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REVIEW 3 major objections 4 minor 47 references

Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film

T0 review · 3 major / 4 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read Both spin Hall conductivity and spin diffusion length rise as temperature falls in epitaxial Bi(110), showing skew scattering under Elliott-Yafet relaxation.

desk verdict Clean temperature-dependent SHH data on epitaxial Bi(110)/Ni that reasonably points to EY + skew scattering, but the key linearity rests on an unchecked constant-ρ_Bi assumption. read the letter →

arxiv 2607.11189 v1 pith:MHTAYNKN submitted 2026-07-13 cond-mat.mtrl-sci

K. Tatsuoka (1) , N. Fukumoto (1) , S. Sakamoto (2) , S. Miwa (2) , Y. Fuseya (3) , J. Fujimoto (4) , R. Ohshima (1) , J. Puebla (1)
show 7 more authors
Y. Ando (5) M. Shiraishi (1) ((1) Kyoto Univ. (2) ISSP Univ. Tokyo (3) Kobe Univ. (4) Saitama Univ. (5) Osaka Metropolitan Univ.)
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords spinHalleffectbismuththinfilmsElliott-Yafetskewscatteringsecond-harmonicdiffusionlengthspin-orbittorquerhombohedralBi(110)
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

Rhombohedral (110) bismuth converts charge current into spin current with unusually high efficiency, yet the microscopic scattering process that produces this conversion has remained unclear. This work measures that conversion from room temperature down to 10 K in epitaxial Bi(110)/Ni bilayers by the second-harmonic Hall method, carefully subtracting thermal artifacts. Both the spin Hall conductivity and the spin diffusion length increase as temperature is lowered. The simultaneous rise of the two quantities implies that spin relaxation is of Elliott-Yafet type (spin lifetime tracks momentum lifetime) and that the dominant conversion mechanism is extrinsic skew scattering rather than intrinsic band effects or side-jump scattering. The result supplies a concrete microscopic picture for the large, orientation-dependent spin Hall effect previously reported in this crystal face and guides how purity and temperature can be used to tune the conversion for spintronic devices.

What carries the argument

Thickness- and temperature-dependent second-harmonic Hall extraction of the damping-like effective field, converted to effective spin Hall conductivity and then fitted to the sech form that isolates bulk spin Hall conductivity and spin diffusion length.

What would settle it

A direct measurement of thickness-dependent resistivity on Bi(110) films (or an independent determination of spin diffusion length by another technique such as nonlocal spin valves) that breaks the observed linear relation between spin Hall conductivity and spin diffusion length.

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Extended reading notes

Core claim

In epitaxial Bi(110)/Ni bilayers the effective spin Hall conductivity and the Bi spin diffusion length both increase with decreasing temperature; their linear correlation shows that spin relaxation follows the Elliott-Yafet mechanism and that charge-to-spin conversion is dominated by skew scattering.

Load-bearing premise

The resistivity of the Bi layer is assumed independent of thickness when the thickness series is fitted, even though pure Bi(110) films cannot be grown on insulating substrates to check that assumption directly.

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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 manuscript reports temperature-dependent second-harmonic Hall measurements of damping-like spin-orbit torque in epitaxial Bi(110)R/Ni bilayers. After separating thermal contributions (ANE/SSE, ordinary Nernst, planar Nernst), the authors extract an effective spin Hall conductivity σ_SH^eff that rises with decreasing temperature for Bi thicknesses ≳ 5.5 nm. Fitting the thickness series of σ_SH^eff to the standard sech form (Eq. 4) yields both the intrinsic spin Hall conductivity σ_SH and the spin diffusion length λ_Bi; both quantities increase upon cooling, and σ_SH scales linearly with λ_Bi. From this the authors conclude that spin relaxation is Elliott–Yafet and that the SHE is dominated by skew scattering, with only a minor intrinsic (Dirac-electron) contribution. Orbital-Hall and interfacial Rashba contributions are argued to be negligible on the basis of prior Bi/Fe ST-FMR data and theory.

