{"id":"e9bcf721-e829-4a0a-978e-9a293960ea2b","arxiv_id":"2412.10236","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A symmetry-based quantum transport theory for unconventional magnets, unified with superconductivity, yields testable predictions for spin-polarized currents, proximity-induced magnetization, and spin-galvanic effects.","lead":"The authors build a unified transport theory for magnets with exchange interactions, such as ferromagnets, antiferromagnets, altermagnets, and p-wave magnets, in contact with superconductors, valid in both normal and superconducting states.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The new effects all scale with symmetry-allowed coefficients γ, χ, K, and β; the paper shows these are permitted but never shows they are nonzero or dominant, leaving the central predictions contingent.","rationale":"This is the same conditional identified by the reader, and it is the most load-bearing concern because every new effect—spin-dependent diffusion in Eqs. (42)-(43), altermagnet spin currents in Eqs. (64)-(65), proximity magnetization in Eq. (80), and the p-wave spin-galvanic temperature dependence in Eq. (92)—is proportional to one of the symmetry-allowed coefficients. Symmetry arguments prevent these terms from being forbidden, but they cannot guarantee that the coefficients are nonzero; accidental cancellations, higher-order disorder corrections, or competing spin-orbit contributions can suppress them in specific materials. This is especially acute for K and β, for which no independent experimental or microscopic estimate is provided. The proposed concrete test directly addresses the gap by computing the coefficients from a microscopic Hamiltonian with disorder. Until such a calculation is done, the paper's predictions remain general but uncalibrated, so the reader's CONDITIONAL verdict should stand.","tokens_in":45724,"tokens_out":20399,"duration_ms":231726,"concrete_test":"Perform a diagrammatic derivation of the NLSM coefficients for representative microscopic models—a two-band d-wave altermagnet (RuO2-like) and a two-band p-wave magnet with odd-parity exchange splitting—using the disorder-averaging method of Refs. [31,32]. If the tensor K or the coefficient β_xz evaluates to zero to leading order in the diffusive limit, the corresponding headline prediction fails; if these coefficients are nonzero, the symmetry-based action is validated. This one check settles whether the unknown coefficients are actually generic.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is that the symmetry-enumerated coefficients in Eq. (22) and Eq. (84) are generically nonzero and survive in the diffusive limit. The paper establishes only that γ, χ, T, K, and β are allowed by charge conjugation, chronology, and spin-space-group symmetries; it never computes them from a microscopic model or estimates their magnitude relative to D and Γ. This is not a cosmetic gap. In Table I, for d-wave altermagnets with two independent components, K and T are independent; a microscopic model could yield K = 0 while T ≠ 0, which would eliminate the proximity-induced magnetization in Eqs. (80)-(81) without suppressing the normal-state spin-splitter. For p-wave magnets, β_xz could vanish at leading order in disorder or be cancelled by a spin-orbit term of the same tensor structure, in which case the temperature dependence in Fig. 3 would not discriminate the exchange mechanism. The framework would remain internally consistent, but the central physical predictions would not follow for real materials, and the equations would reduce to previously known limits.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a Keldysh nonlinear-sigma-model (NLSM) theory for diffusive metals with exchange-type magnetism, covering ferromagnets, antiferromagnets, altermagnets, and p-wave magnets in both normal and superconducting states. The effective action (Eq. (22)) is constructed by enumerating all terms allowed by charge conjugation (Eqs. (12), (15)), chronology symmetry (Eq. (16)), and spin-space-group symmetries up to second order in spatial gradients and first or second order in the exchange coupling τ3σ; the Usadel-type transport equations follow as saddle-point equations (Eqs. (23)-(25)). The authors then derive consequences for each material class: spin-dependent diffusion renormalization and spin-polarized normal and supercurrents in ferromagnets (Sec. IV); a diffusive spin-splitter