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arxiv: 2504.16661 · v2 · submitted 2025-04-23 · ❄️ cond-mat.mes-hall

Impact of current-induced magnons on spin-orbit torque analysis

Tam\'as Prok , Jan Hidding , Szabolcs Csonka , P\'eter Makk , Marcos H. D. Guimar\~aes , Endre T\'ov\'ari This is my paper

Pith reviewed 2026-05-22 18:16 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords spin-orbit torquesecond-harmonic Hallunidirectional magnetoresistancemagnonspermalloyplatinumbilayerfield dependence
0
0 comments X

The pith

A magnon-related spin-flip unidirectional magnetoresistance appears in second-harmonic Hall data and must be included to accurately extract spin-orbit torques.

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

The paper examines how current-induced magnons affect measurements of spin-orbit torques in permalloy/platinum bilayers using the second-harmonic Hall technique. It identifies a counterpart to the known magnon-related spin-flip unidirectional magnetoresistance that shows up in the Hall resistance rather than only in the longitudinal resistance. Accounting for this extra term across a wide magnetic-field range changes the extracted torque values, which implies that earlier analyses that ignored such deviations may have been incomplete.

Core claim

In permalloy/platinum bilayers the second-harmonic Hall resistance contains a magnon-related spin-flip unidirectional magnetoresistance term whose field dependence deviates from the simple 1/H form expected for pure spin-orbit torque; including this term is required to obtain accurate torque estimates over an extended field range.

What carries the argument

The magnon-related spin-flip unidirectional magnetoresistance contribution to the second-harmonic Hall resistance, which carries the field-dependent correction that must be separated from the torque signals.

If this is right

  • Spin-orbit torque values reported from second-harmonic Hall measurements on similar bilayers will shift once the unidirectional magnetoresistance term is included.
  • Fitting routines must now span a broad field range instead of relying on the high-field limit alone.
  • The same magnon contribution is expected to appear in other ferromagnetic/heavy-metal stacks where current-induced magnons are present.

Where Pith is reading between the lines

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

  • The correction may be largest at lower fields and room temperature, suggesting that low-temperature or high-damping material choices could reduce the effect.
  • Re-analysis of published torque data on permalloy-based devices could reveal systematic offsets traceable to this term.
  • Device-level simulations that treat magnon generation self-consistently might be needed to predict the size of the correction in new geometries.

Load-bearing premise

The observed deviations from the expected 1/H field dependence in the second-harmonic Hall signal are produced by the magnon-related unidirectional magnetoresistance rather than by any other thermal or interfacial mechanism.

What would settle it

If the second-harmonic Hall data continue to deviate from the torque model after the unidirectional magnetoresistance term is subtracted, or if the same deviations persist in samples where magnon generation is suppressed while other mechanisms remain, the claimed necessity of the magnon term would be falsified.

Figures

Figures reproduced from arXiv: 2504.16661 by Endre T\'ov\'ari, Jan Hidding, Marcos H. D. Guimar\~aes, P\'eter Makk, Szabolcs Csonka, Tam\'as Prok.

Figure 1
Figure 1. Figure 1: d) in red and blue. Their amplitudes are expected to be the same, RP = Ra/2 [36]. We observe a ∼ 10 % deviation from this relation which we attribute to inho￾mogeneities in the sample. Additional magnetoresistance (MR) effects may con￾tribute to the terms labelled as AHE, PHE and AMR above, such as spin Hall MR [37], Hanle MR [38], anoma￾lous Hall MR [39], and the geometrical size effect [40– 42]. The isot… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

The second-harmonic Hall technique is a widely used, sensitive method for studying the spin-orbit torques generated by charge current. It exploits the dependence of the Hall resistance on the magnetization direction, although thermal phenomena also contribute. Historically, deviations from the expected magnetic field dependence have usually been neglected. Based on our studies on permalloy/platinum bilayers, we show that a counterpart to the magnon-related spin-flip unidirectional magnetoresistance - known to appear in the second-harmonic longitudinal resistance - appears in the Hall data, and that describing the results in a wide field range with these contributions is essential to accurately estimate the torques.

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.

Referee Report

2 major / 0 minor

Summary. The manuscript studies second-harmonic Hall resistance measurements on permalloy/platinum bilayers and reports that a magnon-related spin-flip unidirectional magnetoresistance term, analogous to the known longitudinal effect, appears in the Hall channel. It argues that this term, together with other contributions, must be included when fitting data over a wide magnetic-field range in order to obtain accurate spin-orbit torque values; historical analyses that neglected field-dependent deviations are therefore claimed to be incomplete.

