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Spin current symmetries generated by GdFeCo ferrimagnet across its magnetisation compensation temperature

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Pith's one-line read The paper argues that GdFeCo's spin-Hall and spin-anomalous-Hall torques keep their signs across the magnetisation compensation temperature, with the SAHE torque opposite in sign to the SHE torque.

desk verdict Clean SHE/SAHE spin-current decomposition in GdFeCo, but the SAHE sign-retention headline rests on two endpoint temperatures and should be treated as provisional. read the letter →

arxiv 2511.20379 v2 pith:6M7YFFC5 submitted 2025-11-25 cond-mat.mes-hall cond-mat.mtrl-sci

Héloïse Damas , Michel Hehn , Juan-Carlos Rojás-Sanchez , Sébastien Petit-Watelot This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.mtrl-sci
keywords spincurrentHalleffectanomalousferrimagnetGdFeCospin-torqueferromagneticresonancemagnetisationcompensationspin-orbittorque
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

This paper tries to establish that a ferrimagnet's own spin currents do not change sign when the material passes through its magnetisation compensation temperature, where the net moment vanishes. Using spin-torque ferromagnetic resonance on a GdFeCo/Cu/NiFe stack, the authors separate two spin-current generation mechanisms: the ordinary spin Hall effect (SHE) and the spin anomalous Hall effect (SAHE), in which the spin polarisation is tied to the magnetisation direction. They find that both torque signs stay fixed through compensation, that the SAHE-driven damping-like torque is opposite in sign to the SHE-driven one and dominates far from compensation, and that this can be understood if the SHE originates from Gd 5d electrons and the SAHE from FeCo 3d electrons. If correct, the result reframes earlier reports of sign-changing self-torques in ferrimagnets as absorption effects rather than emission effects, which matters for designing spin-torque devices whose torque direction is temperature stable.

What carries the argument

The key mechanism is the geometrical separation of the spin Hall effect (SHE, charge-to-spin conversion) and the spin anomalous Hall effect (SAHE, magnetisation-tied spin polarisation) using a GdFeCo/Cu/NiFe heterostructure and spin-torque ferromagnetic resonance. Near the compensation temperature (T_M ≈ 146 K) the anisotropy of GdFeCo pins its magnetisation out of plane, so the SAHE spin current—whose polarisation follows the magnetisation—has no component along the detection axis and only the SHE torque appears (perpendicular configuration); away from compensation the magnetisation is pulled in plane and both effects contribute (parallel configuration). Lineshape analysis reads only the SH

What would settle it

A decisive check would be to measure the DC-bias damping-like torque at intermediate temperatures (for instance 175–275 K) while applying a magnetic field strong enough to pull the GdFeCo magnetisation fully in plane, or to detect any in-plane canting near T_M with Hall or torque magnetometry; if the extracted SAHE sign flips at some intermediate temperature, or the 'SHE-only' signal shows SAHE contamination, the conclusion would fail.

Watch

Extended reading notes

Core claim

The paper's central claim is that both spin-current generation channels in the ferrimagnet GdFeCo—the spin Hall effect (SHE) and the spin anomalous Hall effect (SAHE)—produce torques whose signs stay fixed across the magnetisation compensation temperature, even though the net magnetisation reverses. In the GdFeCo/Cu/NiFe devices the SHE damping-like and field-like torques are positive at all temperatures, while the SAHE contribution, seen only in the parallel configuration far from compensation, is opposite in sign to the SHE term and larger in magnitude; because the combined sign is the same at 15 K and 300 K, the SAHE does not invert either. The explanation is that the SHE originates from

Load-bearing premise

Load-bearing premise: near the compensation temperature, where the GdFeCo magnetisation is pinned out of plane by its anisotropy, the SAHE spin current along the detection axis is exactly zero—any small in-plane canting mixes SAHE torque into the 'SHE-only' data and could change the sign conclusion, and the SAHE sign is inferred from only two endpoint temperatures.

