{"id":"385810fa-284c-4577-91fc-03f1551ed801","arxiv_id":"2412.03994","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"A theoretical model shows that the radial Rashba spin-orbit coupling angle at ferromagnet/superconductor interfaces shifts the in-plane angular dependence of the tunneling anomalous Hall conductance, enabling its experimental extraction.","lead":"This paper predicts that the spin-orbit field at a ferromagnet/superconductor interface can have a radial component, and that its angle can be read off from how the Hall conductance shifts when the magnetization direction is rotated. The result gives experimentalists a transport-based way to measure the Rashba angle in twisted van der Waals barriers.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Extraction of θ_R from the predicted shifts assumes a k-independent Rashba angle; realistic twisted-vdW spin textures may spoil the clean Δφ shift, so the protocol needs validation against k-dependent spin-orbit fields.","rationale":"The paper is internally consistent: given the idealized linear-in-k spin-orbit field of Eq. (2) with a single θ_R, the predicted magnetization-angle shifts for the tunneling anomalous Hall effect and the magnetoanisotropic Andreev reflection follow, and the numerical results support them. The reader's weakest-assumption analysis correctly identified the k-independence of θ_R as the soft spot. I agree with that identification. Where I differ from the reader is in the consequence: because the abstract and conclusions present the extraction as a robust way to probe radial Rashba SOC in twisted vdW interfaces, the assumption that the real spin texture matches Eq. (2) is not a peripheral caveat but a load-bearing condition of the central claim. If θ_R is momentum-dependent or the field contains additional lattice-anisotropic terms, the measured shift is a weighted mixture of phases and no longer equals θ_R; the experimental protocol would need to be modified or its interpretation revised. This is not an internal inconsistency, but it is a correctness risk for the headline application. The proposed concrete test—feeding a k-dependent θ_R or a first-principles spin texture into the same scattering calculation—would directly settle whether the clean shift survives. Since the paper does not currently address this possibility, a conditional acceptance is appropriate: the paper should be accepted after either demonstrating robustness against such deformations or explicitly stating and quantifying the limitation. This is a modest, constructive adjustment to the reader's ACCEPT verdict, not a rejection.","tokens_in":19773,"tokens_out":29428,"duration_ms":269835,"concrete_test":"Recompute the tunneling anomalous Hall conductance G_x(φ) using Eq. (13) with the same parameters but replace Eq. (2) by a spin-orbit field with a weakly k-dependent Rashba angle, e.g., θ_R(k) = θ_R0 + δθ(|k|/k_F)^2, and also by a first-principles-derived Ω(k) for a specific twisted vdW bilayer taken from Ref. [36]. For δθ up to about 0.3 rad, check whether the zero crossing of G_x(φ) shifts by θ_R0 or instead by the |k|-weighted average of θ_R(k). If the zero crossing deviates from θ_R0 by more than the targeted experimental precision, the extraction protocol needs a correction or an explicit caveat; if it tracks θ_R0, the concern is resolved. Independently, repeat the MAAR calculation with the same k-dependent θ_R to determine whether the extrema shift by θ_R/2 or by a weighted average.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central extraction scheme is predicated on the spin-orbit field having the exact linear-in-k form of Eq. (2), with a single, k-independent Rashba angle θ_R. The parity argument leading to Eqs. (16)-(17) and the numerical curves in Figs. 3 and 5 all use this isotropic form; the robustness checks in Sec. IV vary chemical potentials and masses but keep Eq. (2) fixed. First-principles calculations of twisted vdW interfaces (e.g., Ref. [36]) find radial Rashba components with spin textures that are not globally isotropic: the local Rashba angle can vary with |k| and with direction around the Fermi surface (e.g., trigonal warping), and higher-order k terms are generally present. If θ_R(k) is not constant, the k∥ integrals in Eqs. (12)-(13) superpose sine and cosine terms with different phase shifts, so the zero crossing of G_x no longer occurs at φ = θ_R(k_F); it occurs at a weighted average, and the clean Δφ = θ_R shift is lost. The same issue affects the Δφ = θ_R/2 MAAR shift, which derives from the leading-order cross term between the rotated Rashba field and the Dresselhaus field; with a k-dependent θ_R the angular integral no longer yields cos(2φ − θ_R) with a single θ_R. Thus the claim that θ_R can be directly read off from a magnetization-angle shift is established only for the idealized isotropic model, not for the realistic twisted vdW systems the paper is intended to address.