{"id":"fc2ecc67-ff5b-42d8-bdf8-b7a602e2c36b","arxiv_id":"2412.10984","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In the helical and broken-helical phases of EuIn2As2, magnetic exchange creates non-relativistic spin textures that yield a phase-distinguishing Edelstein response, about five times larger in the helical phase.","lead":"The authors use spin-symmetry analysis and density functional theory to show that two candidate magnetic phases of the candidate axion insulator EuIn2As2 host exchange-driven, out-of-plane 'odd-parity' spin textures, with an additional in-plane 'g-wave' texture unique to the low-temperature broken-helical phase.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Phase-distinguishing Edelstein signature hinges on hole-doped Fermi level, which is not calculated; χzz vanishes at the stoichiometric Fermi energy.","rationale":"The spin-space-group analysis is internally consistent and the DFT/Wannier results support the predicted spin textures; these parts are credible. The main load-bearing uncertainty is exactly the one identified by the reader: the experimental relevance of the Edelstein contrast depends on the hole-doped chemical potential being in an energy window where χzz is large. The paper states that χzz vanishes at the stoichiometric Fermi level and quotes the factor-of-five contrast at E_F ± 0.3 eV, but it does not compute or estimate the Fermi-level shift from the cited hole doping. A rigid-band shift to match measured carrier densities is a concrete, low-cost check. The absence of this check does not invalidate the symmetry-based prediction of a non-relativistic Edelstein effect in general, but it does mean the strongest practical claim—phase distinguishability via spin-density measurement—is conditional on an unverified assumption. Secondary concerns (U-dependence, missing input files) are reproducibility items, not independent load-bearing flaws. Therefore the reader's CONDITIONAL verdict is appropriate and no change is recommended.","tokens_in":13375,"tokens_out":22549,"duration_ms":216835,"concrete_test":"For each magnetic phase, compute the rigid-band chemical-potential shift Δμ needed to reproduce the experimentally measured hole density (e.g., Hall carrier density or quantum-oscillation frequencies reported in Refs. [34–36]). Then evaluate χzz^intra at E_F^0 + Δμ using the same Wannier/Kubo setup. If the ratio χzz^H/χzz^B at the phase-specific Δμ is not within a factor of two of the quoted ≈5, or if either value is comparable to numerical noise near the nodal energy, the phase-distinguishability claim requires revision to specify the required doping range.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central experimental claim—that the two magnetic phases can be distinguished by a current-induced out-of-plane spin density—requires the real, hole-doped chemical potential to lie in an energy window where χzz^intra is sizable and the computed factor-of-five contrast holds. The authors explicitly state in Sec. IV that 'the spin density vanishes at the Fermi level' for the stoichiometric DFT Fermi energy, and they only quote the factor ≈5 'near the Fermi level, E = EF ± 0.3 eV.' The actual chemical-potential shift corresponding to the experimentally reported hole doping [34–36] is never quantified, so it is unknown whether the doped Fermi surface in either phase lands in the needed window. If the doping shift is small (≪0.3 eV) or places the Fermi level near the nodal regions of the spin texture, the Edelstein response in either or both phases could be near zero, and the proposed phase signature would not be observable. The symmetry analysis guarantees a nonzero tensor in some energy window but not its value at the experimentally relevant chemical potential; the appeal to 'highly hole-doped' crystals is qualitative and does not establish that the effect survives at the operating point.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13479,"tokens_out":7133,"duration_ms":66344,"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":[{"comment":"This is load-bearing because the abstract and conclusion propose the Edelstein contrast as a means to identify the magnetic transition.","section":"Sec. IV, Fig. 4"},{"comment":"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.","section":"Appendix A, Fig. 4"}],"minor_comments":[{"comment":"","section":"Sec. III, Eq. (5)"},{"comment":"","section":"Appendix A"},{"comment":"","section":"Sec. II and III"},{"comment":"","section":"Sec. IV"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know this paper is a solid symmetry-analysis-plus-DFT study of the two non-collinear phases of EuIn2As2. The genuinely new bit is the identification of an in-plane g-wave spin order that exists only in the broken-helical phase, plus the prediction that the non-relativistic Edelstein response along z differs by roughly a factor of five between the helical and broken-helical phases. The symmetry arguments are clear, the minimal Hamiltonians match the spin-space groups, and the DFT band textures confirm the predicted nodal structure. The Kubo calculations are standard practice and appear carefully done. No fitted parameters enter the prediction, so the circularity burden is low.