Significance. If the extraction of σ_SH(T) and λ_Bi(T) is robust, the work supplies a concrete microscopic assignment for the large, orientation-dependent charge-to-spin conversion previously reported in Bi(110)R. Establishing Elliott–Yafet + skew scattering as the dominant channel would place Bi(110)R in the same extrinsic regime as high-conductivity Pt and would guide materials design for low-temperature spin-orbit-torque devices. The careful angular- and field-dependent separation of thermal artifacts is a methodological strength relative to ST-FMR, and the data set is openly archived.

major comments (3)
  1. Section III and Eq. (4): the extraction of σ_SH and λ_Bi rests on the explicit assumption that the Bi resistivity ρ_Bi is independent of thickness. The authors note that single-layer Bi(110)R cannot be grown on insulating substrates, so the assumption is unchecked. In thin Bi films surface scattering commonly makes ρ_Bi rise as t_Bi falls; any such dependence systematically distorts the sech curvature, shifts the extracted λ_Bi, and can manufacture or destroy the linear σ_SH–λ_Bi relation of Fig. 5(d) that underpins the skew-scattering claim. A quantitative sensitivity analysis (or an independent estimate of ρ_Bi(t) from bilayer conductance) is required before the mechanism assignment can be regarded as secure.
  2. Section III, discussion of μ0Ms: the conversion of HDL into σ_SH^eff (Eq. 3) uses a fixed room-temperature value μ0Ms = 0.61 T for all temperatures, while the authors themselves note that Ms(0 K)/Ms(300 K) ≈ 1.06. Because both σ_SH and λ_Bi are obtained from the same thickness series of σ_SH^eff, a temperature-dependent Ms rescales the entire vertical axis of Fig. 5(d) and can alter the apparent slope. The manuscript should either measure Ms(T) on the actual stacks or propagate the known Ms(T) correction through the fits and re-evaluate the linearity.
  3. Section III, final paragraphs: the authors acknowledge that band-gap shrinking at the L-point can enhance the intrinsic SHE upon cooling, yet still assert that skew scattering dominates solely on the basis of the linear σ_SH–λ_Bi plot. Without an independent estimate of the intrinsic contribution (e.g., from the known L-point gap temperature dependence or a comparison with the Bi-Sb data of Ref. [39] under identical analysis), the relative weight of intrinsic versus extrinsic channels remains qualitative. A short calculation or bounding argument would strengthen the claim.
minor comments (4)
  1. Fig. 4 caption: several data points (Ni-only at 50 K/10 K, Bi(9.5 nm) at 10 K) are omitted because fits failed; a brief statement of the failure criterion would help the reader assess completeness.
  2. Eq. (2): the symbols a∇T and b∇T are introduced without units or typical magnitudes; a short parenthetical estimate would clarify that they are sub-dominant.
  3. Page 4: the phrase “the high-purity sample negates the side-jump mechanism” is slightly overstated; high purity suppresses side-jump relative to skew, but does not rigorously exclude it.
  4. References: a few recent works on temperature-dependent SHE in other Dirac/semimetal systems could be added for context, but this is optional.

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity: temperature trends and the σ_SH–λ_Bi linearity are extracted from independent SHH data; self-citations supply background only.

  1. self citation load bearing [Abstract and Sec. I (Introduction), citation of Fukumoto et al. PNAS 2023]
    "the conversion efficiency at room temperature in rhombohedral (110) bismuth is notably large … and such a large SHE is ascribed to the large effective g-factor in bismuth [N. Fukumoto et al., Proc. Nat. Acad. Sci. 120, e2215030120 (2023)]. … Sizable charge-to-spin conversion of the Bi(110)_R at room temperature is already established in Ref. [15]"

    The prior overlapping-author paper is invoked to establish that Bi(110)_R already exhibits large conversion and to fix the room-temperature benchmark against which the new temperature series is compared. The citation is not used to force the temperature dependence or the σ_SH–λ_Bi linearity that form the paper’s central claim, so the circularity is minor and non-load-bearing for the mechanism assignment.

