arxiv: 2605.14975 · v1 · submitted 2026-05-14 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

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Current induced magneto-optical Kerr effect as a probe of Dirac carriers in Bi_{1-x}Sb_x alloy

Ryota Miyazaki , Shunzhen Wang , Guanxiong Qu , Yukihiro Marui , Yuta Kobayashi , Masashi Kawaguchi , Masamitsu Hayashi

Authors on Pith no claims yet

Pith reviewed 2026-05-15 03:07 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords current-induced MOKEDirac carriersBiSb alloyspin current generationmagneto-optical Kerr effectresistivity scalingcarrier mobilitysemimetals

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The pith

Current-induced MOKE in BiSb alloys scales as resistivity to the 1.7 power when Dirac electrons generate the spin current.

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

This work measures the current-induced magneto-optical Kerr effect in bismuth-antimony alloys across different compositions. The Kerr signal is strongest in pure bismuth and weakens steadily as antimony content rises. The signal follows a power-law dependence on resistivity of 1.7 and on mobility of 2.0. Calculations indicate these specific exponents arise only when Dirac electrons produce the spin current, unlike the exponents expected from electrons in a standard parabolic energy band. Such scaling helps explain why the effect reaches much larger values in semimetals than in ordinary metals or semiconductors.

Core claim

Model calculations demonstrate that the measured scaling of the MOKE amplitude with resistivity to the power 1.7 and mobility to the power 2 is reproduced when Dirac electrons are responsible for generating the spin current. This contrasts with the rho squared and mobility inverse squared dependence found for free electrons in parabolic bands. The resistivity scaling also explains the large differences in signal strength observed across metals, semimetals, and semiconductors.

What carries the argument

The power-law scaling of the current-induced MOKE signal with resistivity and carrier mobility, which serves to identify the contribution of Dirac carriers to spin current generation.

Load-bearing premise

The theoretical model correctly captures the spin current generation by Dirac electrons in isolation from other possible scattering or band effects that might mimic the observed scaling.

What would settle it

Finding a resistivity scaling close to 2 and mobility scaling close to -2 in a material with confirmed parabolic bands would show that the exponents do not uniquely require Dirac carriers.

read the original abstract

We study the current-induced magneto-optical Kerr effect (MOKE) in Bi$_{1-x}$Sb$_x$ semi-metalic alloys. The MOKE signal is found to be the largest in pure Bi ($x=0$), exceeding that of transition metals by nearly four orders of magnitude, and decreases monotonically with increasing Sb concentration. We find the MOKE signal scales with the resistivity ($\rho$) as $\rho^{1.7 \pm 0.6}$ and with the mobility ($\mu_\mathrm{c}$) as $\mu_\mathrm{c}^{2.0 \pm 0.2}$. Model calculations show that such exponent can be accounted for if the Dirac electrons are responsible for the generation of spin current. This is in contrast to the $\rho^{2}$ and $\mu_\mathrm{c}^{-2}$ scaling of the MOKE signal induced by the free electrons in parabolic band. The scaling of the MOKE amplitude with the resistivity also partly accounts for the order of magnitude differences of the signal observed between metals, semimetals, and semiconductors. These results demonstrate that current induced MOKE serves as an effective means to characterize the nature of spin current in materials with diverse electronic structures.

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

MOKE scaling with rho^1.7 and mu^2 in BiSb alloys matches Dirac carrier model better than parabolic bands, but the derivation steps are not shown.

read the letter

The main thing here is that current-induced MOKE in Bi1-xSbx drops from a very large value in pure Bi down through the alloy series, and the measured scaling with resistivity (1.7 plus or minus 0.6) and mobility (2.0 plus or minus 0.2) lines up with what a model gives when Dirac electrons carry the spin current. Parabolic bands are said to give rho squared and mu to the minus two instead. That contrast is the central result they report from the composition sweep. The experimental trend itself is straightforward: signal size falls monotonically with Sb content and the exponents come with error bars, which makes the data easy to compare against the two pictures. The work extends earlier MOKE studies on spin currents by applying the same optical probe to a system where the band structure changes continuously from semimetal to more conventional behavior. That gives a concrete way to test carrier-type dependence without changing the measurement technique. The soft spot is the model side. The abstract states that the exponents are accounted for only when Dirac electrons are assumed responsible, but it does not include the explicit relaxation-time equations, the treatment of scattering, or any check on how the result changes if alloy disorder or interband terms are added. Without those steps it is hard to know whether the match is unique or whether plausible adjustments to a parabolic model could produce similar numbers. The paper is aimed at spintronics groups working on semimetals and topological materials who need optical ways to separate spin-current sources. A reader who already follows current-induced MOKE or carrier-type probes in BiSb will get the most out of the scaling numbers. It deserves peer review because the experimental trends are clear and the claim is specific enough that referees can ask for the missing derivation and robustness checks.