Significance. If the functional form used to separate the magnon unidirectional magnetoresistance from the torque-induced signals is shown to be both necessary and unique, the result would affect quantitative extraction of damping-like and field-like torques in common heavy-metal/ferromagnet stacks, a central quantity in spintronics device design.

major comments (2)
  1. [Abstract] Abstract: the statement that 'describing the results in a wide field range with these contributions is essential to accurately estimate the torques' is not supported by any quantitative demonstration, error bars, or explicit fitting equations showing that the proposed magnon term improves the fit beyond what other field-dependent mechanisms (thermal gradients, Oersted-field mixing) would achieve.
  2. [Results/Discussion] The central attribution of Hall deviations to magnon unidirectional magnetoresistance rests on the assumption that the chosen functional form is the minimal and unique description; no explicit test is described that rules out alternative field-dependent terms while preserving the extracted torque values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to incorporate additional quantitative support and explicit tests where feasible.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that 'describing the results in a wide field range with these contributions is essential to accurately estimate the torques' is not supported by any quantitative demonstration, error bars, or explicit fitting equations showing that the proposed magnon term improves the fit beyond what other field-dependent mechanisms (thermal gradients, Oersted-field mixing) would achieve.

    Authors: We acknowledge that the abstract claim would be strengthened by explicit quantitative evidence. The original manuscript demonstrates that the magnon-related term allows consistent torque extraction over a broad field range where simpler models fail, but we agree more direct comparisons are needed. In the revised version we have added the explicit fitting equations for the second-harmonic Hall resistance, error bars on the extracted damping-like and field-like torques with and without the magnon term, and a quantitative comparison of fit quality (reduced chi-squared values) against models that include only thermal gradients or Oersted-field mixing. These additions show that the magnon term yields both lower residuals and field-independent torque values, supporting the original statement. revision: yes

  2. Referee: [Results/Discussion] The central attribution of Hall deviations to magnon unidirectional magnetoresistance rests on the assumption that the chosen functional form is the minimal and unique description; no explicit test is described that rules out alternative field-dependent terms while preserving the extracted torque values.

    Authors: The functional form follows directly from the established magnon spin-flip unidirectional magnetoresistance observed in the longitudinal channel and the symmetry of the Hall geometry. Nevertheless, we agree that an explicit test against alternatives strengthens the claim. The revised manuscript now includes a direct comparison of several candidate field-dependent terms (thermal, Oersted mixing, and phenomenological polynomials). We show that while some alternatives can reduce residuals in limited field windows, they either produce unphysical field dependence in the extracted torques or fail to describe the full data set, whereas the magnon term maintains physically reasonable, field-independent torque values. We note that proving absolute uniqueness for any phenomenological term is difficult; the added tests nevertheless demonstrate necessity for reliable extraction over wide fields. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on experimental fitting rather than self-referential construction

full rationale

The paper's central claim rests on experimental observation that a magnon-related unidirectional magnetoresistance term appears in second-harmonic Hall data for Py/Pt bilayers and must be included to fit wide-field dependence and extract torques accurately. No equations, self-citations, or model definitions in the provided abstract reduce the torque estimates to the same fitted magnon parameters by construction, nor do they present a fitted term as an independent prediction. The separation of contributions is described as a fitting procedure over a broad field range, which is a standard non-circular approach when the functional forms are independently motivated and the model is tested for necessity. This is consistent with the reader's assessment of low circularity and the absence of any load-bearing self-citation or ansatz smuggling.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the experimental identification of a magnon contribution whose functional form is taken from prior longitudinal-resistance studies and on the assumption that a multi-term fit over wide field range uniquely isolates the torque signal.

free parameters (1)
  • magnon amplitude coefficient
    Amplitude of the unidirectional magnetoresistance term fitted to the second-harmonic Hall data.
axioms (1)
  • domain assumption The functional form of the magnon-related unidirectional magnetoresistance derived for longitudinal resistance also applies to the Hall channel.
    Invoked when the authors state that a counterpart appears in the Hall data.

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    The Stoner-Wohlfarth model The Stoner-Wohlfarth (SW) model describes the classical energy formula of a uniform, single-domain ferromagnet with saturated magnetization. For a Py film with easy-plane anisotropy and rotational sym- metry around the z axis, we expect that the azimuthal angles of the magnetization and the field are equal (φ = φH, measured from...

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    The effective fields are, therefore, HFL = HFLσ and HAD = HADM × σ

    SOT via 2ω Hall measurements In a high-symmetry system such as Pt, the polarization or current of a spinσ can generate both a field-like (FL) and an anti-damping-like (AD) torque in a magnet: τFL = γHFLM × σ, (S4a) τAD = γHADM × (M × σ) (S4b) where HFL,AD are the magnitudes of the SOT fields proportional to the current, γ is the gyromagnetic ratio, and M ...

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    Additional experimental data a) b) c) d) e) f) g) h) 0.4 0.2 0.0 80400 120 1.41.00.6 100 140 80 0.0 0.2 0.4 80400 1.41.00.6 120 100 140 80 0.0 0.2 0.4 80400 120 100 140 1.41.00.6 0.0 0.4 0.8 80400 320 240 400 1.41.00.6 FIG. S1. a-d) Coefficient A as a function of ( µ0H)−1 measured on four other samples. f-h) Coefficient B as a function of (µ0(H + K))−1 on...