full rationale

The central claim (both σ_SH and λ_Bi rise with falling T, and their linear relation implies Elliott–Yafet + skew scattering) is obtained by fitting the measured thickness series of σ_SH^eff(T) to the standard sech form (Eq. 4) and then plotting the two extracted parameters against each other (Fig. 5d). No quantity is defined in terms of a later-presented prediction, no fitted parameter is re-labeled as an independent forecast, and no uniqueness theorem is imported from the authors’ prior work to force the mechanism assignment. The sole self-citation that is load-bearing for background (Fukumoto et al. 2023) is used only to establish that Bi(110)_R already shows large room-temperature conversion and to confirm consistency of the present room-temperature σ_SH^eff values; it does not dictate the temperature dependence or the linearity that constitute the new result. The thickness-independent ρ_Bi assumption is an experimental limitation that can bias the extracted slope, but it is an unchecked modeling premise, not a circular reduction of the claim to its own inputs. Consequently the derivation chain is self-contained against the SHH data sets and scores at most 1.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard SHE scaling formulas, literature values for Ni magnetization, and two domain assumptions that cannot be verified inside the present experiment: thickness-independent Bi resistivity and ideal (or at least thickness-independent) interfacial spin transparency. No new particles or forces are invented; free parameters are the usual fit amplitudes extracted from the SHH and thickness series.

free parameters (3)
  • σ_SH(T) and λ_Bi(T)
    Extracted at each temperature by fitting the Bi-thickness series of σ_SH^eff to Eq. (4); these are the quantities whose temperature trends constitute the central claim.
  • μ0Ms of Ni
    Fixed at the room-temperature literature value 0.61 T for all temperatures; a 6 % low-T correction is noted but not applied.
  • ADL, AFL, APNE amplitudes
    Free coefficients obtained by angular and field-dependent fits of the second-harmonic Hall voltage (Eqs. 1–2).
assumptions (4)
  • domain assumption Bi resistivity ρ_Bi is independent of film thickness in the 2–10 nm range studied.
    Explicitly stated as an untested assumption required for the sech fit of Eq. (4); single-layer Bi(110) cannot be grown on insulating substrates.
  • domain assumption Interfacial spin transparency is ideal or at least independent of Bi thickness.
    Used to equate the measured σ_SH^eff with the bulk expression containing only σ_SH and λ_Bi; spin memory loss is acknowledged but argued not to affect the extracted λ_Bi.
  • standard math Spin diffusion length λ ∝ au_p under Elliott-Yafet relaxation (and independent of au_p under D’yakonov-Perel’).
    Standard textbook relation used to map the observed increase of λ_Bi with cooling onto the EY mechanism.
  • standard math Skew-scattering contribution to σ_SH scales linearly with momentum scattering time au_p.
    Taken from the Dirac-electron SHE theory of Fukazawa et al. (2017) and used to interpret the linear σ_SH–λ_Bi plot.

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Pith. "Pith review of Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film." pith.science (2026). https://pith.science/paper/MHTAYNKN

@misc{pith2026260711189,
  author       = {Pith},
  title        = {Pith review of: Temperature dependence of charge-to-spin conversion in rhombohedral (110) bismuth thin film},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHTAYNKN}},
  note         = {Machine review of arXiv:2607.11189}
}
read the original abstract

The amplitude of charge-to-spin conversion, namely the spin Hall effect (SHE), in bismuth (Bi) strongly depends on its crystal orientation. The conversion efficiency at room temperature in rhombohedral (110) bismuth is notably large as expected from its large spin-orbit interaction, and such a large SHE is ascribed to the large effective g-factor in bismuth [N. Fukumoto et al., Proc. Nat. Acad. Sci. 120, e2215030120 (2023)]. Despite the successful observation of the large conversion efficiency, a more detailed physical mechanism of the SHE in (110) bismuth is still elusive and under debate. In this work, we investigate the temperature dependence of charge-to-spin conversion in an epitaxial Bi(110)/Ni bilayer system using the second harmonic Hall method, revealing that both spin Hall conductivity and spin diffusion length augment with decreasing temperature. This finding suggests that spin scattering in (110) bismuth is dominated by the Elliott-Yafet mechanism, and the charge-to-spin conversion is mainly attributed to skew scattering.

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