\n\nThe main soft spot is exactly where the stress-test lands: the computed spin density vanishes at the stoichiometric Fermi level, and the experimental relevance rests on an assumed hole-doping shift. The authors point to known hole doping in this compound, but they never quantify the shift or show that the doped Fermi surface lands in the energy window where the factor-of-five contrast holds. That is a real gap in the chain from prediction to experiment. It is not fatal—the symmetry analysis guarantees a nonzero tensor in some window, and the argument that real samples are hole-doped is plausible—but it should be stated as a quantitative condition, not an assumption.\n\nTwo smaller issues: no code, inputs, or Wannier settings are provided, which makes the numbers hard to reproduce, and there is no sensitivity analysis for U or the broadening Gamma. Those are minor but annoying for a paper whose main quantitative claim is a ratio.\n\nOverall, this is a careful application of recent spin-space-group machinery to a debated material. The reader who cares about EuIn2As2 or exchange-driven spin textures will get value from it. I would send it to a competent referee; it does not deserve a desk reject. I would ask the referee to push on the doping question and the missing code/data.","headline":"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.","tokens_in":14130,"tokens_out":2494,"would_cite":true,"duration_ms":19772,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["EuIn2As2","non-relativistic Edelstein effect","spin space group","spin-momentum locking","non-collinear antiferromagnetism","g-wave order","axion insulator","current-induced spin density"],"falsifier":"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.","tokens_in":13109,"feed_emoji":"🧲","tokens_out":10623,"duration_ms":87701,"temperature":0.7,"pith_summary":"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.","feed_headline":"Two magnetic phases of EuIn2As2 differ fivefold in current-induced spin","feed_subtitle":"Magnetic exchange alone can create an out-of-plane spin response that marks the helical-to-broken-helical transition.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supply the two commensurate coplanar magnetic structures, helical and broken-helical, whose spin symmetries are analyzed.","marker":"[13, 14]"},{"why":"Established EuIn2As2 as a candidate axion insulator, the motivation for probing its true magnetic ground state.","marker":"[9]"},{"why":"Provide the spin point-group and spin space-group formalism used to derive the non-relativistic spin-momentum locking.","marker":"[18, 19]"},{"why":"Algorithm used to determine the spin symmetry operations of the two magnetic orders.","marker":"[23]"},{"why":"Demonstrates non-relativistic torque and Edelstein effects in non-collinear magnets, the mechanism this paper extends to the helical phases.","marker":"[30]"},{"why":"Recent calculation of the highly efficient non-relativistic Edelstein effect in p-wave magnets, providing the comparison class for the present response.","marker":"[31]"},{"why":"Experimental reports of strong hole doping in EuIn2As2, which the authors invoke to argue the effect is observable despite vanishing at the stoichiometric Fermi level.","marker":"[34–36]"}],"fun_headline_variants":["Non-relativistic Edelstein effect differs fivefold in EuIn2As2","Exchange-driven non-relativistic spin response in EuIn2As2","Fivefold spin signal distinguishes EuIn2As2 phases","No spin-orbit needed: fivefold effect in EuIn2As2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Non-relativistic Edelstein effect differs fivefold in EuIn2As2","Exchange-driven non-relativistic spin response in EuIn2As2","Fivefold spin signal distinguishes EuIn2As2 phases","No spin-orbit needed: fivefold effect in EuIn2As2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001422,"raw_usage":{"total_tokens":5758,"prompt_tokens":981,"completion_tokens":4777,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":4697}},"tokens_in":597,"tokens_out":4777,"duration_ms":30797,"temperature":1.0,"reasoning_tokens":4697,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:25:18.857939+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Shinohara, A","cited_arxiv_id":null,"evidence_quote":"Algorithm used to determine the spin symmetry operations of the two magnetic orders."},{"cited_title":"Gonz´ alez-Hern´ andez, P","cited_arxiv_id":null,"evidence_quote":"Demonstrates non-relativistic torque and Edelstein effects in non-collinear magnets, the mechanism this paper extends to the helical phases."}],"review_version":1}