{"id":"5c386e16-d315-4a7d-8026-5fe2103ed2dd","arxiv_id":"2411.14803","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A charge current in an altermagnet produces a transverse magnon spin current via electron-magnon drag, reaching up to about 10% of the electronic spin conductivity near resonances.","lead":"This paper predicts that sending a current through an altermagnet, a new class of magnetic metal, drags its magnons into a transverse spin current, the magnonic version of the spin-splitter effect. The effect needs no spin-orbit coupling and has a strong temperature dependence, offering a distinguishable and potentially efficient route to spin-current generation.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central vulnerability is the unproven exact cancellation of the equilibrium electron-magnon self-energy (Eq. 5); if it fails at the finite chemical potentials used in the main figures, the magnon eigenbasis and all extracted spin conductivities are built on a renormalized spectrum.","rationale":"The reader identified the equilibrium electron-magnon self-energy cancellation as the weakest assumption, and I agree: it is the single step on which the degenerate-magnon basis, the spin-current difference in Eq. (10), and the claimed analogy to the electronic spin splitter effect all rest. My stress-test sharpens the concern by noting that the cancellation is most plausible at mu = 0, while the paper's headline resonances and figures rely on mu values up to +/-1. The conclusion's own caveats about realistic band structures and chiral magnon splitting are acknowledged limitations, but they do not protect the idealized calculation from a failure of the equilibrium self-energy cancellation. The proposed numerical check is direct and inexpensive, and it would settle whether the concern is real. I do not see a circular prediction-as-fit step, and the ad hoc parameters are not fitted to the target output, so the paper deserves a conditional rather than a rejecting verdict; hence the reader's CONDITIONAL verdict should remain unchanged.","tokens_in":16231,"tokens_out":16574,"duration_ms":180590,"concrete_test":"Directly evaluate Eq. (5) on a dense k-grid (e.g., 2048x2048) with the paper's parameters (t = 1, I = 0.5, J = t/100, K = J/10, T = 2J) at the chemical potentials used in the main figures (mu = 0, +/-0.05, +/-1) and for several q, including q = (pi/2, 0), (pi/2, pi/2), and (pi, pi). If max_q |Re Pi^nu_q| is nonzero above numerical noise at any mu != 0, recompute the magnon spectrum with the self-energy included and re-run the Boltzmann calculation of Sec. III; if the transverse spin conductivity sigma^s_perp changes sign or magnitude by more than about 20%, the reported results are not a robust prediction. If the sum is zero at machine precision for all these mu and q, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The assertion in Sec. II.B that Pi^nu_q = 0 after summing over the electron Brillouin zone, so the magnon spectrum remains degenerate, is load-bearing: it justifies using the degenerate gamma_{q,+/-} basis in Eq. (4) and defining the magnon spin current in Eq. (10) as a difference of identical dispersions. No symmetry proof is supplied; Fig. 2 plots only the integrand, not the sum, and the physical reason that the Fermi surfaces are 'balanced' is not quantified. The model has a particle-hole-type symmetry that makes the cancellation transparent at mu = 0 (and q = 0 cancels term by term), but the main numerical results in Fig. 3 scan mu up to +/-1 and use mu = +/-0.05, where the spin-up and spin-down Fermi surfaces have different areas. If Re Pi^nu_q is nonzero at these mu values, the magnon modes are renormalized and split; the subsequent g^nu_q expressions (Eqs. A4-A5) and sigma^s (Eqs. 12-13) are computed in the wrong basis, and the resonance positions that produce the ~10% signal shift. This is a correctness risk for the central claim, not just a quantitative caveat.