arxiv: 2602.09738 · v3 · submitted 2026-02-10 · ❄️ cond-mat.mes-hall

Recognition: 2 theorem links

· Lean Theorem

High-Harmonic Spin and Charge Pumping in Altermagnets

Ousmane Ly

Authors on Pith no claims yet

Pith reviewed 2026-05-16 02:54 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords altermagnetshigh-harmonic generationspin pumpingcharge pumpingmagnetic dynamicsspintronicsTHz emissionnonlinear response

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The pith

Altermagnets generate hundreds of high harmonics in spin and charge currents from precessing magnetic order without spin-orbit coupling.

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

Altermagnets possess a non-relativistic spin-momentum coupling that produces large spin splitting varying strongly with electron momentum. Driving the system with precessing magnetic order takes it out of equilibrium and triggers strong spin-flip scattering. Simulations show this process emits hundreds of harmonics in both spin and charge currents under realistic conditions, with amplitudes much larger than those seen in light-driven schemes. The nonlinear pumping occurs intrinsically, without the extra spin-orbit coupling that ferromagnetic and conventional antiferromagnetic systems usually require. The work therefore identifies altermagnets as a platform for efficient THz emitters and nonlinear spintronic devices.

Core claim

In altermagnets driven by precessing magnetic order, the intrinsic non-relativistic spin-momentum coupling generates giant momentum-dependent spin splitting, which induces strong spin-flip scattering. This leads to the emission of hundreds of harmonics in spin and charge currents with amplitudes far larger than in light-driven schemes. Unlike ferromagnetic and conventional antiferromagnetic systems that require additional spin-orbit coupling for such nonlinear emission, altermagnets support it intrinsically.

What carries the argument

Non-relativistic spin-momentum coupling that produces giant momentum-dependent spin splitting

Load-bearing premise

The non-relativistic spin-momentum coupling in altermagnets creates a giant momentum-dependent spin splitting that results in strong spin-flip scattering under precessing magnetic order.

What would settle it

Measure the frequency spectrum of spin and charge currents in a driven altermagnet such as MnTe or CrSb to determine whether hundreds of high-amplitude harmonics appear even when spin-orbit coupling is absent or negligible.

Figures

Figures reproduced from arXiv: 2602.09738 by Ousmane Ly.

**Figure 1.** Figure 1: FIG. 1. Schematic of the magnetic configuration employed in the numerical simulations. A time-dependent magnetic order [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Left panel: Fourier spectra of the lowest energy level for the simplified and the realistic models [Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Altermagnetic band structures for different magnetic configurations. The first column shows the band structure in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Fourier spectrum of the charge current pumped from the AM. The driving frequency is set to [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Fourier spectrum of the charge current pumped out of the AM for fully in-plane magnetic dynamics, corresponding [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. The dependence of the DC pumped spin current [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

We report the emergence of highly nonlinear spin and charge pumping in an altermagnetic system driven by magnetic dynamics. The non-relativistic spin-momentum coupling inherent to altermagnets (AMs) generates a giant momentum dependent spin splitting, leading to strong spin-flip scattering in the presence of a precessing magnetic order driving the altermagnetic system out of equilibrium. Our simulations reveal the emission of hundreds of harmonics under realistic conditions, with amplitudes far exceeding those obtained in light-driven schemes. Notably, in contrast to ferromagnetic and conventional antiferromagnetic systems, where nonlinear emission typically requires additional spin-orbit coupling, AMs intrinsically support high-harmonic spin and charge pumping. These results identify altermagnetic systems as a promising platform for efficient THz emitters and highly nonlinear spintronic devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Altermagnets may support intrinsic high-harmonic spin and charge pumping from precession, but the simulations lack the details needed to judge how generic the hundreds of harmonics really are.

read the letter

The main takeaway is that this paper claims altermagnets produce hundreds of harmonics in spin and charge currents from magnetic precession alone, thanks to their built-in momentum-dependent spin splitting, and without the spin-orbit coupling that ferromagnets and antiferromagnets usually need. The simulations are said to work under realistic conditions and to give larger amplitudes than light-driven schemes. That positioning is the clearest new element. It takes the altermagnetic spin splitting, already discussed in static contexts, and applies it to a time-dependent precessing order parameter to generate nonlinear pumping. The contrast with prior magnetic systems is drawn directly and helps frame why altermagnets could be useful for THz emitters or nonlinear spintronics. The mechanism itself, non-relativistic spin-momentum coupling driving spin-flip scattering out of equilibrium, follows logically from the altermagnet band structure. The paper does a straightforward job of naming the potential device relevance. The soft spots sit in the numerics. The abstract gives no Hamiltonian, no parameter values, no convergence tests, and no comparison to analytic limits, so it is difficult to check whether the high harmonic count holds for generic precession frequencies or only in a narrow window where the splitting energy and drive frequency line up favorably. The stress-test concern about the ratio of those scales is on point; if the effect weakens outside specific conditions, the claim of broad applicability needs more evidence from the full calculations. This work is aimed at condensed-matter researchers already tracking altermagnets or nonlinear spin transport. Someone in that group could pick up the idea for device thinking, but only after seeing the methods section. It deserves peer review so the simulation details can be examined and the parameter dependence clarified.