effect, its absence for supercurrents, and a proximity-induced equilibrium magnetization in d-wave altermagnets (Sec. V); and a temperature-dependent spin-galvanic effect in p-wave magnets with the parameter-free ratio β(T) of Eq. (92) and Fig. 3. Detailed boundary-value solutions are provided in Appendices C through G.","tokens_in":45882,"tokens_out":38852,"duration_ms":377955,"significance":"If the framework is accepted, it provides a unified symmetry-based transport theory for unconventional magnets, going beyond the standard quasiclassical equations and yielding falsifiable predictions. Its strengths are the transparency of the symmetry construction (Appendix A is a systematic enumeration of allowed terms; Appendix F gives explicit symmetry proofs for the absence of the superconducting spin-splitter), the parameter-free spin-galvanic ratio β(T) in Eq. (92) with a correct and easily verified low-temperature limit of 1/3, concrete device predictions (spin accumulations at sample edges, the lobe-dependent magnetization pattern of Fig. 2), and the useful tensor classification in Table I. The stress-test concern that all new effects are proportional to symmetry-allowed but microscopically uncomputed coefficients does partially land: the paper proves only that γ, χ, T, K, and β are permitted, not that they are generically nonzero, so the central predictions are conditional. Within the effective-theory logic this is the standard status of undetermined couplings, but given the prominence of the new effects, the contingency deserves explicit treatment.","major_comments":[{"comment":"All of the new physical effects reported in Secs. IV-VI are proportional to the symmetry-allowed coefficients γ, χ, T, K, and β introduced in Eqs. (22) and (84). The manuscript establishes only that these coefficients are permitted by charge conjugation, chronology, and the relevant spin space group; it never computes or bounds them from a microscopic model. This is load-bearing, not cosmetic: in Table I the groups 24/1m and 22/2m have two independent tensor components, so T and K are unrelated by symmetry, and a microscopic model could give T ≠ 0 with K = 0. That would eliminate the proximity-induced magnetization in Eqs. (80)-(81) while leaving the normal-state spin-splitter in Eqs. (64)-(66) intact. Likewise, β_xz in Eq. (84) could vanish at leading order in disorder or be canceled by spin-orbit terms of the same tensor structure, in which case the temperature dependence in Fig. 3 would not discriminate the exchange mechanism. The text after Eq. (21) states that the coefficients are assumed small relative to the diffusion contribution, but not that they are generically nonzero. I request either a microscopic estimate for at least one material class (for example, a two-dimensional tight-binding altermagnet or ferromagnet with short-range disorder, computing γ, χ, T, and K in the Born approximation) or an explicit discussion of the mechanisms that generate these coefficients and the conditions under which each predicted effect survives.","section":"Sec. III (after Eq. (21)); Table I; Eqs. (64)-(66), (80)-(81), (84)-(92)"},{"comment":"There is a quantitative inconsistency in the headline proximity-magnetization result. Evaluating Eq. (80) at x = 0 using Σ_n (2n+1)^{-3} = 7ζ(3)/8 gives Mz(0) = -(7ζ(3)/16) gμB Pz Kxx πν γ_B^2 |Δ|^2 D/(πT)^2, whereas Eq. (81) reports the prefactor 7ζ(3)/4 with the same remaining factors: a discrepancy of exactly a factor of 4. In addition, the corresponding appendix formula, Eq. (G10), prints (πT)^3 in the denominator, which is dimensionally inconsistent with the (πT)^2 appearing in Eq. (80) and Eq. (G9). The factor-of-4 discrepancy must be reconciled, and the denominator in Eq. (G10) corrected, before the quoted interface value can be used.","section":"Sec. V.B, Eqs. (80)-(81); Appendix G, Eq. (G10)"},{"comment":"The paper claims that the superconducting spin-splitter effect predicted in Ref. [30] (example 1a) is absent, supported by the symmetry arguments in Appendix F (Mz(q) = Mz(-q); Mz = 0 in the transverse orientation, Eqs. (70)-(72)). These arguments appear internally consistent. However, the manuscript does not identify where the calculation of Ref. [30] fails: whether the source is the linearization in the pair amplitudes, the specific electron-gas model used there, or a difference in the assumed spin space group. Because the absence of the superfluid spin-splitter is a