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REVIEW 2 major objections 4 minor 67 references

Periodic optical driving converts the hidden momentum-odd spin texture of a p-wave magnet into a resonantly enhanced ac spin polarization and a static, rectified orbital polarization — effects that vanish in any period-averaged description.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 23:38 UTC pith:527R7XZF

load-bearing objection Plausible qualitative results on driven p-wave magnets, but Eq. (10) has a clean-limit problem: the interband spin response is written with 1/τ, so it vanishes just where it should resonate; the paper needs a fix before the spin-channel numbers can be trusted. the 2 major comments →

arxiv 2607.15353 v1 pith:527R7XZF submitted 2026-07-16 cond-mat.mes-hall cond-mat.str-el

Dynamical Polarization from Hidden Spin and Orbital Textures in p-Wave Magnets

Yantao Li , Jacob Linder , Pavlo Sukhachov This is my paper
classification cond-mat.mes-hall cond-mat.str-el
keywords p-wave magnetsspin Edelstein effectorbital Edelstein effectFloquet micromotionoptical drivinginterband resonancenonlinear rectificationorbitronics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that a p-wave magnet driven by light develops a net spin polarization that oscillates at the drive frequency, even though both the equilibrium and the period-averaged spin textures are momentum-odd and integrate to zero. This ac spin polarization is resonantly enhanced when the drive frequency approaches the minimum interband gap set by the exchange splitting (ω ≈ 2J_sd). The same drive produces a direct-current orbital angular momentum through a second-order rectification process, provided the electric field has components both parallel and transverse to the spin-splitting direction. The result matters because it turns the hidden momentum-space texture of odd-parity magnets into clean, frequency- and polarization-specific spintronic and orbitronic signals that a period-averaged theory would miss.

Core claim

The paper shows that the micromotion of an optically driven p-wave magnet resolves a momentum-even spin component that oscillates within the driving period, while the momentum-odd texture is restored after period averaging. The linear spin Edelstein response then yields a net ac spin polarization with an interband resonance at the nonrelativistic magnetic gap, originating from spin precession generated by the noncommuting spin-splitting and exchange terms. In the orbital channel, the linear response remains momentum-odd and integrates to zero, but a second-order process rectifies a static, momentum-even orbital polarization when the field has components both parallel and transverse to the sp

What carries the argument

The central mechanism is the Floquet micromotion — the intra-period time dependence of Floquet modes — which exposes instantaneously momentum-even components of spin and orbital textures that are invisible in period-averaged quantities. The spin response is carried by an effective Zeeman field B(k) = {ηJ_sd, 0, M(k)} in which the noncommuting exchange and spin-splitting terms drive spin precession and interband coherence, producing the resonant denominator (ω² − 4J_sd²)² in the interband spin Edelstein tensor. The orbital response is carried by the off-diagonal orbital magnetic moment and interband Berry connection, which generate the second-order rectified tensor components χ^L,(2)_zxy and

Load-bearing premise

All quantitative predictions — the height and shape of the spin resonance and the magnitude of the rectified orbital tensors — rest on a single momentum- and frequency-independent relaxation time τ used for both intraband and interband processes; if real spin relaxation is momentum-dependent, the resonance structure and rectified magnitudes could shift or broaden, though the existence of the effects is symmetry-protected.

What would settle it

A measurement of the ac spin polarization in a driven p-wave magnet as a function of drive frequency: the paper predicts a sharp enhancement near ω = 2J_sd with width set by 1/τ, and a dc orbital magnetization with exactly sin 2θ dependence on the linear-polarization angle; observing neither would falsify the quantitative claims.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Driven p-wave magnets become tunable sources of ac spin polarization with a resonance peak at the exchange-split gap, providing optical access to J_sd.
  • The orbital rectification produces a dc orbital polarization whose magnitude and sign follow E0² sin 2θ, giving a polarization-controlled orbitronic signal.
  • Both effects are invisible to period-averaged Floquet effective-Hamiltonian treatments, so micromotion-based response theory is necessary for driven odd-parity magnets.
  • The resonant spin enhancement scales with the relaxation time τ, so cleaner samples give sharper and larger ac spin signals.
  • The spin and orbital signals have distinct fingerprints — resonant frequency dependence versus sin 2θ polarization dependence — allowing them to be separated experimentally.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same micromotion mechanism likely operates in other odd-parity (f-wave, h-wave) magnets and in altermagnets with noncommuting spin-splitting terms, suggesting a general route from hidden textures to oscillating polarization.
  • The predicted sin 2θ dependence of the dc orbital signal is a clean experimental fingerprint; a null observation while tuning through ω = 2J_sd would implicate the single-τ approximation rather than the symmetry argument.
  • The resonance near ω = 2J_sd could serve as a spectroscopic probe of exchange coupling in p-wave magnets, analogous to spin resonance but driven electrically.
  • Because the spin response is linear and momentum-even while the orbital response is quadratic and momentum-even, lock-in detection at the drive frequency versus dc can cleanly separate the two channels.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This manuscript analyzes the optical driving of a minimal model of a p-wave magnet, combining Floquet micromotion with Kubo linear response and density-matrix perturbation theory. The central claims are: (i) micromotion generates a momentum-even spin texture that gives a finite ac spin Edelstein response, with an interband resonance near the exchange gap; and (ii) the orbital angular momentum, though momentum-odd at linear order, acquires a static momentum-even component at second order via interband rectification, with an E0^2 sin 2θ polarization dependence for linearly polarized light. Analytical expressions for the spin and orbital response tensors are given in Eqs. (5), (9), (10), (12), and (A22)–(A24), and the momentum-space textures are shown in Fig. 2.