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper theoretically studies a ballistic ferromagnet/barrier/superconductor junction with an interfacial spin-orbit field that includes conventional Rashba, radial Rashba (characterized by an angle theta_R), and Dresselhaus contributions. Using a Blonder--Tinkham--Klapwijk-type scattering calculation, the authors compute the tunneling conductance and the transverse (anomalous Hall) conductances as functions of the magnetization direction. The central results are: (i) the out-of-plane magnetoanisotropy is independent of theta_R; (ii) in the presence of weak Dresselhaus SOC, the in-plane magnetoanisotropic Andreev reflection (MAAR) is shifted by Delta_phi = theta_R/2; and (iii) the tunneling anomalous Hall conductances and Hall supercurrents are shifted by Delta_phi = theta_R, allowing a direct experimental determination of theta_R. The shifts are shown to be robust against chemical-potential and effective-mass mismatches between the electrodes.","tokens_in":20083,"tokens_out":12945,"duration_ms":116054,"significance":"The proposed transport signatures are concrete and falsifiable, and the paper gives a transparent first-order parity argument (Eqs. (15)--(19)) that explains the angular structure of the Hall conductances. The numerical solution of the full scattering problem supports the analytic result, and the predicted signals are sizable (up to roughly 10% of the tunneling conductance for the Hall response). The work directly addresses an experimentally relevant quantity, the Rashba angle theta_R in twisted van der Waals barriers, and the robustness checks in Sec. IV strengthen the proposal. The main weakness is the assumption of a strictly linear, k-independent spin-orbit field, which is discussed in the major comments.","major_comments":[{"comment":"The extraction protocol assumes a spin-orbit field that is strictly linear in k with a single, k-independent Rashba angle theta_R. The paper's motivation is the radial Rashba SOC predicted for twisted van der Waals heterostructures (Refs. [21,22,35,36]); however, those first-principles studies describe spin textures that can vary with |k| and with azimuthal direction (e.g., trigonal warping) and can contain higher-order terms. If theta_R = theta_R(k_parallel) is not constant, the k_parallel integrals in Eqs. (12)--(13) superpose contributions with different phase shifts, so the zero crossing of G_x no longer occurs at phi = theta_R(k_F) but at a Fermi-surface average; similarly, the MAAR shift in Sec. III.A becomes a weighted average rather than theta_R/2. The robustness checks in Sec. IV vary masses and chemical potentials but keep the isotropic linear form of Eq. (2) fixed. Since the central message is that theta_R can be read off directly from the measured shifts, the authors should either (i) perform a numerical test with a k-dependent theta_R (for example, theta_R(k) = theta_R0 + delta_theta_R (k/k_F)^2 or an azimuthal modulation) and show that the shift remains equal to the angle characterizing the Fermi-surface average, or (ii) explicitly state that the extracted quantity is an effective angle and discuss its relation to the microscopic theta_R(k). This is a load-bearing limitation of the proposed protocol.","section":"Sec. II, Eq. (2); Sec. IV"}],"minor_comments":[{"comment":"The use of theta_R/2 as the reference angle in the MAAR definition makes the reference coincide with the conductance maximum; this should be stated explicitly to avoid confusion about the sign and the dependence on theta_R.","section":"Sec. III.A, Eq. (14)"},{"comment":"The curves for different theta_R values are not accompanied by a legend; please add a legend or list the theta_R values in the captions to make the figures self-contained.","section":"Fig. 3 and Fig. 5 captions"},{"comment":"The expression for the Hall supercurrent has a line break in the middle of the fraction that makes the formula hard to read; rewriting the equation in a single fraction or with an explicit bracket would improve clarity.","section":"Appendix A, Eq. (A7)"},{"comment":"The spelling 'Bogoljubov' is inconsistent with 'Bogoliubov' used elsewhere in the paper.","section":"Appendix A"},{"comment":"The statement that superconducting junctions enhance the tunneling anomalous Hall effect relative to the normal state would be more informative if the enhancement factor (about two orders of magnitude, based on a comparison of Figs. 5 and 6) were stated explicitly.","section":"Sec. III.B"}],"recommendation":"major_revision","confidential_remarks":"The paper is a competent and clearly written model calculation. Its main risk is overclaiming the direct extraction of theta_R for realistic twisted vdW systems without addressing k-dependent spin textures. If the authors add a robustness check for a k-dependent theta_R or clearly qualify the extracted quantity as an effective angle, I would be happy to see it published."