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arxiv: 2606.07395 · v1 · pith:FBDS5EHGnew · submitted 2026-06-05 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Polar and quadratic magneto-optical Kerr effects in nonmagnetic/ferromagnet bilayers for spin-orbit torque measurements

Yukihiro Marui , Masashi Kawaguchi , Kohji Nakamura , Masamitsu Hayashi This is my paper

Pith reviewed 2026-06-27 21:05 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords magneto-optical Kerr effectspin Hall magnetoresistancespin-orbit torquenonmagnetic/ferromagnetic bilayersanomalous Hall effectplanar Hall effectspin-torque efficiency
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The pith

MOKE signals allow reliable spin-torque efficiency extraction in NM/FM bilayers by avoiding SMR contributions that plague Hall measurements.

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

The paper investigates polar and quadratic magneto-optical Kerr effects in nonmagnetic/ferromagnet bilayers to assess their suitability for spin-orbit torque measurements. It finds that the ratio of quadratic to polar MOKE signals is much smaller than the corresponding ratio of planar to anomalous Hall resistances, even in systems like W/CoFeB where SMR makes the Hall ratio approach unity. This indicates that spin Hall magnetoresistance contributes negligibly to the MOKE response in the visible range. Consequently, the spin-torque efficiency determined from MOKE agrees with values expected from the spin Hall angle of the nonmagnetic layer. The results explain why MOKE provides a reliable method for characterizing spin-torque efficiency where harmonic Hall methods are complicated by large SMR.

Core claim

In NM/FM bilayers, SMR causes the planar Hall resistance to become comparable to the anomalous Hall resistance when the NM has a large spin Hall angle, complicating spin-torque efficiency extraction from harmonic Hall voltages. The polar MOKE corresponds to the anomalous Hall resistance and the quadratic MOKE to the planar Hall resistance in the low-frequency limit. Measurements show the quadratic-to-polar MOKE ratio remains significantly smaller, demonstrating that SMR does not affect MOKE in the visible range, allowing the extracted spin-torque efficiency to match expectations from the NM spin Hall angle.

What carries the argument

Polar and quadratic magneto-optical Kerr effect components, which map to anomalous and planar Hall resistances but without significant SMR contribution at optical frequencies.

If this is right

  • Spin-torque efficiency can be accurately measured using MOKE in bilayers with large SMR effects.
  • MOKE serves as a robust alternative to harmonic Hall voltage measurements for SOT characterization.
  • The negligible SMR in MOKE allows direct correlation to the spin Hall angle of the NM layer.
  • Optical measurements at visible wavelengths isolate FM magnetization dynamics from NM contributions.

Where Pith is reading between the lines

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

  • This implies that the frequency dependence of SMR effects might allow optical methods to probe pure magnetization responses.
  • MOKE could be applied to other systems where transport is affected by interface or NM effects.
  • Testing MOKE at different wavelengths might reveal the onset of SMR contributions.

Load-bearing premise

Polar and quadratic MOKE components at optical frequencies correspond directly to anomalous and planar Hall resistances without additional contributions from the NM layer or interface at those frequencies.

What would settle it

A direct comparison of the quadratic-to-polar MOKE ratio versus the planar-to-anomalous Hall ratio in a W/CoFeB bilayer, or checking if MOKE-derived spin-torque efficiency matches independent measurements like spin pumping.

Figures

Figures reproduced from arXiv: 2606.07395 by Kohji Nakamura, Masamitsu Hayashi, Masashi Kawaguchi, Yukihiro Marui.

Figure 1
Figure 1. Figure 1: Schematic illustration of the experimental setup [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic drawing of the optical setup. BS: beam Figure 2. Schematic drawing of the optical setup. BS: beam [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a-d) The in-plane field The change in Ryx and η which is consistent with Eqs [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: 𝜇!𝐻" (T) 𝜇!𝐻" (T) 𝜇!𝐻" (T) 𝜇!𝐻" (T) 𝑚#𝑅$" (Ω) 𝑚#𝑅$" (Ω) 𝑚#𝜂 % (mrad) 𝑚#𝜂 % (mrad) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Magnetic field dependence of the second harmonic [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: 𝑗 (10) A/m&) 𝑗 (10) A/m&) 𝑗 (10) A/m&) 𝑗 (10) A/m&) 𝜂 '," (µrad) 𝜂 '," (µrad) 𝜂 ',$ (µrad) 𝜂 ',$ (µrad) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a-d) Calculated MOKE signals θP, ηP (a,b) and θQ, ηQ (c,d) plotted as a function of SiO2 thickness tSiO2 (a,c) and FM layer thickness tFM (b,d). (e,f) tSiO2 (e) and tFM (f) dependence of θQ θP , ηQ ηP . (g,h) Real and imaginary parts of rΦ = θQ+iηQ θP+iηP vs. tSiO2 (g) and tFM (h). The vertical dashed line in (a,c,e,g) indicates tSiO2 used in the experiments. To extract r s θ and r s η of a given film sta… view at source ↗
read the original abstract

