Exciting terahertz magnons with amplitude modulated light: spin pumping, squeezed states, symmetry breaking and pattern formation

Egor I. Kiselev; Jonas F. Karcher; Mark S. Rudner; Netanel H. Lindner; Rembert Duine

REVIEW 3 major objections 4 minor 1 cited by

Exciting terahertz magnons with amplitude modulated light: spin pumping, squeezed states, symmetry breaking and pattern formation

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Amplitude-modulated light can parametrically drive terahertz magnons in antiferromagnets, through a mechanism the authors call Modulated Floquet Parametric Driving.

desk verdict Good physics with a units slip in C and an undamped steady-state; the stress-test's 1800x complaint doesn't survive contact with the supplement. read the letter →

arxiv 2507.08147 v1 pith:KLY6BN4V submitted 2025-07-10 cond-mat.mes-hall cond-mat.str-el

Egor I. Kiselev , Jonas F. Karcher , Mark S. Rudner , Rembert Duine , Netanel H. Lindner This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.str-el

keywords antiferromagneticmagnonsterahertzspindynamicsmodulatedFloquetparametricdrivinginstabilitypumpingtwo-modesqueezingmagnonpatternformationinverseHalleffect

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes that a coherent optical beam with a modulated amplitude can resonantly excite antiferromagnetic magnons in the terahertz range without requiring a terahertz source. The mechanism works because the light makes the exchange coupling oscillate, $J(t)=\bar{J}+\delta J\cos(2\omega_d t)$; the $2\omega_d$ component acts as a parametric pump on magnon modes with $\omega_1(k^*)=\omega_d$, and once the modulation depth exceeds a damping-controlled threshold the magnon amplitude grows until nonlinearities saturate it. In the saturated state the authors derive concrete experimental signatures: dc spin pumping into a neighboring normal metal, two-mode squeezed and entangled magnon pairs, and, at finite wavevectors, standing-wave or stripe spin patterns that break the symmetries of the lattice. This matters because antiferromagnetic resonances are naturally in the THz range but are hard to address directly, and modulated optical frequencies up to 10 THz are already achievable in the lab.

What carries the argument

The central object is the modulated Floquet parametric drive (MFPD): a high-frequency optical carrier whose amplitude is modulated at a lower frequency, so the exchange constant acquires the oscillating term $\delta J\cos(2\omega_d t)$. The argument is carried by the linearized Landau-Lifshitz-Gilbert dynamics, where this term couples the magnon eigenmodes $\delta S_{\mathrm{eig},1}$ and $\delta S_{\mathrm{eig},2}$; a slowly varying envelope approximation near $\omega_1(k^*)=\omega_d$ gives exponential growth with rate proportional to $\delta J C\omega_d/(2J)$, and including Gilbert damping turns that growth into the threshold condition of Eq. (10). On the quantum side the same coupling becomes the two-mode squeezing Hamiltonian $\frac{\delta J C}{2}\cos(2\omega_d t)(\alpha_k^\dagger \alpha_{-k}^\dagger+\alpha_k\alpha_{-k})$, which directly produces the entangled magnon pairs of Eq. (17).

What would settle it

Drive a high-quality antiferromagnet capped with a normal metal using an amplitude-modulated optical beam, and record the dc inverse spin Hall voltage while sweeping modulation frequency and power. The paper predicts a sharp onset at the damping-controlled threshold, a microvolt-scale voltage at resonance for realistic hematite/Pt parameters, and no signal for an unmodulated beam of the same intensity; observing a signal that grows smoothly from arbitrarily small drive would falsify the quantitative picture.

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Extended reading notes

Core claim

As the authors state it, the central claim is that the time-dependent exchange coupling created by amplitude-modulated light acts as a parametric pump for antiferromagnetic magnons: $J(t)=\bar{J}+\delta J\cos(2\omega_d t)$, with the resonance condition $\omega_1(k^*)=\omega_d$ for the magnon mode that is pumped. Above the damping-controlled threshold of Eq. (10) the Néel state becomes linearly unstable, and the nonlinear terms in the Landau-Lifshitz-Gilbert equation saturate the growth into a steady state with the magnon amplitudes of Eq. (12). From that steady state the paper obtains three observable consequences: a dc spin current $I_{s,z}=2\omega_d G(a\,\delta b_{H,A}+b\,\delta a_{H,A})$ pumped into an adjacent normal metal (Eq. (15)), a two-mode squeezed magnon state with squeezing parameter $r=t\,\delta J C/(4\hbar)$ (Eq. (17)), and, for $k^*\neq 0$, symmetry-breaking standing-wave and stripe spin patterns in one and two dimensions. All of these follow from the same parametric instability, without the need for direct THz driving.