central claim of Sec. V.B and is explicitly contrasted with Ref. [30], the authors should analyze the origin of the discrepancy rather than merely stating the contrast.","section":"Sec. V.B; Appendix F 3"}],"minor_comments":[{"comment":"The abstract contains two garbled passages: 'we show that spin-galvanic effects which are distinguishable from the spin-galvanic effect induced by spin-orbit coupling only in the superconducting state' is missing a verb, and 'inversionsymmetry broken antiferromagnets' is missing a hyphen. In the paper outline in Sec. I, 'In Sec. VI we extend our model to second order to higher order to capture spin-galvanic effects' is garbled and should be rewritten.","section":"Abstract; Sec. I (outline paragraph)"},{"comment":"The caption 'normalized its the normal state value' should read 'normalized to its normal-state value'; it would also help to state explicitly that the SOC-induced coefficient is temperature-independent and equal to 1 on this normalization.","section":"Fig. 3 caption"},{"comment":"The symbol χaxy appears where the tensor Kxy is meant, and the transformation equations in this appendix mix χ and γ symbols with the K tensor; the notation should be made uniform with Eqs. (59)-(61) and Table I.","section":"Appendix F 2"},{"comment":"The first-order derivative term Tr{αaj σa τ3 ∂jQ} is discarded as a total derivative that renormalizes the exchange field at boundaries. Since several central results, notably the proximity-induced magnetization in Appendix G and the spin-polarized currents in Appendix C, are boundary-sensitive, the authors should state whether αaj is forbidden by the spin space groups of each material class and, where allowed, justify the neglect of its boundary renormalization.","section":"Sec. III, paragraph after Eq. (18)"},{"comment":"The relation between f± and the singlet/triplet amplitudes (fs, ft) is introduced as f± = fs ± ift sign(ωn) in Sec. V.B but is used with slightly different sign and imaginary-unit conventions in Appendix G; stating one explicit convention would allow the reader to verify Eqs. (80)-(81) directly.","section":"Sec. V.B, Eqs. (74)-(79) and Appendix G 1"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The manuscript is within the journal's scope and is a serious contribution; the symmetry-based construction is careful and the appendices are unusually complete and checkable. My recommendation of major revision is driven by (i) a factor-of-4 inconsistency between Eqs. (80) and (81) in the main quantitative formula for the proximity-induced magnetization, (ii) the unresolved contradiction with Ref. [30] on the superconducting spin-splitter, and (iii) the absence of any microscopic estimate for the coefficients on which all new predictions depend. None of these appears fatal: the framework is internally consistent, and the parameter-free temperature dependence of the spin-galvanic coefficient, with its correct 1/3 low-temperature limit, is a strong falsifiable prediction. Note also that several concurrent preprints ([98]-[101]) overlap with the normal-state parts of this work; the manuscript's distinctive added value is the unified normal-plus-superconducting treatment and the two superconducting-state predictions (proximity magnetization and p-wave spin-galvanic temperature dependence). The authors should be asked to pinpoint where Ref. [30]'s calculation diverges from their symmetry argument before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a strong paper, not a flawless one. The main result is a Keldysh nonlinear sigma model for exchange magnets, and the derivation is transparent enough to check. The gamma and chi terms are genuinely new, and their consequences — spin-dependent diffusion in ferromagnets, the diffusive spin-splitter effect, the proximity-induced magnetization at superconductor/altermagnet interfaces, and the temperature-dependent spin-galvanic coefficient in p-wave magnets — follow from the action rather than being put in by hand. The appendices, especially the symmetry constraints and the boundary-value problems, are careful and reproducible. Table I, mapping which altermagnetic spin space groups allow T and K, is a useful reference on its own.