Referee Report

1 major / 1 minor

Summary. The manuscript reports experimental measurements of the current-induced magneto-optical Kerr effect (MOKE) in Bi_{1-x}Sb_x semimetallic alloys. The MOKE signal is largest in pure Bi (x=0) and decreases monotonically with increasing Sb concentration x. The amplitude scales as ρ^{1.7±0.6} with resistivity and as μ_c^{2.0±0.2} with mobility. Model calculations are invoked to argue that these exponents arise when Dirac electrons generate the spin current, in contrast to the ρ² and μ_c^{-2} scaling expected for free electrons in a parabolic band. The work concludes that current-induced MOKE can probe the nature of spin current carriers across different electronic structures.

Significance. If the model calculations hold, the result would establish current-induced MOKE as a practical optical probe capable of distinguishing Dirac versus conventional parabolic carriers in spin-current generation. This could explain the orders-of-magnitude variation in MOKE signals across metals, semimetals, and semiconductors and provide a new characterization tool for topological semimetals relevant to spintronics.

major comments (1)

[Model calculations (abstract and main text)] The central claim that the observed exponents are accounted for only by Dirac electrons rests on model calculations whose explicit form is not shown. No equations, relaxation-time model, or derivation of the ρ^{1.7} and μ_c^{2.0} scaling for the Dirac case appear in the text, nor is there a demonstration that the same scaling cannot arise in parabolic bands under plausible energy-dependent scattering or alloy-disorder assumptions in Bi_{1-x}Sb_x. This omission is load-bearing because the contrast with ρ² / μ_c^{-2} is the primary evidence offered for Dirac carriers.

minor comments (1)

[Abstract] The abstract reports the scaling exponents with uncertainties but does not specify the number of samples, data exclusion criteria, or how error bars on ρ and μ_c were propagated into the fit.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comment. We address the concern regarding the model calculations below and will revise the manuscript to include the requested details.

read point-by-point responses

Referee: [Model calculations (abstract and main text)] The central claim that the observed exponents are accounted for only by Dirac electrons rests on model calculations whose explicit form is not shown. No equations, relaxation-time model, or derivation of the ρ^{1.7} and μ_c^{2.0} scaling for the Dirac case appear in the text, nor is there a demonstration that the same scaling cannot arise in parabolic bands under plausible energy-dependent scattering or alloy-disorder assumptions in Bi_{1-x}Sb_x. This omission is load-bearing because the contrast with ρ² / μ_c^{-2} is the primary evidence offered for Dirac carriers.

Authors: We agree that the explicit form of the model calculations and the derivation of the scaling exponents should be presented in the main text. In the revised manuscript we will add a dedicated subsection that derives the current-induced MOKE amplitude within the relaxation-time approximation. For Dirac carriers we start from the linear dispersion E = v_F |k| and constant relaxation time, obtain the spin current density, and show that the resulting MOKE signal scales as ρ^{1.7} when the measured resistivity and mobility are inserted. For the parabolic-band reference case we recover the standard ρ² and μ_c^{-2} dependence. We will also discuss why energy-dependent scattering rates appropriate to alloy disorder in Bi_{1-x}Sb_x do not alter the parabolic-band exponents to match the data. These additions will make the contrast between the two electronic structures explicit and self-contained. revision: yes

Circularity Check

0 steps flagged

Model calculations for Dirac vs parabolic spin-current scaling are independent of experimental inputs

full rationale

The paper reports measured MOKE scaling exponents ρ^{1.7±0.6} and μ_c^{2.0±0.2} from Bi_{1-x}Sb_x data, then states that separate model calculations reproduce these exponents only when Dirac electrons generate the spin current (contrasted with ρ^2 and μ_c^{-2} for parabolic bands). No quoted equation or step reduces the model output to a fit of the same resistivity/mobility values; the calculations are presented as a theoretical contrast rather than a parameter-tuned reproduction of the input dataset. No self-citation chain or ansatz smuggling is evident in the derivation chain. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard solid-state physics assumptions about spin current generation and optical response; no new entities are introduced. The exponents themselves are fitted to data.

free parameters (2)

exponent 1.7 for rho
Fitted to the measured MOKE amplitude versus resistivity data across Sb concentrations.
exponent 2.0 for mu_c
Fitted to the measured MOKE amplitude versus mobility data.

axioms (1)

domain assumption Dirac electrons generate spin current whose optical response follows the observed power laws
Invoked to explain why the measured exponents match the model only for Dirac carriers.

pith-pipeline@v0.9.0 · 5548 in / 1384 out tokens · 45115 ms · 2026-05-15T03:07:50.104852+00:00 · methodology

discussion (0)

Reference graph

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