{"id":"276f99fe-1dae-4692-9b11-2bc4f996af66","arxiv_id":"2608.03551","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Bulk antiferromagnetic KV2Se2O is predicted to have d-wave altermagnetic surface states and a large surface nonlinear Edelstein effect that explains existing spin-splitting observations.","lead":"This paper calculates that the (001) surface of the antiferromagnet KV2Se2O should show d-wave altermagnetic spin splitting even though the bulk is magnetically compensated. It predicts a large surface-localized nonlinear Edelstein response that could be measured and would resolve a disagreement between neutron and photoemission experiments.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central prediction depends on the assumed ideal VO-terminated (001) surface with bulk AFM order persisting; the paper's Figs. 4–5 show SeK termination removes the V-d surface states and suppresses the μ=0.2 eV NLEE peak, making the 125-value signature conditional on an unverified termination.","rationale":"The paper's qualitative claim—that a PT-symmetric bulk AFM can host d-wave surface altermagnetism—is grounded in a clear symmetry analysis and supported by slab DFT/Wannier calculations. The symmetry constraints on the Edelstein tensors (Appendix C) are standard and parameter-free, and the layer-resolved calculation showing surface localization is a reasonable approach. However, the quantitative headline result, including the abstract's 'large nonlinear Edelstein response' and the explicit value ~125 e^2τ^2a^2/(2π)^2ℏ, is obtained for a specific surface termination. The authors themselves show in Figs. 4–5 that SeK termination removes the V-d surface states and suppresses the response at μ=0.2 eV, and they note that terraces with opposite moments will cause cancellation. The reader's weakest_assumption correctly identified this ideal-surface assumption. I agree that this is the most load-bearing concern because it affects both the ARPES reconciliation (which requires VO-terminated surface states) and the proposed experimental signature (the 125-value NLEE peak). The concern does not invalidate the qualitative conclusion, but it means the quantitative prediction is not directly transferable to a real sample unless the termination is verified. Since the paper already frames its claims conditionally and acknowledges termination sensitivity, the appropriate verdict remains CONDITIONAL, and my analysis does not change the reader's verdict.","tokens_in":18156,"tokens_out":26039,"duration_ms":240146,"concrete_test":"Compute the surface/cleavage energy of the (001) surface of the AFM phase for VO and SeK terminations using the same PBEsol settings, and compare with the termination identified in the STM data of Ref. [66]. If SeK termination is thermodynamically preferred or is the one observed, recompute the NLEE for that termination: based on Fig. 5, the μ=0.2 eV peak and the 125 value would not be realized, and the reconciliation of ARPES via VO surface states would need to be reconsidered.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—χ^(2)_zxx ≈ 125 e^2τ^2a^2/(2π)^2ℏ and its d-wave angular dependence—is computed for an ideal, unreconstructed VO-terminated (001) slab in which the bulk (0,0,1/2) AFM order is rigid up to the surface. The paper's own Sec. III B and Figs. 4–5 show that this is not a generic property: when the top surface is SeK-terminated, the V-d surface states near μ=0.2 eV disappear, the top-surface electronic structure reverts toward the spin-degenerate bulk, and the layer-resolved NLEE peak at z≈60 Å is suppressed. Terrace averaging over opposite magnetic moments also reduces the signal, as the paper acknowledges. Nothing in the manuscript establishes that the surfaces of the crystals used in the ARPES [59] and STM [66] experiments are VO-terminated, that the AFM order persists unmodified to that termination, or that terraces are large enough to avoid cancellation. The symmetry argument for the existence of some surface altermagnetism is robust, but the 'fully explain' claim for the ARPES experiments and the specific 125-value signature both require the VO-terminated surface; without independent evidence of that termination, the central claim is conditional on an unverified structural assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses DFT and Wannier-based surface calculations to argue that in the bulk antiferromagnetic (0,0,1/2) phase of KV2Se2O, the (001) surface exhibits d-wave altermagnetism: despite bulk PT symmetry and Kramers degeneracy, the surface states are spin-split with d-wave symmetry. The authors further compute a