_3$, establishing p-wave magnets as high-efficiency non-relativistic spin-charge converters.

Load-bearing premise

The whole result hinges on CeNiAsO having exactly the periodic, all-spins-in-one-plane magnetic pattern the calculation assumes; if the real magnetic order is incommensurate or its symmetry is only approximate, the tensor components and the 25-fold enhancement could change or wash out.

Editorial extensions

If this is right

  • Charge-to-spin conversion no longer requires heavy elements or inversion-breaking crystal fields; coplanar p-wave magnets with light elements should show Edelstein responses comparable to or larger than standard spin-orbit systems.
  • The NREE tensor in p-wave magnets has only out-of-plane susceptibility components, so rotating the electric-field direction or measuring the spin-polarization direction cleanly distinguishes this effect from the in-plane Rashba Edelstein effect.
  • CeNiAsO, with its predicted susceptibility of about 13 $\hbar$ Å/V, becomes a concrete candidate material for efficient spin-orbit-torque-type devices based on a non-relativistic mechanism.
  • The vanishing of the inter-band contribution means the effect is governed entirely by the Fermi-surface intra-band term, giving a transparent single-band picture of the spin accumulation.
  • The angular dependence of the NREE in the Kagome model shows a nodal direction independent of chemical potential, providing a sharp experimental signature for p-wave magnets.

Reading between the lines

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

  • By the same symmetry logic, other coplanar non-collinear magnets carrying the $[C_{2\perp}\|\mathbf{t}]$ element should show the same out-of-plane-only NREE tensor, so a systematic computational screen of such magnetic orders could turn up materials with even larger responses than CeNiAsO.
  • The calculation fixes the magnetic order to an exact commensurate pattern, whereas the experimentally reported magnetism in CeNiAsO can be incommensurate; if the real order breaks the $[C_{2z}\|\mathbf{t}_{a/2}]$ symmetry, the predicted 25-fold enhancement may be reduced or averaged away, and this is a testable open question.
  • One could test the mechanism directly by comparing in-plane and out-of-plane Edelstein responses in a heavy-element candidate: a dominant out-of-plane component would confirm that exchange-driven NREE, not spin-orbit coupling, is doing the work.
  • If the NREE is as strong as predicted, current-driven manipulation of the coplanar order itself—analogous to spin-orbit torques but without spin-orbit coupling—becomes a plausible route, which the paper only gestures at.
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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

3 major / 5 minor

Summary. The paper proposes a non-relativistic Edelstein effect (NREE) in p-wave magnets, i.e., coplanar non-collinear magnets with a combined spin-rotation-and-translation symmetry [C2⊥||t] that preserves time-reversal symmetry in momentum space. Using Kubo linear response, the authors compute the NREE susceptibility in a minimal four-band model and in a Kagome-lattice model, finding a large, strongly anisotropic, out-of-plane spin polarization. They then perform DFT-based Wannier tight-binding calculations for CeNiAsO and report a unit-cell-integrated NREE susceptibility of about 13 ℏÅ/V, which they state is 25 times larger than the values for LuFeO3 and for archetypal relativistic Rashba/topological-insulator systems. The paper concludes that p-wave magnets are promising materials for efficient charge-to-spin conversion without spin-orbit coupling.

Significance. The conceptual advance is significant: identifying a non-relativistic, exchange-driven charge-to-spin conversion mechanism in p-wave magnets, with a distinctive out-of-plane polarization and strong anisotropy, would broaden the materials palette for spintronics beyond heavy-element SOC systems. The symmetry-based classification and the explicit model calculations are strengths; the minimal-model and Kagome results are internally consistent and the tensor forms follow from the stated spin group. The DFT calculation for CeNiAsO is a concrete material prediction, but its validity depends on assumptions about the magnetic ground state and on numerical inputs that are not fully disclosed in the main text. If the material-specific claim is confirmed, the work would be an important step toward practical NREE devices; however, the current manuscript leaves the central quantitative claim under-supported.