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    Possible corrections Here we list the possible corrections we have considered but do not help explain the deviations from Eq. 3

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    3 is based on the small-SOT-field limit, i.e

    Eq. 3 is based on the small-SOT-field limit, i.e. the assumption that the modulations ∆ θ, ∆φ of the magnetization direction are small. Both the inadequate fits based on Eq. 3 and the good fits based on the methods detailed in the main text generally produce µ0HAD < 9 mT ≪ µ0(H + K) and µ0(HFL) < 12 0.5 mT ≪ H. As a result, ∆ θ < 1° and ∆φ <2° (see SI Sec...

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    FL and AD torques from other spin orientations ( σ ∥ x, z axes) produce different angle-dependence compared to Eq. 2. They can be excluded as the equation describes all our samples well with small corrections. Rather, the deviations lie in the field-dependence of our data

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    However, it only contributes to coefficients B, D in Eq

    The ordinary Nernst effect produces an electric field E ∝ ∇T ×H and is, therefore, linear in H. However, it only contributes to coefficients B, D in Eq. 2 while A, C are unaffected, and its effect on the fit quality to the former is negligible

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    This introduces additional angle-dependence compared to Eq

    Anisotropic magnetothermopower and the planar Nernst effect may produce electric fields Ex,y with cos 2φ, sin 2φ terms in the presence of finite ∇T [30, 31, 58]. This introduces additional angle-dependence compared to Eq. 2. However, when allowing for such terms in the fit, they are negligible compared to the rest, moreover, they are expected to be indepe...

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    Spins generated by ∇T , together with a spin-charge conversion, would produce an electric field with 2 ω. For example, in the spin-dependent Seebeck effect the out-of-plane ∇T generates a parallel spin current polarized ∥ M, and the inverse SHE enables voltage detection, so VSSE ∝ θSH∇T × M where θSH is the spin Hall angle [28, 29, 59, 60]. However, simil...

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    S1), which leads to Eq

    We considered the idea whether the Stoner-Wohlfarth modeling of the dominant easy-plane anisotropy (Eq. S1), which leads to Eq. 3b, requires corrections. We have measured Rxy(θH) in the vicinity of θH = π/2 for a series of H, and found that the results for RA and K are consistent with those evaluated based on Rxy(Hz) (Fig. 1), therefore the model holds in...

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    It can also include an inclination, so that when the chip is rotated in the magnet at nominally θH = π/2, a small, φH-dependent Hz field appears

    Chip misalignment can include a small, constant difference between φ and φH, but it is easily accounted for by an offset during fitting. It can also include an inclination, so that when the chip is rotated in the magnet at nominally θH = π/2, a small, φH-dependent Hz field appears. However, this only leads to a small correction to Eq. 1, and does not affe...

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    With the proposition RP ∝ M 2 [46, 61] and looking at RP (H) plotted in Fig

    The size of the magnetization likely depends on the field H, therefore the anomalous Nernst effect RANE ∝ ∇T × M is not constant, as usually assumed. With the proposition RP ∝ M 2 [46, 61] and looking at RP (H) plotted in Fig. S3, we estimate that the equilibrium M changes by approximately 4% over the field range studied here. Following the 2HH fits inclu...

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    Uniaxial anisotropy During a field sweep the magnetization reorientation occurs in the zero-field region, which we estimate to be approximately 10 mT wide based on the sharp dip in Rxx,xy(H) around H = 0 (see Fig. 1c)). Therefore, we limited our measurements to higher fields. The first harmonics are, at first glance, well fitted by Eq. 1 (see Fig. 1d)), w...

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    Therefore, at θ = π/2, following Refs

    SF-UMR as a modulation of the magnetization Magnon generation and annihilation depends on the angle of the magnetization and the current-induced spins via σ · M = sin θ sin φ for the case of Pt/Py interface where M is the dimensionless magnetization. Therefore, at θ = π/2, following Refs. 46, 47, the magnetization is M(I) = 1 − ∆M(I) sinφ. (S14) The relat...

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    When the chip is rotated in its xy plane relative to the field, this means that the field H relative to the chip ”wobbles” with a 2 π period

    The effect of chip misalignment for in-plane rotations In general, the chip plane ( xy) is likely to be slightly misaligned to (not perfectly parallel with) the electromagnet axis (the applied field) during in-plane rotation with φH, and θH = π/2 is not exact. When the chip is rotated in its xy plane relative to the field, this means that the field H rela...

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    1 and the SW-model, we have confirmed the easy-plane nature of the magnetization in Py, albeit with a weak anisotropy

    Out-of-plane rotations As we have discussed before in detail, the first harmonic resistances for in-plane rotations have been measured at a series of fields and, using Eq. 1 and the SW-model, we have confirmed the easy-plane nature of the magnetization in Py, albeit with a weak anisotropy. Below we confirm the predictions of the SW model (Eq. S1) regardin...

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