Editorial extensions

If this is right

  • If the sign of generated spin currents is fixed across compensation, the sign changes of damping-like self-torque previously observed in single-layer GdFeCo and GdFeCo/Cu bilayers must be attributed to changes in spin-current absorption, not to the emission process.
  • Ferrimagnetic spin sources can exert torques on an adjacent detector layer whose sign is robust to temperature drift through compensation, which is useful for spin-torque devices operated over wide temperature ranges.
  • Because the SHE and SAHE channels have opposite signs, the net damping-like torque can be switched from positive to negative by moving between the out-of-plane (SHE-only) and in-plane (SHE+SAHE) configurations, giving a temperature-controlled torque sign switch.
  • The sublattice assignment predicts that changing the Gd:FeCo ratio or substituting the rare earth should change the relative weights of the two channels while preserving their individual signs.
  • The SAHE dominance of the damping-like torque far from compensation means that single-layer ferrimagnet self-torque devices will be governed by the FeCo 3d channel, not by the net magnetisation.

Reading between the lines

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

  • If the sublattice decomposition holds, measurements of the two torque signs on a series of Gd_x(FeCo)_{1-x} alloys should show the SAHE/SHE amplitude ratio tracking the FeCo fraction; that is a direct, testable extension the paper does not report.
  • The same two-component picture might explain sign behaviour in other RE-TM ferrimagnets, such as FeTb, where multiple self-torque reversals were reported—if those reversals are set by sublattice composition gradients rather than by compensation points, the present framework gives a way to separate those contributions.
  • A quantitative implication left implicit is that the SAHE torque efficiency should scale with the magnetisation direction of the FeCo sublattice rather than with the net magnetisation; an experiment measuring torque amplitude as a function of a controlled in-plane field angle near T_M could confirm this.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports ST-FMR measurements on a GdFeCo(10)/Cu(4)/NiFe(4) heterostructure from 15 K to 300 K, with a magnetisation compensation temperature T_M ≈ 146 K. Lineshape analysis is used to isolate the SHE contribution, while DC-bias measurements detect the combined SHE+SAHE contributions. The central claim is that both the SHE- and SAHE-driven torque efficiencies retain their sign across T_M, and that the SAHE-driven damping-like torque is opposite in sign to the SHE-driven term and dominates in the parallel configuration. A sublattice model is proposed in which the SHE originates from Gd 5d electrons and the SAHE from FeCo 3d electrons with opposite spin-orbit coupling signs. The paper further suggests that previously reported sign changes of the self-torque in single-layer GdFeCo are due to variations in spin-current absorption rather than to sign changes of the generated spin currents.

Significance. If the sign-retention claim holds, this is a valuable advance: it would distinguish spin-current generation from spin-current absorption in ferrimagnets and identify sublattice-specific SHE/SAHE channels. The paper has real strengths: complementary lineshape and DC-bias techniques, a Pt/NiFe control sample, consistent positive SHE signs from lineshape analysis over the entire temperature range, and an explicit discussion of the limitations of the proposed model, including the conflict with Hund's third rule. The main weakness is that the SAHE sign across T_M is inferred from only two endpoint temperatures in the parallel configuration, so the headline claim is not directly supported by the data.