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies electron-magnon coupling in a minimal two-band d-wave altermagnet model coupled to degenerate antiferromagnetic magnons. It claims that the equilibrium electron-magnon self-energy cancels over the Brillouin zone, leaving magnons degenerate, while an applied electric field imprints the altermagnetic spin texture onto magnons through drag. Using a Boltzmann transport approach in the relaxation-time approximation, the authors derive nonequilibrium magnon distributions and compute transverse and longitudinal magnon spin conductivities. The central result is a magnonic spin-splitter effect: a charge current induces a transverse magnon spin current with the same angular symmetry as the electronic spin-splitter effect, reaching about 10% of the electronic spin conductivity near electron-magnon resonances, with a distinctive temperature dependence. The paper also discusses experimental detection schemes and acknowledges several material-specific limitations.","tokens_in":16337,"tokens_out":5550,"duration_ms":58326,"significance":"If the central claim survives scrutiny, this is a valuable prediction: it identifies a mechanism for generating magnon spin currents without spin-orbit coupling, directly extending the altermagnetic spin-splitter effect to the magnon sector. The derivation is explicit and internally coherent, follows a well-established linear-response/Boltzmann framework (Ref. 52), and yields falsifiable numerical predictions for a stated model. The authors are also commendably transparent about acknowledged limitations: chiral magnon splitting in real materials, the need for realistic band structures, and the absence of experimental estimates for magnon relaxation lengths. The principal weakness is that the equilibrium self-energy cancellation is asserted rather than proven, and several quantitative inputs are chosen without sensitivity analysis. These issues affect the reliability of the central numerical claim, but they are addressable within the manuscript's scope.","major_comments":[{"comment":"The claim that Π±q = 0 after summation over the electron Brillouin zone is load-bearing for the entire calculation, but it is asserted rather than demonstrated and is not established by the plotted data. Figure 2 shows the real part of the self-energy integrand at four magnon momenta, not the momentum-summed result, and no symmetry proof is supplied. The cancellation is transparent at μ = 0 and q = 0, yet the main results in Figs. 3 and 4 use μ = ±0.05 and scan μ up to ±1, where the spin-up and spin-down Fermi surfaces are shifted relative to each other even though their areas remain equal. If Re Π±q is nonzero at these parameters, the magnon modes are renormalized and split, so the γ± basis used in Eq. (4), the g±q expressions (A4)-(A5), and the spin conductivity σs (Eqs. 12-13) are all evaluated in the wrong eigenbasis, and the resonance positions producing the ~10% ratio shift. Please provide a proof valid for the finite-μ parameters of the main figures, or a numerical Brillouin-zone sum of Re Π±q for those parameters, and quantify how σs changes if the cancellation is approximate rather than exact.","section":"Sec. II.B, after Eq. (5)"},{"comment":"The restriction to exactly degenerate magnon modes is acknowledged to be unrealistic for candidate materials (the next-nearest-neighbor exchange exceeds 1.5 meV in RuO2, Ref. 76), but the paper does not quantify the impact on the central prediction. Since σs is defined as the difference of the two chiral conductivities σ+ − σ− in Eqs. (12)-(13), an intrinsic chiral splitting modifies equilibrium occupations, group velocities, and the on-shell conditions in Eqs. (A4)-(A5) in a way that cannot be assumed to be a small correction at the temperatures and chemical potentials considered. The closing statement that accounting for chiral splitting \"is likely to enhance the overall signal\" is not supported by a calculation. I ask for an estimate of the effect of a 1.5 meV splitting on the transverse magnon spin conductivity, or, failing that, a clear statement that the quantitative prediction applies only to the degenerate model.","section":"Sec. II.A; Sec. V"},{"comment":"The relaxation-time assignments τ↑ = τ↓ = τe and τ+ = τ− = τm are introduced without justification and are used to obtain the numerical ratios, including the ~10% comparison with the electronic spin conductivity. The spin dependence of electron-magnon and electron-impurity scattering is generally not identical, and unequal τ+ and τ− would alter the balance between the two chiral magnon populations. Please either justify these equalities from a scattering calculation or show that the reported sign changes and magnitudes are robust over a plausible range of τ↑/τ↓ and τ+/τ−.","section":"Appendix A"}],"minor_comments":[{"comment":"The phrase \"By solving the problems, see Appendix A\" should read \"By solving the coupled Boltzmann equations, see Appendix A\".","section":"Sec. II.C"},{"comment":"The functions Q1 and Q2 are used in Eqs. (A4)-(A5) before they are