layer-resolved nonlinear Edelstein susceptibility and predict χ^(2)_zxx ≈ 125 e²τ²a²/(2π)²ℏ at μ = 0.2 eV on an ideal VO-terminated surface, with the out-of-plane spin response following the d-wave angular dependence and disentangled from the in-plane linear Edelstein response. They argue that this reconciles the ARPES/STM evidence for altermagnetism with the neutron diffraction evidence for bulk antiferromagnetism, and they propose the surface nonlinear Edelstein effect as a key detection signature.","tokens_in":18415,"tokens_out":11678,"duration_ms":110065,"significance":"The symmetry-based argument for surface altermagnetism is rigorous and the DFT/Wannier workflow is standard, so the qualitative conclusion — that a PT-symmetric bulk antiferromagnet can host d-wave spin-split surface states — is robust and of broad interest for the Lieb-lattice family. The layer-resolved nonlinear Edelstein calculation, the explicit discussion of termination and terrace sensitivity, and the separation of linear and nonlinear contributions are valuable strengths. The predicted χ^(2) value is large and falsifiable, and no parameter is fitted to the response itself; τ and μ enter only as an overall scale and a reporting point. However, the central quantitative signature is conditional on an ideal, unreconstructed VO-terminated surface and on the position of V-d surface states in a DFT calculation without Hubbard U, so the advertised quantitative prediction requires careful qualification.","major_comments":[{"comment":"The central quantitative prediction, χ^(2)_zxx ≈ 125 e²τ²a²/(2π)²ℏ at μ = 0.2 eV, is computed for an ideal, unreconstructed VO-terminated (001) surface in which the bulk (0,0,1/2) antiferromagnetic order is preserved rigidly up to the surface. This assumption is load-bearing: Figs. 4 and 5 show that a SeK-terminated surface removes the V-d surface states near μ = 0.2 eV and suppresses the layer-resolved peak, and the text acknowledges that terrace averaging reduces the signal. The manuscript provides no experimental evidence that the surfaces measured in Refs. [59] and [66] are VO-terminated, that the magnetic order is unmodified at that termination, or that magnetic domains and terraces are large enough to avoid cancellation. The abstract's statement that the results 'fully explain' the experiments is therefore not supported by the evidence presented. I recommend either providing evidence or a strong argument for the VO termination, or substantially rephrasing the claim so that the termination-dependent NLEE signature is explicitly presented as conditional on the ideal-surface assumption.","section":"Sec. III B and Figs. 4-5"},{"comment":"The claim that the calculations 'fully explain the recent seemingly contradicting experimental evidence' overstates what is demonstrated. The manuscript shows that the calculated (001) surface states of the AFM phase have a d-wave spin-splitting pattern qualitatively similar to the measured photoemission data, but it does not compare the calculated spectral function, band positions, or constant-energy maps with the ARPES results of Ref. [59], nor does it analyze the spin-selective STM data of Ref. [66] beyond a qualitative statement. If the authors wish to claim a full explanation, a direct comparison with the experimental spectra (or at least a clear statement of which experimental features are reproduced and which are not) is needed; otherwise the wording should be tempered to 'qualitatively consistent with'.","section":"Abstract and Sec. IV"},{"comment":"Equation (7) defines tan θ = |δS_oop|/|δS_ip| = χ^(2)_zxx E_0 / χ^(1)_zx, but Table I shows that the even (intraband) linear Edelstein tensor has only in-plane components: for E ∥ x̂, the induced in-plane spin is δs_y = χ^(1)_xy E_0, while χ^(1)_zx = 0. The denominator should be χ^(1)_xy (or the corresponding magnitude of the in-plane linear response). Since Fig. 6b,c reports numerical values of θ, please verify the convention and the numerical implementation; if the calculation actually used χ^(1)_xy, then the displayed equation and notation should be corrected accordingly.","section":"Sec. III C, Eq. (7)"}],"minor_comments":[{"comment":"The text contains several typographical errors ('contradicgting', 'conecept', 'anfiterromagnetic', 'repsonse', 'sucebtibility', 'not showned', 'direcitons') that should be corrected before publication.","section":"Throughout"},{"comment":"The figure caption and the main text use inconsistent panel labels: the text refers to Figs. 2a-c, 2d, and 2f-h, while the caption lists (b-d), (e), and (f-h) with overlapping and duplicated entries. Please