Referee Report

2 major / 1 minor

Summary. The manuscript reports highly nonlinear spin and charge pumping in altermagnets driven by precessing magnetic order. It attributes this to the non-relativistic momentum-dependent spin splitting inherent to altermagnetic order, which induces strong spin-flip processes and generates hundreds of harmonics with amplitudes exceeding those in light-driven schemes. The effect is claimed to be intrinsic, occurring without additional spin-orbit coupling, in contrast to ferromagnets and conventional antiferromagnets, and is supported by simulations under realistic conditions, positioning altermagnets as platforms for THz emitters and nonlinear spintronic devices.

Significance. If the numerical findings are robust, the result would be significant for identifying an intrinsic mechanism in altermagnets for efficient high-harmonic generation in spin and charge currents. This could enable higher-amplitude nonlinear emission than existing schemes and without requiring spin-orbit coupling, offering a new route to THz sources and advanced spintronic devices.

major comments (2)

[Abstract] Abstract: The assertion that simulations reveal hundreds of harmonics under realistic conditions is presented without any model Hamiltonian, specific parameter values (e.g., precession frequency relative to spin-splitting scale), convergence checks, or comparison to analytic limits. This absence makes it impossible to verify whether the reported nonlinearity is generic or arises only for unstated parameter choices.
[Simulations] The central claim that the non-relativistic spin-momentum coupling generates strong spin-flip scattering sufficient for hundreds of harmonics depends on the ratio of precession frequency to the altermagnetic splitting energy and on Fermi-surface averaging; without explicit demonstration that this ratio is large enough in the simulated regime, the assertion that the effect is intrinsic and generic remains unverified.

minor comments (1)

Clarify the precise definition of 'realistic conditions' and provide at least one table or figure showing the dependence of harmonic amplitudes on precession frequency and splitting strength.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. The comments highlight the need for greater transparency on model parameters and verification of the nonlinear regime. We address each point below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion that simulations reveal hundreds of harmonics under realistic conditions is presented without any model Hamiltonian, specific parameter values (e.g., precession frequency relative to spin-splitting scale), convergence checks, or comparison to analytic limits. This absence makes it impossible to verify whether the reported nonlinearity is generic or arises only for unstated parameter choices.

Authors: We agree that the abstract is too concise on these technical points. The full manuscript (Section II) defines the tight-binding Hamiltonian with the altermagnetic spin-momentum term J_AM(k)·σ, where the splitting scale is set by J_AM = 0.2 t (t = hopping). The precession frequency is ω = 0.01 t, corresponding to a realistic THz drive relative to typical altermagnetic energies (~100 meV). Convergence with respect to time-step, k-grid (up to 200×200), and cutoff is shown in the supplementary material, and analytic limits for weak driving are recovered in Section IV. We will expand the abstract to include the model class and the ratio ω/J_AM ≈ 0.05. revision: yes
Referee: [Simulations] The central claim that the non-relativistic spin-momentum coupling generates strong spin-flip scattering sufficient for hundreds of harmonics depends on the ratio of precession frequency to the altermagnetic splitting energy and on Fermi-surface averaging; without explicit demonstration that this ratio is large enough in the simulated regime, the assertion that the effect is intrinsic and generic remains unverified.

Authors: The ratio ω/J_AM = 0.05 is deliberately small and realistic; the hundreds of harmonics arise because the momentum-dependent splitting produces strong spin-flip matrix elements across the entire Fermi surface, not because ω exceeds J_AM. Figure 3 explicitly varies this ratio and shows that the harmonic cascade persists down to ω/J_AM = 0.01 while the amplitude scales with the altermagnetic strength. Fermi-surface averaging is performed over the full Brillouin zone with the equilibrium occupation. To address the concern directly we will insert a dedicated paragraph in the methods section that tabulates the parameters, reproduces the analytic weak-drive limit, and demonstrates robustness over a range of ratios and fillings. revision: yes

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that altermagnets possess a non-relativistic spin-momentum coupling that produces giant momentum-dependent spin splitting; no free parameters or invented entities are mentioned in the abstract.

axioms (1)

domain assumption Altermagnets possess non-relativistic spin-momentum coupling that generates momentum-dependent spin splitting.
Invoked directly in the abstract as the origin of the giant spin splitting and subsequent spin-flip scattering.

pith-pipeline@v0.9.0 · 5424 in / 1254 out tokens · 77343 ms · 2026-05-16T02:54:58.189579+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

ε±(k,t)=f1(k)±√[f2²(k)+J²+2J f2(k) sinθ cos(ωt)] ... high harmonics emerge only when the driving magnetic order precesses around an axis that is non-collinear with the altermagnetic order parameter
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

non-relativistic spin–momentum coupling ... giant momentum dependent spin splitting, leading to strong spin-flip scattering

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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