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a clean, competently executed BTK/Green's-function study of a vertical ferromagnet/barrier/superconductor junction with a Rashba field that mixes conventional and radial components, parametrized by the Rashba angle θ_R. What's new is concrete: the in-plane magnetization-angle traces of the tunneling anomalous Hall conductances G_x and G_y shift rigidly by Δφ = θ_R, and with a weak Dresselhaus term the MAAR trace shifts by θ_R/2. The parity expansion around Eq. (15) and the numerical solution of the full boundary-matching problem agree, and Sec. IV checks robustness against mass and chemical-potential mismatches. The Hall result is a direct generalization of their earlier work [48] and is consistent with the symmetry analysis in Ref. [60]. There is no circularity: the conductances are defined independently of θ_R.\n\nThe real soft spot is the one the stress-test note identifies. The extraction protocol assumes the interface spin-orbit field has the exact linear-in-k form of Eq. (2) with a single, k-independent θ_R. The robustness checks vary masses and Fermi momenta but keep that form fixed. If a real twisted vdW barrier has a spin texture that is trigonally warped, or θ_R varies with momentum or carrier density, the k∥ integrals in Eqs. (12)–(13) superpose different phase shifts and the clean zero-crossing at φ = θ_R becomes a weighted average. The paper does hedge in the Conclusions — \"as long as the underlying symmetry of the Rashba fields is not destroyed\" — but it never tests what happens when that symmetry is broken. That is a limitation, not a fatal flaw, and it is exactly what a referee should ask for: either a discussion of why first-principles spin textures for twisted vdW interfaces are consistent with a rigid θ_R, or an explicit calculation with k-dependent θ_R.\n\nThe θ_R/2 MAAR shift is shown numerically but not derived analytically; the spin-orbit-field interference picture in Fig. 1(f) is plausible, but the same formal support as the Hall result would be preferable.\n\nWho is this for? Anyone working on superconducting spintronics, proximity effects, or spin- and momentum-selective tunneling in van der Waals heterostructures. It deserves a serious referee. I would send it out; the machinery is standard, the result is useful, and the main open point is a model limitation the authors can address in revision.","headline":"A solid, standard-machinery paper that turns θ_R into measurable magnetization-angle shifts; the extraction is clean under the linear model, with a k-dependence caveat that revision should address.","tokens_in":20594,"tokens_out":4171,"would_cite":true,"duration_ms":36780,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Radial Rashba spin-orbit coupling can be extracted from the in-plane magnetization shift of the tunneling anomalous Hall conductance in ferromagnet/superconductor junctions.","keywords":["radial Rashba spin-orbit coupling","tunneling anomalous Hall effect","magnetoanisotropic Andreev reflection","ferromagnet/superconductor junction","twisted van der Waals barrier","Rashba angle","spin-orbit texture","Andreev reflection"],"falsifier":"Measure $G_x(\\phi)$ and $G_y(\\phi)$ on a junction with a twisted van der Waals barrier and check whether the traces are fitted by a single rigid shift of the sine and cosine forms. If the phase offset changes with bias, carrier density, or barrier thickness, or if the curves distort rather than translate, then the linear-rotation form of Eq. (2) is falsified rather than confirmed.","tokens_in":2280,"feed_emoji":"🧲","tokens_out":1949,"duration_ms":153471,"temperature":0.7,"pith_summary":"At a ferromagnet/barrier/superconductor tunnel junction whose barrier carries radial Rashba spin-orbit coupling, this paper predicts that the in-plane transport magnetoanisotropies pick up rigid angular shifts set by the Rashba angle $\\theta_\\mathrm{R}$. Specifically, the tunneling anomalous Hall conductances follow $G_x \\propto -\\alpha \\sin(\\phi-\\theta_\\mathrm{R})$ and $G_y \\propto \\alpha \\cos(\\phi-\\theta_\\mathrm{R})$, and the in-plane