Recent studies have revealed that spin Hall magnetoresistance (SMR) contributes to both the anomalous and planar Hall resistances in nonmagnetic metal (NM)/ferromagnetic metal (FM) bilayers. This effect becomes pronounced when the NM layer exhibits a large spin Hall angle, as in W/CoFeB bilayers. In such systems, the ratio of planar to anomalous Hall resistances, normally small in single CoFeB layers, can approach unity. This unusually large ratio complicates the determination of spin-torque efficiency using harmonic Hall voltage measurements. To overcome this limitation, magneto-optical Kerr effect (MOKE) measurements have been proposed as an alternative approach. Here, we investigate the polar and quadratic MOKE components, which correspond to, respectively, the anomalous and planar Hall resistances in the low-frequency limit to clarify whether the MOKE measurements are suitable for characterizing the spin-torque efficiency. We find that the ratio of quadratic to polar MOKE signals in NM/FM bilayers is significantly smaller than the corresponding Hall resistance ratio, indicating that SMR contributes negligibly to the MOKE response in the visible range. Consequently, the spin-torque efficiency extracted from MOKE measurements agree well with those expected from the spin Hall angle of the NM layer. These results clarify the reason why MOKE measurements provide reliable determination of the spin-torque efficiency.

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

0 major / 3 minor

Summary. The paper experimentally compares polar and quadratic magneto-optical Kerr effect (MOKE) signals with anomalous and planar Hall resistances in NM/FM bilayers (e.g., W/CoFeB). It reports that the quadratic-to-polar MOKE ratio is substantially smaller than the corresponding planar-to-anomalous Hall ratio, indicating negligible spin Hall magnetoresistance (SMR) contribution to MOKE at visible wavelengths. Consequently, spin-torque efficiencies extracted from MOKE agree with values expected from the NM layer's spin Hall angle, validating MOKE as a reliable alternative when Hall measurements are complicated by SMR.

Significance. If the result holds, the work provides a practical optical method for spin-orbit torque characterization in bilayers with large spin Hall angles, where electrical methods suffer from SMR contamination. The direct side-by-side comparison on identical samples and consistency with independently known spin Hall angles are strengths. This strengthens the case for MOKE-based measurements in the field.

minor comments (3)
  1. The abstract states the central finding without numerical values, error bars, or sample details; the main text should ensure all key ratios and efficiencies are reported with uncertainties in the results section for reproducibility.
  2. Figure captions and legends should explicitly state the optical wavelength used for MOKE and confirm that single-FM-layer controls are shown alongside bilayer data to support the negligible-SMR conclusion.
  3. Notation for the quadratic MOKE component should be defined once in the methods or early results section to avoid ambiguity when comparing to the planar Hall resistance.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. The referee's summary accurately reflects our key finding that the quadratic-to-polar MOKE ratio is substantially smaller than the planar-to-anomalous Hall ratio in NM/FM bilayers, confirming negligible SMR contribution to visible-range MOKE and validating MOKE-based spin-torque efficiency measurements.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript is an experimental study that measures polar/quadratic MOKE ratios versus planar/anomalous Hall ratios on the same NM/FM bilayers and compares the extracted spin-torque efficiencies to the independently known spin Hall angle of the NM layer. No derivation chain, equation, or parameter is shown to reduce to a self-defined input or to a self-citation whose validity depends on the present work. The stated correspondence between MOKE components and Hall resistances is presented as an empirical mapping to be tested, not as an identity imposed by construction. The central claim therefore rests on external benchmarks and direct observation rather than internal re-labeling of fitted quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that optical-frequency Kerr rotation directly maps to the DC Hall resistivities without additional frequency-dependent interface or NM-layer contributions; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Polar and quadratic MOKE signals correspond to anomalous and planar Hall resistances in the low-frequency limit
    Stated explicitly in the abstract as the basis for comparing the two techniques

pith-pipeline@v0.9.1-grok · 5790 in / 1367 out tokens · 15029 ms · 2026-06-27T21:05:40.805068+00:00 · methodology

discussion (0)

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Reference graph

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