\n\nThe soft spots are real but modest. The biggest one is the one the stress-test note names: gamma, chi, K, and beta are symmetry-allowed, but their microscopic magnitude is never estimated. A specific material could have K = 0 or beta_xz suppressed by disorder, and then the headline predictions would not appear. That does not invalidate the framework — the action and equations stand on their own — but it does mean the new physics is conditional on coefficients the paper leaves unfixed. This is a common situation in quasiclassical transport, and I would not treat it as a fatal objection, but the authors should be asked to state more explicitly that these are material-specific parameters, and ideally to give at least one microscopic estimate or a way to extract them from existing tight-binding models.\n\nTwo smaller issues. The claim that the normal-state altermagnet equations are 'unprecedented' is overdressed: the note in the acknowledgements points to Ref. [98], which appeared during submission, but the main text still asserts novelty. That should be fixed in revision, not a reason for rejection. Second, the disagreement with Ref. [30] on the absence of the superconducting spin-splitter effect is asserted with a symmetry argument but the error in [30] is not identified. The symmetry proof looks sound, and it agrees with the clean-limit result of Ref. [92], but a referee will want a few more sentences pinning down where the earlier calculation goes wrong.\n\nReadership: people doing diffusive transport in altermagnets and superconductor/magnet hybrids will want this paper. It deserves a serious peer review. The right outcome is probably acceptance after the authors tighten the novelty claims and say more about the status of the coefficients.","headline":"A symmetry-based NLSM framework for exchange magnets that mostly delivers; the new transport effects are real consequences of the allowed terms, but their magnitude depends on coefficients the paper does not compute.","tokens_in":46450,"tokens_out":2690,"would_cite":true,"duration_ms":31420,"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":"The paper derives a single symmetry-constrained nonlinear-sigma-model action whose saddle point yields diffusive transport equations for ferromagnets, antiferromagnets, altermagnets, and p-wave magnets, in both normal and superconducting…","keywords":["nonlinear sigma model","Usadel equation","altermagnetism","p-wave magnetism","diffusive transport","superconducting proximity effect","spin-polarized currents","spin-galvanic effect"],"falsifier":"Measure the temperature dependence of the spin-galvanic coefficient in a superconducting p-wave magnet in a Zeeman field and compare it with Eq. (92): the paper predicts a smooth drop of the coefficient to $1/3$ of its normal-state value as $T\\to 0$, whereas a spin-orbit-only contribution would be temperature independent. A flat curve would falsify the exchange-driven mechanism.","tokens_in":45440,"feed_emoji":"🧲","tokens_out":9123,"duration_ms":97113,"temperature":0.7,"pith_summary":"This paper aims to establish a single low-energy transport theory for diffusive magnetic metals in which magnetism comes from exchange interactions, valid in both the normal and superconducting states. The authors construct the most general nonlinear-sigma-model action allowed by charge-conjugation, chronology, and spin-space-group symmetries up to second order in spatial gradients and first order in the exchange coupling. The saddle-point equations of this action reduce to the usual quasiclassical Usadel equations in standard limits but contain extra symmetry-allowed gradient terms. Those terms predict spin-dependent diffusion and spin-polarized currents in ferromagnets, the diffusive spin-splitter effect in altermagnets, a spontaneous magnetization at superconductor/altermagnet interfaces, and a temperature-dependent spin-galvanic effect in p-wave magnets. If correct, the theory provides a general framework for nonequilibrium transport in arbitrary magnetic systems combined with superconductivity.","feed_headline":"One action captures diffusive spin transport in four magnetic metals","feed_subtitle":"Ferromagnets, altermagnets and p-wave magnets follow from one action; superconductivity included","key_machinery":"The central object is the effective action $S_M[Q]$ in Eq. (22), a Keldysh nonlinear $\\sigma$ model for the soft-mode matrix field $Q$, which at the saddle point equals the quasiclassical Green's function $g$. The action contains the standard diffusion, time-derivative, pairing, exchange-field, and spin-relaxation terms, and adds the symmetry-allowed third-rank tensor terms $\\gamma_{ajk}\\tau_3\\sigma_a\\partial_j Q\\partial_k Q$ and $i\\chi_{ajk}\\tau_3\\sigma_a Q\\partial_j Q\\partial_k Q$. The spin space group, the set of independent real-space and spin-space symmetry operations under which the crystal is invariant, determines which tensor components survive. Charge conjugation forces the tensors to be symmetric in the spatial indices, and chronology symmetry forces the coefficients to be real. Varying the action under the constraint $Q^2=1$ produces the matrix current and torque in Eqs. (24)-(25), whose continuity equation is the generalized Usadel equation; for p-wave magnets an additional second-order-in-exchange term with tensor $\\beta_{kc}$ is added in Eq. (84).","core_discovery":"The paper's central claim is that a single Keldysh nonlinear sigma model action, Eq. (22), containing only terms allowed by charge conjugation, chronology symmetry, and the material's spin space group, is a complete low-energy description of diffusive transport in exchange-dominated magnets, in normal and superconducting states. At the saddle point this action yields the generalized Usadel equations, Eqs. (23)-(25). The new symmetry-allowed gradient terms add phenomena absent from the standard quasiclassical equations: a spin-dependent diffusion renormalization and spin-polarized currents in ferromagnets; the diffusive spin-splitter effect in altermagnets, with no superconducting analogue; the proximity-induced magnetization at superconductor-altermagnet interfaces; and a temperature-dependent spin-galvanic effect in p-wave magnets that can be distinguished from the spin-orbit-induced effect only in the superconducting state. The authors also find that only d-wave altermagnets acquire the new transport tensors in the diffusive limit, while g-wave and i-wave altermagnets behave like conventional antiferromagnets in their dirty-limit transport properties.","pith_inferences":["Beyond the paper: the same diffusive framework implies that altermagnetic spin splitting survives in disordered films, not only in ideal clean crystals, so a dirty polycrystalline altermagnet should still accumulate opposite spins on opposite edges under a charge current.","Beyond the paper: the predicted pattern of proximity-induced magnetization around a superconducting island, same sign on opposite sides and opposite sign on perpendicular sides, could be used as a non-invasive magnetic probe of altermagnetic lobe orientation in scanning magnetometry.","Beyond the paper: if the temperature signature of the p-wave spin-galvanic effect holds, the same experiment could separate exchange-driven from spin-orbit-driven band splitting in materials where both mechanisms are present, a distinction the paper identifies but does not fully exploit.","Beyond the paper: because the action is built from symmetry at fixed order in gradients, its predictive power will be strongest when the coefficients $\\gamma$, $\\chi$, $K$, and $\\beta$ are measured across materials with different disorder levels; systematic variations would show where the gradient expansion breaks down."],"forward_implications":["In ferromagnets, an applied charge current automatically carries a spin-polarized current, with spin-dependent conductivities $\\sigma_{\\uparrow,\\downarrow}=\\frac{1}{2}\\sigma_D(1\\pm\\gamma P)$; in Josephson junctions with three noncoplanar ferromagnetic domains this produces an anomalous current proportional to $\\gamma\\,\\mathbf{m}_3\\cdot(\\mathbf{m}_1\\times\\mathbf{m}_2)$.","In the normal state of diffusive d-wave altermagnets, a charge current creates a transverse spin accumulation, the spin-splitter effect, whose sign and magnitude are set by the tensor $T_{jk}$; the effect vanishes for supercurrents, where the magnetization is even under current reversal.","In superconductor/altermagnet bilayers, gradients in the superconducting pair amplitude generate an equilibrium magnetization localized near the interface, with the sign pattern determined by the d-wave lobe orientation and no external current required.","In p-wave magnets, the spin-galvanic effect is indistinguishable from the spin-orbit-induced one in the normal state, but in the superconducting state its coefficient depends on temperature and falls to one third of its normal-state value at $T=0$.","Because the action is not linearized in the superconducting order parameter, the resulting transport theory describes equilibrium and nonequilibrium situations at arbitrary