Significance. If the results hold, the paper identifies a new mechanism for resonant ac spin generation and dc orbital rectification in p-wave magnets, with distinct frequency and polarization signatures that are experimentally testable. The Floquet micromotion approach applied to hidden momentum-odd textures is a useful contribution, and the orbital rectification selection rule is a crisp, falsifiable prediction. The connection to the interband Berry connection is also valuable. However, the central quantitative formula for the interband spin resonance, Eq. (10), is internally inconsistent, and the correct clean-limit behavior is not established. This weakens the paper's main quantitative claim until corrected.

major comments (2)
  1. [§3, Eq. (10)] The interband spin Edelstein tensor is written as χ_inter^{τ→∞} ≈ (emα_j/2πτ)(ω²+4J_sd²)/(ω²−4J_sd²)². In the clean limit τ→∞ this expression vanishes, implying that the resonant ac spin polarization disappears in cleaner samples. This contradicts the standard Kubo formula in Eq. (7), where τ appears only through i/τ in the denominator; taking τ→∞ yields a finite dissipative part set by the joint density of states and a reactive part set by the principal value. It also contradicts the paper's own spin-dynamics result, Eq. (5), whose resonance amplitude at ω≈2B grows as τ (since D_ω≈−4iB/τ). As written, Eq. (10) would falsify the abstract's claim of a resonantly enhanced spin polarization. The authors must provide the correct evaluation of the k-integral and reconcile it with Eq. (5).
  2. [§3, Eq. (10) and Fig. 3(a)] The double-pole frequency dependence (ω²−4J_sd²)^{-2} is not what is expected for a 2D interband transition at a parabolic band-edge minimum. A standard 2D parabolic band edge gives a constant joint density of states above threshold and a logarithmic reactive singularity, not a double pole. Furthermore, the calculation is performed for μ>J_sd, so the Γ point (where 2B has its minimum 2J_sd) has both bands occupied: n_F(ε_+)−n_F(ε_−)=0 there. The allowed interband transitions occur in the annulus k_F^+<k<k_F^−, so the absorption edge and the reactive anomaly are at 2B(k_F^+)>2J_sd, not at 2J_sd. Unless αk_F/J_sd is extremely small, the resonance location and line shape claimed in Eq. (10) and Fig. 3(a) are incorrect. The authors should clarify the role of Pauli blocking and present the explicit joint density-of-states calculation.
minor comments (4)
  1. [Fig. 2 caption] Typo: 'multipled' should be 'multiplied'.
  2. [Eq. (10) notation] The notation 'τ→∞' above the arrow is misleading. If the expression is an asymptotic expansion for large τ, please specify the control parameter and which terms are kept; if it is meant to be the τ→∞ limit, the 1/τ prefactor makes the expression zero and cannot describe the clean limit.
  3. [Eq. (5)] The explicit factor 1/M(k) in Eq. (5) appears singular at the Γ point. Substituting S_z0 shows this factor is cancelled (S_z0 ∝ M(k)), but the presentation is confusing. Please present the simplified expression.
  4. [General] The Supplemental Material, which contains the derivations of Eqs. (10) and (A22)–(A24), is not included with the manuscript. Given that the main-text derivation of Eq. (10) is a major point of concern, the SM should be made available to the referee.

Circularity Check

0 steps flagged

No significant circularity: response tensors are derived outputs from a published model; only self-reference is model import.

full rationale

The central claims — resonant ac spin Edelstein response near 2J_sd and rectified dc orbital polarization proportional to E0^2 sin 2θ — are computed from Kubo and density-matrix perturbation theory applied to the Hamiltonian in Eq. (1). No parameter is fitted to the predicted quantities: χ^(S);intra, χ^(S);inter, and χ^(L,2) are explicit functions of m, α, J_sd, τ, μ, and the driving field, with the resonance position, momentum parities, and polarization dependence following from the algebra of the Hamiltonian. The single-relaxation-time approximation (Eq. 3, Eqs. A18–A19; footnote [63]) is a stated modeling assumption, not a hidden fit to the output. The only self-citation carrying the model is Ref. [2] for the p-wave magnet minimal model; this is an input model used by several groups, not a claimed derivation, so importing it is not a circular reduction of the paper's predictions. Footnote [63] concedes the relaxation-time approximation cannot distinguish Dyakonov-Perel from Elliott-Yafet relaxation, and Eq. (10)'s 'τ→∞' label is questionable because the displayed 1/τ prefactor would make the expression vanish in that limit; these are internal-consistency/correctness concerns, not circularity. Thus the derivation chain is self-contained conditional on the model, and no prediction reduces by construction to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