major comments (3)
  1. [Material Candidate: CeNiAsO] The paper states that CeNiAsO 'shows a co-planar commensurate magnetic order' and cites Wu et al. (Ref. [47]), whose title is 'Incommensurate Magnetism Near Quantum Criticality in CeNiAsO.' This is a direct factual discrepancy: the cited experimental work reports an incommensurate magnetic ground state. The DFT calculation constrains the moments to a commensurate coplanar order with the exact spin-space symmetry [C2z||t_a/2], but if the true order is incommensurate, that symmetry is not exact, and the derived tensor form (only χ_zx and χ_zz) and the nodal-line protection are not strictly valid. The 13 ℏÅ/V susceptibility could be modified or averaged away. The authors must clarify the experimental magnetic structure, justify the commensurate approximation used in the calculation, or explicitly reframe the CeNiAsO result as a hypothetical commensurate phase rather than a prediction for the physical ground state.
  2. [Methods / Eq. (3)] The intra-band susceptibility in Eq. (3) scales as 1/Γ, where Γ is the quasiparticle broadening. The main text specifies Γ = 0.1 eV for the minimal model and Γ = 0.01 eV for the Kagome model, but it never reports the Γ used for the Wannier tight-binding calculation of CeNiAsO. Without this value, the quoted absolute magnitude of 13 ℏÅ/V is not reproducible. Please state the Γ value (or the range of values) used in the material calculation and discuss how the claimed enhancement depends on this parameter.
  3. [Abstract and Discussion] The abstract and the concluding paragraph claim the CeNiAsO NREE is '25 times larger' than the 'maximally achieved relativistic EE' and than 'other reported NREE,' but the numerical comparison in the main text is only made against LuFeO3 (0.5 ℏÅ/V, giving a factor of about 26). The corresponding value for the relativistic benchmark (α-Sn, Ref. [20]) or for the Rashba 2DEG in comparable units is not given. Moreover, the Rashba 2DEG susceptibility is a sheet quantity (units ℏ/V·Å) while the CeNiAsO value is a unit-cell-integrated bulk quantity (units ℏÅ/V), so the direct comparison may be dimensionally inconsistent. Please provide the specific benchmark value used and, if necessary, recast the comparison in a consistent dimensional framework.
minor comments (5)
  1. [Eq. (2)] The text above Eq. (2) calls the object a 'spin-current response function,' but the equation and the surrounding discussion refer to the spin-density response to an electric field; please correct the terminology.
  2. [Fig. 4f] The caption states that dashed curves show 'modifications of the specific components in the presence of SOC,' but the Methods describe calculations with constrained moments and with SOC switched off. It would be helpful to state explicitly how the SOC-included results were obtained (e.g., a separate DFT calculation with SOC, or a perturbative treatment).
  3. [Introduction] The phrase 'the much larger spin-splitting (almost 2 orders of magnitude larger) relative to the relativistic EE' is a quantitative claim but no source or figure is given in the main text; please provide a reference or move the quantitative statement to the SI.
  4. [References] Ref. [35] is cited as 'Arxiv Prepr.'; please update it with the published version or a complete arXiv identifier.
  5. [Abstract] The word 'demonstrate' overstates what is a theoretical prediction; consider using 'show' or 'predict.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CeNiAsO NREE susceptibility is a first-principles Kubo response calculation with no fitted parameters, and the p-wave classification from the authors' prior work is a parameter-free symmetry derivation independent of the computed magnitude.

full rationale

The central quantitative claim (CeNiAsO χ_zx ~ 13 ℏÅ/V, about 25 times the LuFeO3 value of 0.5 ℏÅ/V) is obtained from a Kubo linear-response calculation on a DFT-derived Wannier tight-binding Hamiltonian. No parameter of the response calculation is fitted to the target observable; the inputs are the crystal structure and an assumed magnetic order, and the benchmarks (LuFeO3 from Ref. [33], Rashba 2DEG estimate) are external to the present authors' work. The p-wave classification and the symmetry-allowed tensor form (only χ_zx and χ_zz) are taken from the authors' own Ref. [35], but that is a parameter-free group-theoretic spin-symmetry classification whose assumptions (coplanar order, [C2⊥||t]) do not include the computed susceptibility magnitude; under the stated evidence rules it counts as independent support rather than circularity. The out-of-plane spin polarization follows from the defining [C2⊥||t] symmetry, but the paper explicitly states that the polarization magnitude is k-dependent and not protected, and the numerical magnitude is a computed result rather than a restatement of the definition. One nontrivial caveat is empirical rather than circular: the paper calls the CeNiAsO order "co-planar commensurate" and cites Wu et al. PRL 122, 197203, whose title reports "Incommensurate Magnetism Near Quantum Criticality in CeNiAsO." If the true magnetic order is incommensurate, the exact [C2z||t_a/2] symmetry and the associated tensor form are not exact. This is a correctness/consistency risk, not a self-referential derivation, and does not affect the circularity score.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central quantitative prediction (13 hbar Angstrom/Volt and the 25x ratio) depends on the broadening Gamma as a free parameter, and the material-specific calculation rests on the unverified commensurability of the magnetic order and on a PBE treatment of Ce 4f electrons. No new particles or mediators are introduced.