major comments (3)
  1. [§IV B, Fig. 5, Table I] The claim that the SAHE-driven DL torque retains its sign across T_M rests on only two endpoint measurements in the parallel configuration: ξ_DL^{SAHE+SHE} = −0.20±0.03 at 15 K and −0.45±0.07 at 300 K. No SAHE data are reported at intermediate temperatures, and in the perpendicular configuration the SAHE contribution vanishes by symmetry (Eq. 5). Thus an even number of sign reversals between 15 K and 300 K would be entirely invisible to this dataset. The wording in §V A ('the SAHE sign also remains unchanged across both the magnetisation and the angular compensation points') is too strong; at minimum the claim should be softened to 'consistent with no sign change between the two endpoints', or additional in-plane measurements at intermediate temperatures should be provided.
  2. [§II, Fig. 2(c), Eq. (5), §V B] The separation of SHE and SAHE in the perpendicular configuration assumes that the GdFeCo magnetisation is exactly out-of-plane, so that the SAHE spin current component along z vanishes. The paper itself raises the possibility of 'a small canting of the magnetisation away from the out-of-plane direction' to explain the amplitude enhancement of ξ_DL near T_M. If such a canting exists, the SAHE contribution is not strictly zero and would enter the 'SHE-only' lineshape/DC-bias data. Since the SAHE DL torque is opposite in sign and can dominate (as at 15 K and 300 K), even a modest canting could affect the extracted SHE sign near T_M. The authors should quantify the maximum permissible canting angle consistent with their measurements, or provide direct evidence (e.g. angle-dependent Hall/FMR data within the ST-FMR field range) that the magnetisation is out-of-plane to within the required acc
  3. [§III C, Eq. (7), Table I] In the parallel configuration the DC-bias linewidth measurement gives only the sum ξ_DL^{SAHE} + ξ_DL^{SHE}; an independent SHE value at those temperatures is not reported (Table I lists '-' under ξ_DL^{SHE} for 15 K and 300 K). The decomposition into an opposite-sign SAHE term therefore relies on an assumed or interpolated SHE contribution, and the propagation of uncertainties from the SHE reference into the inferred SAHE value is not shown. The problem is compounded near T_M, where the SHE-only values have large or unstated uncertainties (+0.05±0.06 at 120 K; 'unclear' at 150 K). The paper should report the individual SHE and SAHE efficiencies with full uncertainty propagation at each temperature, or explicitly state the interpolation and its uncertainties.
minor comments (4)
  1. [Abstract and §V] Grammar: 'both effects originates' should be 'both effects originate'; §I has 'producting'; §III B has 'is not consider as a reliable method'.
  2. [Table I] The LS sign entries are reported without confidence or error bars, and the 150 K DC-bias entry is listed as 'unclear'. Providing a measure of sign confidence (e.g. sign of V_S/V_A with uncertainty, or number of repeated spectra) would strengthen the sign-retention argument.
  3. [§VI] The statement that previously reported self-torque sign changes 'can be driven by variations in spin current absorption' is an extrapolation from torques measured on a Cu/NiFe detector to self-torques in GdFeCo itself. It is a reasonable hypothesis, but it should be explicitly labelled as such, since the measured absorption properties are those of NiFe, not necessarily of GdFeCo.
  4. [§V A, Fig. 6] The proposed sublattice model is post hoc and, as the authors acknowledge, the inferred λ_SOC signs conflict with Hund's third rule. This is not a fatal flaw, but it means the model does not provide independent support for the sign-retention claim; a reformulation or a caveat that the model is speculative would help.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: torque signs are extracted from measured ST-FMR lineshapes and DC-bias linewidth/field shifts via standard susceptibility equations, not fitted to the conclusion.

full rationale

The paper's derivation chain is not circular. The SHE torque sign is obtained directly from ST-FMR lineshape analysis (Eq. 6) across the full temperature range, and the combined SHE+SAHE sign from DC-bias linewidth and resonance-field modulations (Eqs. 7–8). These are standard, externally established ST-FMR susceptibility relations; no parameter is fitted to the target sign-retention conclusion. The separation of SHE from SAHE relies on the geometric configuration (magnetization in-plane vs. out-of-plane) rather than on any assumption about the sign being tested. The sublattice attribution (Gd 5d for SHE, FeCo 3d for SAHE) is presented as a qualitative, post hoc explanation and is explicitly flagged as incomplete: the authors state that their inferred lambda_SOC signs conflict with Hund's third rule and raise open questions. Self-citations [21, 53] supply the DC-bias susceptibility framework, but the central sign observations do not reduce to those citations; they are independent measurements with stated uncertainty. The main weakness—that SAHE sign retention across T_M is inferred from only two endpoint temperatures (15 K and 300 K)—is an extrapolation/robustness concern, not a definitional or fitted-input circularity. The conclusion about previously reported self-torque sign changes arising from absorption is an interpretation beyond the directly measured quantities, but again not a circular step.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central sign claims rest on standard ST-FMR susceptibility theory, the assumed spin symmetries, and geometric assumptions about magnetization orientation. The microscopic explanation adds an ad hoc sublattice assignment with an acknowledged sign discrepancy. No free parameter is fitted to force the sign result; the fitted efficiencies are the measured outputs.