Load-bearing premise

The load-bearing premise is that the saturated magnon amplitudes used to predict spin pumping are computed without Gilbert damping, so the predicted signal size near threshold ignores the very damping that creates the threshold.

Editorial extensions

If this is right

Terahertz magnon resonances can be excited with amplitude-modulated optical light, bypassing the need for dedicated THz sources.
A driven antiferromagnet in contact with a normal metal should inject a dc spin current, measurable as a microvolt-scale inverse spin Hall voltage for realistic hematite/Pt parameters.
The parametrically driven magnon state is a two-mode squeezed vacuum in which magnons of opposite momenta are entangled, offering a route to squeezed and entangled states for quantum magnonics.
Driving at finite wavevector selects standing-wave and stripe spin textures that break translational and rotational symmetry, so the drive acts as a switch into a symmetry-broken dynamical phase.
Because the high quality factor of the magnon mode lets it accumulate drive energy over many cycles, the required optical powers are roughly two orders of magnitude lower than in direct exchange-modulation schemes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The authors do not spell this out, but the sharp threshold in Eq. (10) gives an experimental discriminant between MFPD and laser heating: an unmodulated beam of identical average intensity should produce no dc spin-pumping signal, while a modulated beam should show an abrupt onset.
Since the resonant wavevector $k^*$ is set by where $\omega_1(k)=\omega_d$, sweeping the modulation frequency should continuously tune the stripe wavelength in two-dimensional systems, turning the predicted pattern formation into a frequency-controlled texture.
The same parametric-pair Hamiltonian should apply to any bosonic collective mode whose coupling responds quadratically to light, such as optical phonons or exciton-polaritons; the squeezing and pattern-formation predictions may therefore transfer beyond magnons.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a serious paper, worth refereeing, but it needs a round of revision on two specific points. The MFPD idea is theirs from the plasmon papers, so the new thing here is the application to AF magnons: threshold, steady states, spin pumping, two-mode squeezing, and stripe pattern formation. The linear instability and the squeezing derivation are clean; the pattern-formation numerics (Dedalus) and the TenPy quantum simulation are concrete evidence.

I checked the stress-test note about C. It doesn't hold up. The supplement defines C = ∂logD1/∂J − ∂logD4/∂J; at k=0 with Dx,Dz ≪ J, D1≈2 and D4≈sqrt((Dx+Dz)/J), so C≈1/(2J), not Dx/(8J^2). Plugging C≈1/(2J) into Eq. (10) gives δJ/J roughly 2–3×10^-5 for their parameters, matching the paper's estimate. So the central low-power claim is not off by 1800x.

That said, there is a real units inconsistency: the supplement's C has units 1/energy, while the main text Eq. (8) uses it as dimensionless. The threshold formula Eq. (10) only makes dimensional sense with C in 1/energy. So the paper is internally consistent in one place and wrong in another; the authors need to clarify what C is and fix Eq. (8) accordingly. This is a typo-level fix, not a load-bearing flaw.

The bigger soft spot is the steady state. Supplement C derives Eq. (12) from the LLG with no Gilbert damping. So the amplitudes scale as sqrt(δJ) and are finite for any δJ>0, including below the threshold. In the damped system the saturated amplitude should vanish at threshold and grow as sqrt(δJ−δJ_th). The paper then uses Eq. (12) at 'δJ of the order of the threshold' for the spin-pumping and inverse-spin-Hall estimates, which will overestimate the effect near threshold. That needs a quantitative redo. The mechanism survives, but the numbers in Sec. VI are not trustworthy as written.

There are also minor typos (e.g., 'eigenvelue', Dz=−0.2 in Supplement D) that should be caught.

Bottom line: the qualitative mechanism is sound, the derivations are mostly clean, and the paper opens a practical route to THz magnons without THz sources. With the damping issue fixed and C clarified, it would be a solid contribution. A serious referee should engage with it; I'd send it out with a request for revision.

Referee Report

3 major / 4 minor

Summary. The paper proposes Modulated Floquet Parametric Driving (MFPD) as a way to excite THz antiferromagnetic magnons using amplitude-modulated optical light. The modulation of the exchange coupling J(t) = J̄ + δJ cos(2ω_d t) is argued to parametrically drive a magnon mode when the modulation frequency matches the magnon frequency, with a damping-controlled threshold given by Eq. (10). Above threshold, nonlinearities saturate the instability into steady states, which the paper uses to predict spin pumping into an adjacent metal, dynamical pattern formation in one and two dimensions, and the generation of two-mode squeezed magnon states. The analytic results are supplemented by classical LLG simulations with Dedalus and tensor-network simulations with TenPy.