renumber the panels consistently.","section":"Fig. 2 caption"},{"comment":"The statement 'kinetic energy cutoff of 10^-7 eV for the plane-wave basis' is dimensionally implausible; this is likely a convergence threshold for the total energy rather than a kinetic-energy cutoff. Please clarify.","section":"Appendix A"},{"comment":"The sensitivity of the NLEE peak to the DFT treatment of V-d correlations is not discussed; since the peak at μ = 0.2 eV is dominated by V-d surface states, a brief statement of the expected shift under a Hubbard U correction or a U-scan comparison would improve confidence in the quantitative value.","section":"Sec. III B"},{"comment":"The sentence describing Fig. 6c says θ is plotted as a function of the applied electric field while also fixing E0 = 1000 V/cm; please clarify the field range and the role of E0 in that panel.","section":"Sec. III C"},{"comment":"The statement that θ reaches 90° at μ = 0.23 eV because the linear response crosses zero should acknowledge that the arctangent of a divergent ratio is discontinuous there; the statement is acceptable but the discontinuity should be noted.","section":"Sec. III C"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for cond-mat.str-el, and I regard the core qualitative result — d-wave surface altermagnetism on a PT-symmetric bulk antiferromagnet — as sound. The stress-test concern about the VO termination is a missing-evidence issue rather than a circularity issue, and it does land: the quantitative NLEE signature is conditional on an ideal surface. The manuscript is repairable by tempering the 'fully explain' language, adding a direct ARPES comparison or clearly marking the absence of one, fixing Eq. (7), and addressing the surface-assumption caveats. I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"X,\n\nHere's my read of Jaeschke-Ubiergo et al. The core qualitative claim holds up: in the (0,0,1/2) AFM phase of KV2Se2O, the (001) surface breaks the PT symmetry of the bulk and hosts d-wave spin-split surface states, and the nonlinear Edelstein effect is a clean surface-localized probe of them. The symmetry analysis is careful, the decomposition of the Edelstein tensor into time-reversal even/odd parts is useful, and the layer-resolved calculation showing the response peaks at the surface and cancels in the bulk is convincing.\n\nWhat's actually new here is the material-specific part: slab DFT/Wannier calculations for KV2Se2O, the comparison of VO vs SeK terminations, slab-parity effects, and the prediction that the NLEE chi^(2)_zxx reaches ~125 (in units of e^2 tau^2 a^2 / (2pi)^2 hbar) with a d-wave angular dependence. That is a concrete, falsifiable signature and goes beyond the earlier surface-altermagnetism framework paper.\n\nNow the soft spots. The abstract says the results 'fully explain' the neutron + ARPES experiments. That is too strong. The paper never quantitatively compares its surface spectral function to the ARPES data; it shows qualitative similarity of the splitting pattern. And the specific 125-value prediction is computed for an ideal, unreconstructed VO-terminated (001) surface with bulk AFM order persisting rigidly to the top layer. The paper's own Figs. 4 and 5 show that SeK termination removes the V-d surface states near mu=0.2 eV and suppresses the surface NLEE peak. So the headline number is conditional on a termination that is plausible but not established for the crystals in Refs. [59] and [66]. Terrace cancellation is acknowledged but not quantified. The reader's stress-test note is right on this point.\n\nMinor concerns: the quoted number has a tau^2 dependence, and tau is a free parameter; the mu=0.2 eV peak position depends on the GGA-PBEsol placement of the V-d states, without Hubbard U. These are normal caveats for this kind of prediction, not fatal flaws. The paper also does not ship code/data, but the WannierTools workflow is standard enough.\n\nOverall: a solid, useful paper that deserves a real peer review. I would push the authors to soften 'fully explain' to something like 'consistent with,' and to state explicitly that the large NLEE response is a prediction for VO-terminated surfaces, not a generic property. Those are revisions, not rejections.\n\nBring it to the reading group if you want a concrete example of surface altermagnetism with an experimentally addressable signature. I'd cite it if I were working on altermagnet transport.