magnetoanisotropic Andreev reflection shifts by $\\theta_\\mathrm{R}/2$ when a weak Dresselhaus field is added. Since $\\theta_\\mathrm{R}$ quantifies the spin texture of the interfacial spin-orbit field (spin parallel versus perpendicular to momentum), reading these shifts would provide a direct electrical probe of twisted van der Waals barriers. The calculation uses ballistic scattering theory and shows that the shifts survive chemical-potential and mass mismatches between the electrodes, which is why the authors propose them as a robust extraction scheme.","feed_headline":"Hall conductance shift reads out the radial Rashba angle","feed_subtitle":"In-plane magnetization sweeps reveal the Rashba angle as a rigid shift, making interfacial spin textures electrical.","key_machinery":"The central object is the interfacial spin-orbit field $\\hat{\\Omega}(\\mathbf{k}_\\parallel)$ of Eq. (2), a single vector field combining conventional Rashba, radial Rashba, and Dresselhaus terms, with the radial content quantified by $\\theta_\\mathrm{R}$. The argument is carried by a parity expansion of the tunneling-anomalous-Hall conductance in powers of $\\hat{m}\\cdot\\hat{\\Omega}(\\mathbf{k}_\\parallel)$ [Eq. (15)]: the zeroth-order term vanishes by parity, the first-order term survives, and it evaluates to $G_x \\propto -\\alpha \\sin(\\phi-\\theta_\\mathrm{R})$ and $G_y \\propto \\alpha \\cos(\\phi-\\theta_\\mathrm{R})$. The same spin-orbit field, when it interferes with a weak Dresselhaus component, modulates spin-flip Andreev reflection and therefore the subgap tunneling conductance, producing the $\\Delta\\phi = \\theta_\\mathrm{R}/2$ shift of the in-plane magnetoanisotropic Andreev reflection; the shift is most pronounced when the Dresselhaus strength approaches the Rashba strength.","core_discovery":"The paper's central claim is that the Rashba angle $\\theta_\\mathrm{R}$ of the interfacial spin-orbit field leaves a distinctive fingerprint in tunneling transport: it re-angles the in-plane magnetization dependence. For the tunneling anomalous Hall conductances the result is $G_x \\propto -\\alpha \\sin(\\phi-\\theta_\\mathrm{R})$ and $G_y \\propto \\alpha \\cos(\\phi-\\theta_\\mathrm{R})$ (Eqs. (16)-(17)), so a full in-plane magnetization sweep directly exposes $\\theta_\\mathrm{R}$ as the phase offset, and the same $\\Delta\\phi=\\theta_\\mathrm{R}$ shift appears in the Hall supercurrent responses on the superconducting side. In the tunneling conductance, $\\theta_\\mathrm{R}$ is invisible when only Rashba coupling is present---out-of-plane and in-plane magnetoanisotropies are $\\theta_\\mathrm{R}$-invariant---but once a Dresselhaus field is added, the in-plane conductance trace and the magnetoanisotropic Andreev reflection acquire a $\\Delta\\phi=\\theta_\\mathrm{R}/2$ shift. The authors verify numerically that these shifts survive chemical-potential and mass mismatches and argue, from the rotation symmetry of the spin-orbit field, that the shifts are protected against other perturbative effects as long as that symmetry is intact.","pith_inferences":["If the scheme works, the twist angle of a van der Waals barrier could be mapped electrically: each twist angle would correspond to a measured $\\theta_\\mathrm{R}$, giving a transport-based alternative to spin-texture probes.","Because the extraction assumes a momentum-independent $\\theta_\\mathrm{R}$, a momentum-dependent Rashba angle would show up as a deviation from a rigid shift; the distortion of the trace would itself become a probe of the spin texture's momentum structure.","Because the normal-state Hall effect shows the same shift (though two orders of magnitude smaller), the extraction might also be feasible without superconductivity if the sensitivity can be improved.","Measuring both the $\\theta_\\mathrm{R}/2$ shift in the conductance channel and the $\\theta_\\mathrm{R}$ shift in the Hall channel on the same junction would provide a consistency check: confirming the factor-of-two ratio would strengthen the interpretation."],"forward_implications":["Measuring $G_x(\\phi)$ and $G_y(\\phi)$ at zero bias gives a direct experimental readout of $\\theta_\\mathrm{R}$ from the phase offset, with no need for Dresselhaus coupling.","The same $\\Delta\\phi=\\theta_\\mathrm{R}$ shift appears in Hall supercurrent responses on the superconducting side, offering a second independent probe of the Rashba angle.","When Dresselhaus coupling is present, the in-plane tunneling conductance and the magnetoanisotropic Andreev reflection shift by $\\theta_\\mathrm{R}/2$, providing a complementary extraction route that also signals the presence of Dresselhaus physics.","The