Significance. If correct, the mechanism is significant: it offers a route to drive THz magnons without THz sources, with potential consequences for antiferromagnetic spintronics and quantum magnonics. The paper includes a clean linear parametric instability analysis, a quantum two-mode squeezing derivation, and numerical simulations of pattern formation. However, the central quantitative claims—the low-power threshold and the spin-pumping voltage estimate—currently rest on an inconsistent definition of the coupling coefficient C and on steady-state amplitudes derived without damping. These issues are load-bearing and need to be resolved before the proposal's practical viability can be assessed.

major comments (3)

[Supplement B and Eq. (10)] The definition of the coupling coefficient C is inconsistent with the threshold formula and with the text. In the main text, immediately after Eq. (8), C is called dimensionless, and Eq. (10) uses it in δJ/J > (1/(JSC))·4αω_dℏ/(4J + D_x + 2D_z). In Supplement B, however, C is defined as C = ∂log D_1/∂J − ∂log D_4/∂J, which has dimensions of inverse energy. For k = 0 and D_z, D_x ≪ J, D_1 ≈ D_4 ≈ 2, so J·C ≈ D_x/(8J) ≈ 2.5×10^{-4} for J = 50 meV, D_x = 0.1 meV. Inserting this into Eq. (10) yields δJ/J ≈ 3.6×10^{-2}, about 1800 times larger than the quoted δJ/J ≈ 2×10^{-5}. If instead C is treated as the dimensionless O(1) coefficient suggested by a direct Mathieu-type linearization of Eq. (A5), then Eq. (10) is dimensionally inconsistent as written. The supplement's C therefore does not appear to be the coefficient governing the coupling in Eqs. (8) and (9). This must be reconciled, and the threshold estimate and the field-reduction factor in Sec. VI must be recomputed with the correct coefficient.
[Supplement C and Sec. VI, Eqs. (12)-(15)] The steady-state amplitudes in Eq. (12) are derived from the amplitude equations (A11) without including Gilbert damping. As a result they scale as √δJ and vanish only as δJ → 0, not at the finite threshold δJ_th of Eq. (10). The spin-pumping formulas (13)-(15) and the inverse spin Hall voltage estimate in Sec. VI are then evaluated at 'δJ of the order of the threshold'. At threshold, the saturated amplitude in a damped parametrically driven system should instead vanish, scaling roughly as √(δJ − δJ_th) above threshold. The quantitative spin-pumping estimate therefore needs revision: either the amplitude equations must be solved with damping included, or the estimate must be restricted to δJ sufficiently above threshold with the appropriate suppression factor.
[Sec. V, Eq. (16) and the squeezing parameter r] The dimensions/prefactors in the quantum treatment should be checked carefully. The Hamiltonian in Eq. (16) has a pair-generation term with coefficient δJ·C/2, while the interaction-picture Hamiltonian is later written as H_int = δJ/(4J)·C(α†_{k*}α†_{−k*} + α_{k*}α_{−k*}), and the squeezing parameter is r = tδJ C/(4ℏ). Depending on whether C is dimensionless or has units of 1/J, and on how δJ is normalized relative to J, these expressions change by factors of J and ω_d. The relation between the classical coupling in Eq. (8), which contains ω_1 ≈ ω_d and δJ/J, and the quantum coupling in Eq. (16) should be stated explicitly so that the squeezing parameter is unambiguous.

minor comments (4)

[Figure 2 caption] The caption says 'according to Eq. (2)' but the dispersions are given by Eq. (5); please correct the reference.
[Supplement D] The simulation parameters list 'D_z = 0.1, D_z = −0.2' twice. The second should presumably be D_x, since the model requires D_x > 0; please fix this typo and confirm the sign convention used in the simulation.
[Sec. VI, Discussion] The sentence 'Since δJ ∼ √E' appears to be a typo: from Eq. (2), δJ ∝ E^2, so a threshold δJ/J = 2×10^{-5} corresponds to a field-amplitude reduction factor of about 1/√(2×10^{-5}) ≈ 200. Please clarify the proportionality.
[Supplement C, Eq. (A11)] The symbols in Eq. (A11) mix δJ, ϵ, and δJ̃; the sentence 'we wrote ϵδJ̃ = δJ' should define the dimensionless and dimensional quantities more explicitly to avoid confusion about the expansion parameter.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the magnon predictions are derived from the LLG dynamics with stated input J(t), not from fitted data or from a self-citation chain.