\n\nBest,\n[You]","headline":"The surface altermagnetism story for KV2Se2O is qualitatively solid, but the headline NLEE number is tied to a VO termination that the paper's own data show is not generic.","tokens_in":19018,"tokens_out":2115,"would_cite":true,"duration_ms":18099,"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":"The (001) surface of antiferromagnetic KV2Se2O is a d-wave altermagnet.","keywords":["surface altermagnetism","KV2Se2O","nonlinear Edelstein effect","d-wave spin splitting","antiferromagnet","Lieb lattice","spin-orbit coupling","surface states"],"falsifier":"Measure the electric-field-induced out-of-plane spin density on a VO-terminated (001) surface of KV2Se2O at $\\mu=0.2$ eV: if the surface altermagnetism picture is right, the signal must be invariant under reversing the field, must vanish for fields along the (110) and (1-10) diagonals, and must reverse when the magnetic order is reversed. Observing instead the field-odd in-plane pattern of the linear Edelstein effect, or no out-of-plane signal, would falsify the prediction.","tokens_in":1876,"feed_emoji":"🧲","tokens_out":10660,"duration_ms":167812,"temperature":0.7,"pith_summary":"KV2Se2O has two experimental faces: neutron diffraction says the bulk is an antiferromagnet with (0,0,1/2) order, while photoemission and spin-selective scanning tunneling microscopy see d-wave spin splitting. This paper predicts that both are true: the (001) surface of the antiferromagnetic phase is an emergent d-wave altermagnet even though the bulk bands stay spin-degenerate, because the surface breaks time reversal and inversion while keeping a compensating combined spin-space symmetry. The paper's new, testable signature is a surface-localized nonlinear Edelstein response, $\\chi^{(2)}_{zxx} \\approx 125\\, e^2\\tau^2 a^2/(2\\pi)^2\\hbar$ at chemical potential 0.2 eV, which follows the same d-wave pattern and can be disentangled from the ordinary linear Edelstein response by symmetry. If correct, surface-sensitive probes and bulk probes are not in conflict; they are measuring different parts of the same crystal.","feed_headline":"KV2Se2O hides a d-wave altermagnet at its (001) surface","feed_subtitle":"A surface-only effect explains why photoemission sees spin splitting while neutrons see an antiferromagnetic bulk.","key_machinery":"The machinery is the surface magnetic point group 4'm'm: in the bulk the magnetic group preserves inversion and time reversal, eliminating spin splitting and all Edelstein responses, while at the (001) surface inversion and time reversal are broken but a symmetry combining a fourfold real-space rotation with a twofold spin rotation still connects opposite magnetic moments layer by layer, enforcing compensation and d-wave spin splitting. On this symmetry scaffold, the quantitative prediction is carried by a layer-projected semiclassical transport formula, $\\chi^{(2)}_{\\alpha ij}(\\ell) = \\chi_0 \\sum_n \\int d^2k\\, (\\partial s^\\alpha_{n,\\ell}/\\partial k_i)\\, v^j_n\\, \\delta(\\varepsilon_n - E_F)$ with $\\chi_0 = e^2\\tau^2 a^2/(2\\pi)^2\\hbar$, evaluated on a slab built from density-functional tight-binding states. The response peaks where spin-orbit coupling creates avoided crossings of opposite-spin V-d surface states with high group velocity, about $0.5\\times10^{6}$ m/s.","core_discovery":"The central claim is that the (001) surface of bulk-antiferromagnetic KV2Se2O realizes emergent surface altermagnetism: despite spin degeneracy in the bulk enforced by combined inversion and time-reversal symmetry, the surface states are spin-split with d-wave symmetry, with nodal directions along the (110) and (1-10) diagonals, so the surface spin polarization alternates in momentum space while the surface remains magnetically compensated. This reconciles the neutron diffraction measurement of bulk antiferromagnetic order with photoemission and tunneling evidence of d-wave spin splitting. The paper's new quantitative prediction is the surface nonlinear Edelstein effect: an in-plane electric field induces an out-of-plane spin density $\\delta s_z = \\chi^{(2)}_{zxx}(E_x^2 - E_y^2)$, with $\\chi^{(2)}_{zxx} \\approx 125\\, e^2\\tau^2 a^2/(2\\pi)^2\\hbar$ at $\\mu=0.2$ eV, localised at the top layer and carrying the same d-wave angular dependence, which makes the surface altermagnetism detectable and separable from the linear in-plane Edelstein response.","pith_inferences":["If the response is truly surface-localized and termination-dependent, the nonlinear Edelstein signal could serve as a diagnostic of which surface termination a cleave actually exposes, since only the VO termination gives the $\\mu=0.2$ eV peak.","The field-reversal protocol used to separate $\\chi^{(1)}$ from $\\chi^{(2)}$ should generalise to other time-reversal-odd surface responses, giving a