free parameters (5)
  • Quasiparticle lifetime broadening Gamma = Not reported for CeNiAsO; 0.01 eV in the Kagome model and 0.1 eV in the Rashba comparison.
    The intraband susceptibility in Eq. (3) is proportional to 1/Gamma. The reported NREE value of 13 hbar Angstrom/Volt for CeNiAsO therefore depends on the unspecified Gamma; a smaller (longer-lived) broadening would inflate the 25x ratio, and a larger one would shrink it. This is the main free parameter controlling the headline efficiency.
  • Exchange-dependent hopping ratio tJ/t = 0.25
    Chosen for the minimal model band structure (Fig. 2b); increasing tJ increases the response (Fig. 2d), so the illustrative magnitude is parameter-dependent.
  • Exchange and hopping strength |J| = |th| = 1.0 eV
    Set by hand in the Kagome model; sets the energy scale of the spin splitting and the response.
  • Canting angle theta_s = pi/6 (30 degrees)
    Chosen for the Kagome calculation; the response magnitude depends strongly on theta_s and vanishes at the collinear limit 90 degrees, so the illustrative value is a choice.
  • Rashba strength alpha_R and mass m0 for comparison = alpha_R = 1e-9 eV*m, m0 = free-electron mass
    Used to convert the Rashba 2DEG Edelstein response to a susceptibility for the comparison in Fig. 2d; typical literature values, but affects the claimed order-of-magnitude advantage.
assumptions (4)
  • domain assumption The p-wave magnet classification and symmetry constraints from Ref. [35] correctly identify CeNiAsO and dictate the allowed NREE tensor components.
    The paper selects the material and predicts the chi_zx and chi_zz components based on the spin-space group from the authors' own prior work; if the classification is incomplete, the response tensor could differ.
  • standard math The Kubo linear-response expression with constant relaxation time Gamma describes the current-induced spin accumulation.
    Eqs. (2)-(4) employ the standard Kubo formula; the constant-Gamma approximation simplifies vertex corrections and broadening.
  • domain assumption The experimental magnetic order of CeNiAsO is commensurate with the T-t symmetry used in the DFT setup.
    The paper states 'co-planar commensurate magnetic order' and cites Ref. [47] titled 'Incommensurate Magnetism Near Quantum Criticality in CeNiAsO'; the discrepancy is unaddressed.
  • domain assumption PBE-GGA without LDA+U or DMFT accurately describes the Ce 4f states near the Fermi level.
    Ce is a rare-earth ion with strongly correlated 4f electrons; Ref. [47] emphasizes quantum criticality and heavy-fermion behavior. The band structure used to compute the NREE may be sensitive to the 4f position.

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Cite this review

Pith. "Pith review of Highly Efficient Non-relativistic Edelstein effect in p-wave magnets." pith.science (2026). https://pith.science/paper/QPFI4VPN

@misc{pith2026241116378,
  author       = {Pith},
  title        = {Pith review of: Highly Efficient Non-relativistic Edelstein effect in p-wave magnets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QPFI4VPN}},
  note         = {Machine review of arXiv:2411.16378}
}
read the original abstract

The origin and efficiency of charge-to-spin conversion, known as the Edelstein effect (EE), has been typically linked to spin-orbit coupling mechanisms, which require materials with heavy elements within a non-centrosymmetric environment. Here we demonstrate that the high efficiency of spin-charge conversion can be achieved even without spin-orbit coupling in the recently identified coplanar p-wave magnets. The non-relativistic Edelstein effect (NREE) in these magnets exhibits a distinct phenomenology compared to the relativistic EE, characterized by a strongly anisotropic response and an out-of-plane polarized spin density resulting from the spin symmetries. We illustrate the NREE through minimal tight-binding models, allowing a direct comparison to different systems. Through first-principles calculations, we further identify the p-wave candidate material CeNiAsO as a high-efficiency NREE material, revealing a 25 times larger response than the maximally achieved relativistic EE and other reported NREE in non-collinear magnetic systems with broken time-reversal symmetry. This highlights the potential for efficient spin-charge conversion in p-wave magnetic systems.

Figures

Figures reproduced from arXiv: 2411.16378 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of a relativistic Rashba spin-texture [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Schematic of the lattice model with a coplanar [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Direct space magnetic order of the Kagome lattice with twice propagation along the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Top (a) and side (b) view of the unit cell of CeNiAsO crystal and the co-planar magnetic order with [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Forward citations

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Pith tools

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