defined in Eqs. (A6)-(A7); please define them at first use or reorder the presentation.","section":"Appendix A"},{"comment":"No numerical details are given for the Brillouin-zone integrations or the δ-function broadening in Eqs. (5), (9), and (A4)-(A5). Without this information the 10% ratio and the resonance features cannot be reproduced; please add the relevant numerical parameters.","section":"Figs. 3 and 4"},{"comment":"The sentence \"measurement the (possibly unidirectional) magnetoresistance response\" is missing a word and should read \"measuring the (possibly unidirectional) magnetoresistance response\".","section":"Sec. IV"},{"comment":"The text refers to \"Fig. 4(b)\" for the temperature dependence, but the temperature curves appear in panel (c); please correct the cross-reference.","section":"Fig. 4"},{"comment":"Ref. 80 is an arXiv preprint; if a peer-reviewed version is available by publication, it should be updated.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal's scope, and the proposed magnonic spin-splitter effect is sufficiently novel and falsifiable to merit consideration. My main concern is the unsupported finite-μ cancellation of the equilibrium self-energy; this is a correctness risk for the central derivation, not merely a presentational issue. I do not see evidence of circular reasoning, and the many self-citations are consistent with the authors' prior contributions to the framework being used."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper does something genuinely new: it predicts that a charge current in an altermagnetic metal drags the two magnon chiralities into a transverse spin current, with the same angular symmetry as the electronic spin splitter effect. Prior work on magnon spin Nernst and magnon Edelstein effects didn't produce this specific mechanism, and the authors correctly identify the physics: in equilibrium the electron-magnon interaction cancels, but an electric field imbalances the two spin Fermi surfaces, so the drag becomes finite. The calculation is a clean extension of Cheng and Zhang's coupled electron-magnon Boltzmann theory to an altermagnetic Fermi surface, and the paper is clearly written. The claimed magnitude, up to about 10% of the electronic spin conductivity near electron-magnon resonances, is a concrete, testable prediction.\n\nThe main soft spot is the assertion in Sec. II.B that the equilibrium electron-magnon self-energy vanishes identically after the BZ sum, leaving the magnon spectrum degenerate. That cancellation is load-bearing: the magnon spin current in Eq. (10) and the g^nu_q expressions in the Appendix are built in the degenerate basis. The text says it, and Fig. 2 shows the integrand, but there's no proof that the sum is zero. At mu=0 particle-hole symmetry makes the cancellation transparent, but the figures use mu=0.05 and scan to +/-1, where the spin-up and spin-down Fermi surfaces have different areas. If Re Pi^nu_q is nonzero there, the magnon modes renormalize and split, the eigenbasis changes, and the resonance positions that produce the ~10% signal shift. This is a correctness risk, not just a quantitative caveat. It's likely fixable—either by proving the cancellation under the model's symmetry, or by computing the self-energy explicitly and showing it's small at the parameters used—but the manuscript as written asserts rather than shows.\n\nThe secondary approximations—equal relaxation times for both spins and chiralities, and no chirality mixing—are stated honestly but not quantified. The authors acknowledge them, so a sensitivity analysis would be enough.\n\nThis is a paper for specialists in altermagnetism and magnon transport. The central idea is plausible and the presentation is honest, including the discussion of experimental detection. The missing self-energy proof is the one thing that stands between this and a solid referee report. I'd send it to peer review, with a clear request that the referee push for the cancellation proof or a quantified error estimate.","headline":"A plausible and clearly worked-out prediction of a magnonic spin splitter effect in altermagnets, but the unproven cancellation of the equilibrium magnon self-energy is a load-bearing gap that needs fixing before I'd trust the numbers.","tokens_in":17053,"tokens_out":2697,"would_cite":false,"duration_ms":25670,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["82D40","82C70"],"pacs":["75.76.