No parameters are fitted to experimental data. Model inputs (λ, ᾱ, J_sd, μ, τ, eA, ω) are taken from the model definition or set to illustrative values for the figures (Fig. 2 caption: eA_x=eA_y=0.1a^-1, ω=J_sd/4; Fig. 3: τ=100J_sd^-1, μ=2J_sd). The headline predictions — resonance at ω=2J_sd, momentum parities, E0^2 sin 2θ dependence — are structural and independent of those values. No new entities are postulated: the hidden spin polarization and the orbital polarization are responses of the standard spin and orbital-magnetic-moment operators to an applied vector potential, so no independent falsifiable handle beyond the predicted response signatures is needed. The paper rests on the validity of the two-sector p-wave magnet model (imported from the authors' earlier PRL, Ref. [2], widely used by the cited community), the Γ-point continuum projection for all analytic work, a single momentum-independent relaxation time, standard Floquet/Kubo/density-matrix formalisms, and a specific decomposition of the orbital magnetic moment (Ref. [66]).

axioms (6)
  • domain assumption The two-sector minimal lattice model (Eq. 1), with combined translation×time-reversal symmetry τT, describes p-wave magnets.
    The whole calculation runs on this model, imported from Brekke, Sukhachov, Giil, Brataas, Linder, PRL 133, 236703 (2024) — Ref. [2], same authorship group. Applicability to experimental candidates (Gd3Ru4Al12, NiI2, CeNiAsO) is asserted via Refs. [4,9,10], not re-derived.
  • domain assumption The Γ-point continuum expansion, projected onto one sector η: H = ξ_k + M(k)σ_z + ηJ_sd σ_x (Eq. 2), captures the physics; all analytic results are leading order in α k_F / J_sd.
    Used for Eqs. (5), (9), (10), (12), (A22)-(A24); the only lattice-model check is Fig. 2, at one parameter set (α_y=0, ω=J_sd/4).
  • domain assumption A single momentum- and frequency-independent relaxation time τ governs intra- and interband dynamics (Eq. 3; Eqs. A18-A19).
    Footnote [63] concedes the approach does not distinguish Dyakonov-Perel from Elliott-Yafet mechanisms. The quantitative lineshapes and the resonant peak structure in Eqs. (10) and (A22)-(A24) depend on it.
  • standard math Floquet formalism: quasienergy spectrum and micromotion decomposition of Eqs. (A1)-(A6).
    Standard background in the driven-matter literature (Refs. [43-50]); used to define the textures in Fig. 2.
  • standard math Kubo linear response (Eqs. A14, 7-8) and the quantum-Liouville/density-matrix approach with a relaxation-time collision integral (Eq. A15).
    Standard response theory; yields the spin Edelstein tensor and the second-order orbital tensors.
  • domain assumption The orbital magnetic moment matrix elements m^(0), m^(1), m^(2) of Eqs. (A8)-(A11), with L̂ = −m̂/(g_L μ_B).
    Orbital observable defined via the Cysne-Souza-Rappoport decomposition (Ref. [66]); the orbital rectification result depends on the off-diagonal (non-Abelian) parts.

pith-pipeline@v1.3.0-alltime-deepseek · 11824 in / 29895 out tokens · 289628 ms · 2026-08-01T23:38:26.731023+00:00 · methodology

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read the original abstract

Period-averaged descriptions often miss essential features of driven quantum matter. We show that the micromotion of an optically driven $p$-wave magnet unveils a hidden net spin polarization, absent from both the equilibrium and period-averaged spin textures, which remain odd in momentum. This spin polarization oscillates at the drive frequency and is resonantly enhanced at the interband gap set by nonrelativistic exchange splitting. The drive further activates an orbital angular momentum governed by interband quantum geometry. While its linear response remains momentum-odd, nonlinear rectification yields a static, momentum-even orbital polarization for suitably oriented driving fields. These results establish $p$-wave magnets as a source of resonant ac spin and rectified dc orbital polarization: effects invisible to any period-averaged treatment.

Figures

Figures reproduced from arXiv: 2607.15353 by Jacob Linder, Pavlo Sukhachov, Yantao Li.

Figure 1
Figure 1. Figure 1: FIG. 1. Panel (a) shows the schematics of a light-driven [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Panels (a) and (e) show the period-averaged spin and orbital angular momentum textures, respectively. Panels (b)–(d) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Panels (a) and (b) show the spin Edelstein response [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

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