full rationale

I find no circular step that reduces a prediction to its inputs by construction. The central input, J(t) = Jbar + δJ cos(2ωd t), is obtained from the Hubbard model via Schrieffer-Wolff (Supplement A), citing external prior work. The instability threshold (Eq. 10), steady-state amplitudes (Eq. 12), spin-current formula (Eq. 15), and two-mode squeezing Hamiltonian (Eq. 16) are all derived from the stated LLG equations and quantization procedure with explicit assumptions; they are not fitted to data and do not assume the results they predict. Self-citations [31,32] are used only to attribute the MFPD concept to previous plasmon work, not as load-bearing justification for the magnon results. I also flag, as a correctness risk rather than circularity, the internal inconsistency in Supplement B: C is defined as ∂log D1/∂J − ∂log D4/∂J, which has units of 1/J, while the main text calls C dimensionless and uses it in Eq. (8) and Eq. (10); this affects the quantitative threshold estimate but does not constitute circular reasoning. Similarly, the steady-state amplitudes of Eq. (12) are derived with zero damping and then used at threshold, a physical approximation issue, not a circularity. Overall, the derivation chain is self-contained and externally checkable, so the circularity score is low.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper does not fit any parameters to experimental data; all free quantities are material parameters chosen for illustration. The main unstated input is the form J(t) = J̄ + δJ cos(2ωd t) (Eq. (2)), justified by the Hubbard-model supplement. The steady-state derivation quietly drops the damping term, which is the principal weak point of the quantitative predictions.

assumptions (6)

domain assumption Adiabatic amplitude modulation: for ωd << Ω, the time-dependent exchange takes the form J(t) = J̄ + δJ cos(2ωd t) with δJ = (Ē²/4) ∂²J/∂E² evaluated at E=0.
Supplement A derives J(E) from a Hubbard model with Peierls substitution; the sinusoidal form and second-order scaling in E are used throughout the paper (Eq. (2)).
domain assumption The Landau-Lifshitz-Gilbert equation (3) with constant Gilbert damping α describes the spin dynamics.
Eq. (3) is the starting point for all classical results; interface-enhanced damping is neglected in the spin pumping analysis.
domain assumption Only one pair of magnon branches (ω1/2) is resonantly driven; the splitting from ω3/4 is assumed large.
Stated in Sec. II after Eq. (7): 'we assume that the splitting between ω1/2 and ω3/4 is large enough'.
standard math Rotating-wave / slowly-varying envelope approximation: higher harmonics at 2ωd, 3ωd are dropped.
Used in Supplement B to obtain Eq. (A7) and in Supplement C for the amplitude equations.
ad hoc to paper The steady-state amplitude equations (Supplement C) are solved without including Gilbert damping; linear damping effects are added only perturbatively for the threshold.
The fixed point b ∝ sqrt(δJ) has no finite-threshold offset; this assumption underlies the spin-pumping estimate in Sec. VI.
domain assumption For the 2D simulations, the continuum LLG with effective fields given by Eqs. (A15) to (A17) faithfully represents the lattice model.
Supplement E: continuum approximation used for k* << 1/a_l; the stripe pattern selection depends on this.

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Cite this review

Pith. "Pith review of Exciting terahertz magnons with amplitude modulated light: spin pumping, squeezed states, symmetry breaking and pattern formation." pith.science (2026). https://pith.science/paper/KLY6BN4V

@misc{pith2026250708147,
  author       = {Pith},
  title        = {Pith review of: Exciting terahertz magnons with amplitude modulated light: spin pumping, squeezed states, symmetry breaking and pattern formation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KLY6BN4V}},
  note         = {Machine review of arXiv:2507.08147}
}

read the original abstract

We show how amplitude modulated, coherent high-frequency drives can be used to access otherwise difficult to reach collective resonances and off-resonantly induce parametric instabilities. In particular, we demonstrate that difficult to access antiferromagnetic resonances in the THz range can be parametrically excited with signals at optical frequencies via a mechanism that we call Modulated Floquet Parametric Driving (MFPD). We study spin pumping and the formation of entangled, two-mode squeezed magnon pairs in anisotropic antiferromagnets under MFPD. Furthermore, we show that MFPD induces transitions to symmetry breaking steady-states in which dynamical spin patterns are formed by resonant magnon pairs.

Figures

Figures reproduced from arXiv: 2507.08147 by the authors.

**Figure 3.** a) Spin oscillations in an MFPD driven AF (1D chain). The oscillations of the spin component Sx on one of the two Néel sublattices are shown for driving above the threshold (Eq. (10)). After a period of amplitude oscillations, the spins enter a steady state with a constant amplitude. Td = 2π/ωd is the duration of one modulation cycle. We used the parameters Dz = 0.2J, Dx = 0.1J, δJ = 0.05J, S = 1 and α = 2.5 · 10−3 … view at source ↗

Discussion (0). Continue with ORCID to comment.

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