background-free route to isolate surface altermagnetism in transport measurements.","Because opposite antiferromagnetic domains contribute with opposite sign, spatial mapping of the induced out-of-plane spin density could image magnetic domain structure at the surface instead of averaging it away."],"forward_implications":["The apparent contradiction between neutron diffraction and photoemission is resolved: the former sees bulk antiferromagnetic order, the latter sees d-wave surface altermagnetism.","An in-plane electric field induces an out-of-plane spin density quadratic in the field and invariant under field reversal, so it can be cleanly separated from the linear in-plane Edelstein signal.","A VO-terminated (001) surface at $\\mu=0.2$ eV should show a strong peak in $\\chi^{(2)}_{zxx}$; a SeK-terminated surface suppresses that peak.","The surface nonlinear Edelstein response is estimated at roughly 125 $e^2\\tau^2 a^2/(2\\pi)^2\\hbar$, about two orders of magnitude above earlier model estimates, making detection realistic, for example through the inverse spin Hall effect in a normal-metal cap.","The same surface-altermagnetism mechanism is expected to apply to other stacked Lieb-lattice antiferromagnets, widening the pool of detectable altermagnetic surfaces."],"supporting_citations":[{"why":"introduces emergent surface altermagnetism and predicts d-wave surface splitting for antiferromagnetic KV2Se2O, the starting point of this work","marker":"[53]"},{"why":"reports d-wave spin splitting from photoemission that the surface altermagnetism scenario must reproduce","marker":"[59]"},{"why":"reports neutron diffraction bulk (0,0,1/2) antiferromagnetic order that conflicts with naive bulk altermagnetism","marker":"[60]"},{"why":"provides spin-selective scanning tunneling microscopy evidence of altermagnetic splitting used as independent support for the surface picture","marker":"[66]"},{"why":"predicted nonlinear Edelstein response in d-wave altermagnets and supplies the baseline magnitude this paper exceeds","marker":"[17]"},{"why":"provides symmetry analysis of the nonlinear Edelstein effect in altermagnets, including possible response without spin-orbit coupling, used to frame the result","marker":"[18]"},{"why":"supplies the surface Green's function renormalization method used to obtain surface spectral functions and slab electronic structure","marker":"[73]"}],"fun_headline_variants":["Surface of KV2Se2O exposes d-wave altermagnet","KV2Se2O surface spin splitting follows d-wave pattern","Nonlinear Edelstein effect spots KV2Se2O surface altermagnet","KV2Se2O (001): hidden d-wave altermagnetism","KV2Se2O (001) surface: d-wave altermagnet"],"cache_read_input_tokens":21120,"weakest_assumption_plain":"The quantitative prediction assumes an ideal, unreconstructed VO-terminated (001) surface where the bulk (0,0,1/2) antiferromagnetic order persists unchanged up to the surface, magnetic domains and terraces are large enough to avoid averaging the signal away, and the density-functional treatment without an added Coulomb-correction term places the V-d surface states at the correct energy.","fun_headline_variants_meta":{"raw":{"variants":["Surface of KV2Se2O exposes d-wave altermagnet","KV2Se2O surface spin splitting follows d-wave pattern","Nonlinear Edelstein effect spots KV2Se2O surface altermagnet","KV2Se2O (001): hidden d-wave altermagnetism","KV2Se2O (001) surface: d-wave altermagnet"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000964,"raw_usage":{"total_tokens":4107,"prompt_tokens":955,"completion_tokens":3152,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":571,"completion_tokens_details":{"reasoning_tokens":3056}},"tokens_in":571,"tokens_out":3152,"duration_ms":19474,"temperature":1.0,"reasoning_tokens":3056,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:49:01.579917+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the electric-field-induced out-of-plane spin density on a VO-terminated (001) surface of KV2Se2O at $\\mu=0.2$ eV: if the surface altermagnetism picture is right, the signal must be invariant under reversing the field, must vanish for fields along the (110) and (1-10) diagonals, and must reverse when the magnetic order is reversed. Observing instead the field-odd in-plane pattern of the linear Edelstein effect, or no out-of-plane signal, would falsify the prediction.","supporting_citations":[{"cited_title":"Spin-neutral currents for spintronics","cited_arxiv_id":"2103.09219","evidence_quote":"predicted nonlinear Edelstein response in d-wave altermagnets and supplies the baseline magnitude this paper exceeds"}],"review_version":2}