shifts survive chemical-potential and mass mismatches between the electrodes, so the extraction scheme should work in real junctions made of dissimilar materials.","The $\\theta_\\mathrm{R}$ shift is argued to be protected by the rotation symmetry of the spin-orbit field, so it should survive weak disorder, charging, and strain as long as the field symmetry is preserved."],"supporting_citations":[{"why":"Supplies the skew-Andreev-reflection mechanism and the tunneling-anomalous-Hall-effect conductance formula that this paper generalizes to nonzero Rashba angle.","marker":"[48]"},{"why":"Establishes the tunneling anomalous Hall effect for Rashba-coupled magnetic tunnel junctions and its in-plane magnetization anisotropy.","marker":"[4]"},{"why":"Identifies spin-flip Andreev reflection as the origin of transport magnetoanisotropies and defines the magnetoanisotropic Andreev reflection that the paper extends.","marker":"[5]"},{"why":"Provides the earlier symmetry analysis of radial Rashba transport and the argument that $\\theta_\\mathrm{R}$ acts as a rotation of the spin-orbit field.","marker":"[60]"},{"why":"First-principles prediction of radial Rashba spin-orbit fields in twisted van der Waals heterostructures, motivating the physical relevance of $\\theta_\\mathrm{R}$.","marker":"[36]"},{"why":"Blonder-Tinkham-Klapwijk scattering formalism underlying the numerical computation of tunneling and Hall conductances.","marker":"[71]"},{"why":"Furusaki-Tsukada Green's-function method used to compute the Hall supercurrent responses.","marker":"[80]"}],"fun_headline_variants":["Rashba angle extracted from Hall conductance shifts","Magnetization sweep reads the radial Rashba angle","Spin-orbit angle revealed by superconductor junction transport","Radial Rashba angle shifts Hall response in magnet sweep","Probing radial Rashba angle via tunneling Hall shift"],"cache_read_input_tokens":22656,"weakest_assumption_plain":"The extraction scheme assumes that the interfacial spin-orbit field is exactly the linear-in-wave-vector form of Eq. (2), with a single momentum-independent Rashba angle $\\theta_\\mathrm{R}$ that enters purely by rotating the field; if the barrier's spin texture is more complex or $\\theta_\\mathrm{R}$ varies over the Fermi surface, the predicted rigid shifts would no longer directly measure the interface property.","fun_headline_variants_meta":{"raw":{"variants":["Rashba angle extracted from Hall conductance shifts","Magnetization sweep reads the radial Rashba angle","Spin-orbit angle revealed by superconductor junction transport","Radial Rashba angle shifts Hall response in magnet sweep","Probing radial Rashba angle via tunneling Hall shift"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000534,"raw_usage":{"total_tokens":2615,"prompt_tokens":1042,"completion_tokens":1573,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":658,"completion_tokens_details":{"reasoning_tokens":1506}},"tokens_in":658,"tokens_out":1573,"duration_ms":30353,"temperature":1.0,"reasoning_tokens":1506,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:52:30.916163+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $G_x(\\phi)$ and $G_y(\\phi)$ on a junction with a twisted van der Waals barrier and check whether the traces are fitted by a single rigid shift of the sine and cosine forms. If the phase offset changes with bias, carrier density, or barrier thickness, or if the curves distort rather than translate, then the linear-rotation form of Eq. (2) is falsified rather than confirmed.","supporting_citations":[{"cited_title":"Costa, A","cited_arxiv_id":null,"evidence_quote":"Supplies the skew-Andreev-reflection mechanism and the tunneling-anomalous-Hall-effect conductance formula that this paper generalizes to nonzero Rashba angle."},{"cited_title":"Matos-Abiague and J","cited_arxiv_id":null,"evidence_quote":"Establishes the tunneling anomalous Hall effect for Rashba-coupled magnetic tunnel junctions and its in-plane magnetization anisotropy."},{"cited_title":"H ¨ogl, A","cited_arxiv_id":null,"evidence_quote":"Identifies spin-flip Andreev reflection as the origin of transport magnetoanisotropies and defines the magnetoanisotropic Andreev reflection that the paper extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the earlier symmetry analysis of radial Rashba transport and the argument that $\\theta_\\mathrm{R}$ acts as a rotation of the spin-orbit field."},{"cited_title":"Frank, P","cited_arxiv_id":null,"evidence_quote":"First-principles prediction of radial Rashba spin-orbit fields in twisted van der Waals heterostructures, motivating the physical relevance of $\\theta_\\mathrm{R}$."}],"review_version":1}