+j","72.25.Ba","75.30.Ds"],"model":"deepseek-v4-flash","headline":"A charge current can drag magnons into a transverse spin current in altermagnets, no spin-orbit coupling needed.","keywords":["altermagnets","magnon drag","spin current","magnetic spin Hall effect","electron-magnon interaction","spin splitter effect","Boltzmann transport","magnon spin conductivity"],"falsifier":"Measure the transverse magnon spin conductivity in a clean altermagnet film as a function of temperature: if the signal does not vanish below the magnon gap and then grow with temperature, or if its sign reversal cannot be observed, the predicted magnon drag mechanism is not the dominant source.","tokens_in":15857,"feed_emoji":"🧲","tokens_out":1576,"duration_ms":16764,"temperature":0.7,"pith_summary":"This paper argues that in altermagnets—magnetic metals with a spin-split Fermi surface but no net magnetization—a plain charge current can generate a transverse magnon spin current through the electron-magnon interaction. The effect mirrors the electronic spin splitter effect but lives in the magnon sector, so it carries both a chemical-potential dependence inherited from electrons and a strong temperature dependence from thermally activated magnons. The authors show that at equilibrium the electron-magnon coupling cancels and leaves the magnon spectrum degenerate, while an applied electric field breaks the balance and drags the two magnon chiralities in opposite transverse directions. If correct, this provides a spin-current generation mechanism that does not rely on spin-orbit coupling, with a predicted conductivity reaching about 10% of the electronic spin conductivity near resonances, making it experimentally accessible.","feed_headline":"Charge current drags magnons into transverse spin flow in altermagnets","feed_subtitle":"No spin-orbit coupling needed: the magnon spin current tracks the electronic spin splitter effect, reaching ~10% of it near resonances.","key_machinery":"The central object is the electron-magnon interaction Hamiltonian in a d-wave altermagnet, obtained from a Holstein-Primakoff transformation of a two-sublattice Heisenberg antiferromagnet with an easy-axis anisotropy. The interaction couples each electron spin-flip process to a superposition of the two magnon chiralities through the matrix elements $W^\\nu_q$ of the magnon diagonalization matrix. The key identity is that the equilibrium magnon self-energy $\\Pi^\\nu_q$ vanishes exactly when summed over the electron Brillouin zone, so the magnon spectrum stays degenerate; out of equilibrium, the electric-field-induced Fermi-surface imbalance makes the scattering rates chiral-dependent, and the Boltzmann equation then yields the nonequilibrium magnon distributions $g^\\nu_q$ from which the magnon spin currents are constructed.","core_discovery":"The central claim is that a charge current flowing in an altermagnetic metal induces a transverse magnon spin current whose angular symmetry matches that of the electronic magnetic spin Hall effect (MSHE). Concretely, the authors compute a magnon spin conductivity $\\sigma^s_\\perp$ from a coupled electron-magnon Boltzmann treatment and find it is nonzero with the same fourfold angular dependence as the electronic MSHE, while the total magnon charge-like current $\\sigma^m_\\perp$ vanishes because the two chiralities cancel. The magnon spin current inherits a strong dependence on chemical potential, changing sign near electron-magnon resonances ($\\epsilon_{k,\\uparrow} \\approx \\epsilon_{k+q,\\downarrow}$), where its magnitude can reach roughly 10% of the electronic spin conductivity. The paper states this as the efficient generation of spin currents via magnons, without reliance on the material's spin-orbit coupling.","pith_inferences":["If the equilibrium cancellation of the electron-magnon self-energy is only approximate in real materials, the residual renormalization could split the magnon bands and either suppress or enhance the predicted drag current; the paper acknowledges this but does not quantify it.","Because the derivation assumes equal relaxation times for the two magnon chiralities, any chiral-dependent scattering (e.g., from impurities or phonons) would break the exact cancellation of $\\sigma^m_\\perp$ and could produce a net magnon flow even without electron splitting.","The 10% ratio estimate is tied to the simple square-lattice models; in realistic altermagnets with multiple orbitals and complex Fermi surfaces, the electron-magnon resonances may shift, so a first-principles band-structure calculation would be needed to predict the magnitude