free parameters (3)
  • Magnetisation compensation temperature T_M = ≈146 K
    Estimated from Hall voltage sign reversal (Fig. 2a); defines the temperature axis central to the sign claims.
  • Torque efficiencies ξ_DL and ξ_FL' (SHE, SAHE+SHE) = e.g., ξ_SHE_DL = +0.05±0.06 at 120 K, ξ_SAHE+SHE_DL = -0.45±0.07 at 300 K
    Extracted by fitting ST-FMR lineshape and DC-bias linewidth/resonance-field slopes (Eqs. 6-8); their signs are the paper's central claim.
  • Angular compensation temperature estimate = T_M + 30 K
    Taken from refs [50,51], not measured here; used in discussing angular compensation sign stability.
assumptions (6)
  • domain assumption Spin current symmetries: σ_SHE = y and σ_SAHE = m_GdFeCo (Eqs. 2-3)
    Definitions inherited from prior SHE/SAHE literature; the central decomposition relies on these symmetries.
  • domain assumption In the perpendicular configuration near T_M, GdFeCo magnetization is exactly out-of-plane, making SAHE spin current vanish
    Section II, Fig. 2(c), Eq. 5 discussion; any canting would mix SAHE into 'SHE-only' data.
  • domain assumption In the parallel configuration, GdFeCo and NiFe magnetizations are collinear, so SAHE torques on NiFe vanish and LS isolates SHE
    Section III B; collinearity makes m_GdFeCo × m_NiFe = 0, so SAHE torque terms vanish.
  • domain assumption DC-bias linewidth and resonance-field shifts are linear sums of independent SHE and SAHE torques
    Eqs. (7-8); absence of interference or additional torque symmetries is assumed.
  • domain assumption AMR dominates the ST-FMR voltage so lineshape decomposition (Eq. 6) applies
    Standard ST-FMR assumption; if other magnetoresistive effects contribute, the sign extraction could be affected.
  • ad hoc to paper Relative sign of λ_SOC in Gd and FeCo can be inferred from AHE signs, and SHE/SAHE are carried by Gd 5d and FeCo 3d electrons respectively
    Section V A, Fig. 6; qualitative explanatory model, not derived from first principles, and the paper acknowledges a discrepancy with Hund's third rule.

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Pith. "Pith review of Spin current symmetries generated by GdFeCo ferrimagnet across its magnetisation compensation temperature." pith.science (2026). https://pith.science/paper/6M7YFFC5

@misc{pith2026251120379,
  author       = {Pith},
  title        = {Pith review of: Spin current symmetries generated by GdFeCo ferrimagnet across its magnetisation compensation temperature},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6M7YFFC5}},
  note         = {Machine review of arXiv:2511.20379}
}
read the original abstract

Ferrimagnets, composed of antiferromagnetically coupled magnetic sublattices whose net magnetisation can be tuned by temperature, offer a unique platform for probing the symmetry of the spin currents they generate and for identifying the sublattice contributions to these currents. Here, we investigate the spin current symmetries produced by GdFeCo ferrimagnet at a fixed concentration and across a broad temperature range, including the magnetisation compensation point. Using complementary techniques based on spin-torque ferromagnetic resonance spectroscopy, we separate the contributions of the spin Hall effect (SHE) and the spin anomalous Hall effect (SAHE). We show that the torques arising from both mechanisms retain their sign across the magnetisation compensation temperature, and that the SAHE-driven damping-like torque has the opposite sign to the SHE-driven term. We suggest that both effects originates from distinct electronic subsystems: the SHE emerging from Gd 5d electrons, and the SAHE from FeCo 3d electrons. Consequently, the SHE sign remains insensitive to the magnetisation state, whereas the SAHE sign does not invert at compensation, reproducing our observations. Together, these insights clarify the interplay between sublattices in ferrimagnetic spin transport and highlight the potential of ferrimagnetic spin currents to generate spin torques in adjacent layers or within the ferrimagnet itself.

Figures

Figures reproduced from arXiv: 2511.20379 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Symmetry of the spin Hall effect (SHE) for the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Hall voltage [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Summary of the lineshape analysis for temperatures [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5. (a) DL and (b) FL’ torque efficiencies extracted by [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic of the electron conduction for the (a) spin [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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