temperatures, both well below and above the critical temperature."],"supporting_citations":[{"why":"Supplies the symmetry-based nonlinear-sigma-model construction for spin-orbit coupling that this paper adapts to exchange magnetism.","marker":"[33]"},{"why":"Defines altermagnetism and the spin-space-group classification used to restrict the tensor coefficients.","marker":"[5]"},{"why":"Introduces p-wave magnets, the noncollinear inversion-broken antiferromagnets treated in Sec. VI.","marker":"[6]"},{"why":"Predicted the clean-limit spin-splitter effect whose diffusive counterpart the action reproduces in the normal state.","marker":"[91]"},{"why":"Earlier weak-superconductivity linearized Usadel theory for altermagnets whose superconducting spin-splitter prediction this paper argues against.","marker":"[30]"},{"why":"Clean-limit result that the magnetization is even under current reversal, supporting the paper's no-spin-splitter conclusion in the superconducting state.","marker":"[92]"},{"why":"Provides the standard quasiclassical Usadel and triplet-proximity framework that the generalized equations extend.","marker":"[2]"},{"why":"Supplies the Kuprianov-Lukichev boundary conditions used to compute proximity-induced magnetization in superconductor/altermagnet junctions.","marker":"[93]"},{"why":"Shows that spin relaxation emerges naturally from momentum-dependent spin splitting, supporting the presence of the relaxation term in altermagnets.","marker":"[76]"}],"fun_headline_variants":["One action unifies spin transport in four magnetic metals and superconductors","Unified quantum transport action for magnets and superconductors","Single theory describes diffusive spin transport in exotic magnets and superconductors","Four magnetic metals, one action: diffusive spin transport with superconductivity","One action predicts spin-splitting, proximity moments, and spin-galvanic effects"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes that the symmetry-allowed coefficients $\\gamma$, $\\chi$, $K$, and $\\beta$ are generically nonzero in real materials, and that no neglected higher-order or spin-orbit term cancels or overwhelms the effects they produce.","fun_headline_variants_meta":{"raw":{"variants":["One action unifies spin transport in four magnetic metals and superconductors","Unified quantum transport action for magnets and superconductors","Single theory describes diffusive spin transport in exotic magnets and superconductors","Four magnetic metals, one action: diffusive spin transport with superconductivity","One action predicts spin-splitting, proximity moments, and spin-galvanic effects"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0008,"raw_usage":{"total_tokens":3597,"prompt_tokens":1100,"completion_tokens":2497,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":716,"completion_tokens_details":{"reasoning_tokens":2404}},"tokens_in":716,"tokens_out":2497,"duration_ms":18501,"temperature":1.0,"reasoning_tokens":2404,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:12:39.283416+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the temperature dependence of the spin-galvanic coefficient in a superconducting p-wave magnet in a Zeeman field and compare it with Eq. (92): the paper predicts a smooth drop of the coefficient to $1/3$ of its normal-state value as $T\\to 0$, whereas a spin-orbit-only contribution would be temperature independent. A flat curve would falsify the exchange-driven mechanism.","supporting_citations":[{"cited_title":"Gonz´ alez-Hern´ andez, L.ˇSmejkal, K","cited_arxiv_id":null,"evidence_quote":"Predicted the clean-limit spin-splitter effect whose diffusive counterpart the action reproduces in the normal state."},{"cited_title":"Quasiclassical theory of superconducting spin-splitter effects and spin-filtering via altermagnets","cited_arxiv_id":"2403.04851","evidence_quote":"Earlier weak-superconductivity linearized Usadel theory for altermagnets whose superconducting spin-splitter prediction this paper argues against."},{"cited_title":"Kuprianov and V","cited_arxiv_id":null,"evidence_quote":"Supplies the Kuprianov-Lukichev boundary conditions used to compute proximity-induced magnetization in superconductor/altermagnet junctions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that spin relaxation emerges naturally from momentum-dependent spin splitting, supporting the presence of the relaxation term in altermagnets."}],"review_version":1}