and sign of the effect in a specific compound such as RuO$_2$.","The temperature-dependent sign reversal of the transverse magnon spin conductivity suggests a way to directly probe the electron-magnon resonance energy scale, potentially mapping the spin-split Fermi surface via transport rather than spectroscopy."],"forward_implications":["Altermagnetic metals can produce magnon-mediated spin currents without spin-orbit coupling, offering a new route for spin generation in spintronic devices.","The magnon spin current's strong temperature dependence—vanishing below the magnon gap and switching sign as temperature rises—provides an experimental fingerprint to separate it from the electronic MSHE.","Because the magnon spin conductivity can reach about 10% of the electronic one near resonances, the effect should be detectable in nonlocal transport or magnetoresistance measurements on altermagnet/ferromagnet bilayers.","The effect gives a chemical-potential knob: tuning the Fermi level can reverse the sign of the transverse magnon spin current, enabling electrically controlled spin-current polarity.","The longitudinal magnon spin current, which flows along the charge current with a strength independent of current direction, accompanies the transverse one and may be measurable as an additional signal."],"supporting_citations":[{"why":"Defines the electronic spin splitter effect (MSHE) in altermagnets, whose symmetry the magnonic MSHE is claimed to mimic.","marker":"[41]"},{"why":"Provides the coupled electron-magnon Boltzmann transport formalism with relaxation times that the paper extends to two magnon chiralities.","marker":"[52]"},{"why":"Supplies the electron-magnon self-energy theory in ferromagnets that is adapted here to antiferromagnetic magnons.","marker":"[83]"},{"why":"Reports chiral magnon splitting in altermagnetic RuO2, used to discuss the regime where the degenerate-magnon assumption may break down.","marker":"[76]"},{"why":"Provides the model Hamiltonian for altermagnetic electrons with momentum-dependent spin splitting used in the calculations.","marker":"[65]"}],"fun_headline_variants":["Magnon drag yields spin currents without spin-orbit coupling","Altermagnets: charge current drags magnons into spin flow","Spin currents from magnon drag in altermagnets, no SOC needed","Magnon drag creates transverse spin currents in altermagnets","Charge current induces magnon spin current in altermagnets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes that the equilibrium electron-magnon self-energy cancels exactly when summed over the electron Brillouin zone, so the magnon spectrum remains degenerate and only the electric-field-driven imbalance matters.","fun_headline_variants_meta":{"raw":{"variants":["Magnon drag yields spin currents without spin-orbit coupling","Altermagnets: charge current drags magnons into spin flow","Spin currents from magnon drag in altermagnets, no SOC needed","Magnon drag creates transverse spin currents in altermagnets","Charge current induces magnon spin current in altermagnets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00075,"raw_usage":{"total_tokens":3306,"prompt_tokens":880,"completion_tokens":2426,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":496,"completion_tokens_details":{"reasoning_tokens":2336}},"tokens_in":496,"tokens_out":2426,"duration_ms":16808,"temperature":1.0,"reasoning_tokens":2336,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:52:10.182337+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the transverse magnon spin conductivity in a clean altermagnet film as a function of temperature: if the signal does not vanish below the magnon gap and then grow with temperature, or if its sign reversal cannot be observed, the predicted magnon drag mechanism is not the dominant source.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the electronic spin splitter effect (MSHE) in altermagnets, whose symmetry the magnonic MSHE is claimed to mimic."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the coupled electron-magnon Boltzmann transport formalism with relaxation times that the paper extends to two magnon chiralities."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the electron-magnon self-energy theory in ferromagnets that is adapted here to antiferromagnetic magnons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports chiral magnon splitting in altermagnetic RuO2, used to discuss the regime where the degenerate-magnon assumption may break down."}],"review_version":1}