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arxiv: 2311.11933 · v1 · pith:FU2FDMCYnew · submitted 2023-11-20 · ❄️ cond-mat.mes-hall

Spin Hall conductivity in Bi_(1-x)Sb_x as an experimental test of bulk-boundary correspondence

YongXi Ou , Wilson Yanez-Parre\~no , Yu-sheng Huang , Supriya Ghosh , C\"uneyt \c{S}ahin , Max Stanley , Sandra Santhosh , Saurav Islam
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Anthony Richardella K. Andre Mkhoyan Michael E. Flatt\'e Nitin Samarth
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Pith reviewed 2026-05-24 06:09 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords spin Hall conductivitybulk-boundary correspondencetopological insulatorBi1-xSbxcharge-to-spin conversionspin-orbit entanglement
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The pith

Spin Hall conductivity measured in Bi1-xSbx films matches bulk tight-binding predictions across topological and trivial compositions.

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

The paper examines whether bulk-boundary correspondence extends to non-conserved spin currents by studying charge-to-spin conversion in epitaxial Bi1-xSbx films. Composition is varied over the full range to produce both trivial and topological band structures, verified in situ by angle-resolved photoemission. Spin-torque ferromagnetic resonance extracts the effective spin Hall conductivity, which agrees closely with intrinsic values calculated from bulk tight-binding models. The match holds even though the films are interfaced with a metallic ferromagnet, indicating that bulk spin-orbit entanglement below the Fermi energy sets the observed conversion efficiency.

Core claim

The effective spin Hall conductivity in Bi1-xSbx films agrees with the intrinsic spin Hall conductivity of the bulk bands calculated by tight-binding methods, supplying evidence that strong spin-orbit entanglement of bulk states well below the Fermi energy determines the spin Hall conductivity in these epitaxial films interfaced with a ferromagnet.

What carries the argument

Spin-torque ferromagnetic resonance measurements of charge-to-spin conversion efficiency compared to tight-binding calculations of the bulk intrinsic spin Hall conductivity.

Load-bearing premise

The spin-torque ferromagnetic resonance signal directly reflects the intrinsic bulk spin Hall conductivity without dominant contributions from the ferromagnet interface or extrinsic mechanisms.

What would settle it

Spin Hall conductivities extracted from the films that deviate markedly from the bulk tight-binding predictions, especially if the deviation changes with film thickness or different ferromagnet interfaces.

Figures

Figures reproduced from arXiv: 2311.11933 by Anthony Richardella, C\"uneyt \c{S}ahin, K. Andre Mkhoyan, Max Stanley, Michael E. Flatt\'e, Nitin Samarth, Sandra Santhosh, Saurav Islam, Supriya Ghosh, Wilson Yanez-Parre\~no, YongXi Ou, Yu-sheng Huang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

Bulk-boundary correspondence is a foundational principle underlying the electronic band structure and physical behavior of topological quantum materials. Although it has been rigorously tested in topological systems where the physical properties involve charge currents, it remains unclear whether bulk-boundary correspondence should also hold for non-conserved spin currents. We study charge-to-spin conversion in a canonical topological insulator, Bi$_{1-x}$Sb$_x$, to address this fundamentally unresolved question. We use spin-torque ferromagnetic resonance measurements to accurately probe the charge-to-spin conversion efficiency in epitaxial Bi$_{1-x}$Sb$_x$~thin films of high structural quality spanning the entire range of composition, including both trivial and topological band structures, as verified using {\it in vacuo} angle-resolved photoemission spectroscopy. From these measurements, we deduce the effective spin Hall conductivity (SHC) and find excellent agreement with the values predicted by tight-binding calculations for the intrinsic SHC of the bulk bands. These results provide strong evidence that the strong spin-orbit entanglement of bulk states well below the Fermi energy connects directly to the SHC in epitaxial Bi$_{1-x}$Sb$_x$~films interfaced with a metallic ferromagnet. The excellent agreement between theory and experiment points to the generic value of analyses focused entirely on bulk properties, even for topological systems involving non-conserved spin currents.

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 reports spin-torque ferromagnetic resonance (ST-FMR) measurements of charge-to-spin conversion efficiency in epitaxial Bi_{1-x}Sb_x thin films spanning the full composition range (trivial to topological regimes, verified by in vacuo ARPES). The effective spin Hall conductivity (SHC) deduced from these data is compared to tight-binding calculations of the intrinsic bulk SHC and reported to show excellent agreement, which the authors interpret as evidence that bulk-boundary correspondence holds for non-conserved spin currents and that bulk spin-orbit entanglement dominates the response even at a ferromagnet interface.

Significance. If the central interpretation is robust, the work would provide a direct experimental test of bulk-boundary correspondence in the spin sector for a canonical topological material, with the parameter-free character of the tight-binding comparison (no free parameters or ad-hoc entities) constituting a clear strength. The composition-dependent data set linking trivial and topological regimes would add weight to the conclusion that analyses focused on bulk properties remain predictive for spin Hall effects in heterostructures.

major comments (2)
  1. [Abstract] Abstract: the claim that ST-FMR directly yields the intrinsic bulk SHC (and thereby tests bulk-boundary correspondence) rests on the untested assumption that interfacial torques are subdominant across the full composition range; no quantitative error bars, data-exclusion criteria, or interface-isolation controls are described, which is load-bearing for the central claim given that spin current is non-conserved.
  2. [Results/Discussion (ST-FMR analysis)] The mapping from measured torque efficiency to bulk SHC would be strengthened by explicit demonstration that the signal scales with BiSb thickness rather than saturating at the interface (e.g., via a thickness series or control samples with fixed interface but varying bulk thickness); without such data the numerical agreement with bulk calculations alone does not rule out dominant interfacial contributions.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for raising these important points regarding the interpretation of our ST-FMR data. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that ST-FMR directly yields the intrinsic bulk SHC (and thereby tests bulk-boundary correspondence) rests on the untested assumption that interfacial torques are subdominant across the full composition range; no quantitative error bars, data-exclusion criteria, or interface-isolation controls are described, which is load-bearing for the central claim given that spin current is non-conserved.

    Authors: We agree that potential interfacial contributions merit explicit discussion. In the revised manuscript we will add quantitative error bars to the extracted SHC values, clarify the data-analysis and exclusion criteria, and include a dedicated paragraph addressing why interfacial torques are expected to be subdominant. This argument rests on the observed composition dependence, which tracks the bulk band-structure evolution (including the topological transition) rather than remaining constant as would be anticipated for purely interfacial effects. revision: partial

  2. Referee: [Results/Discussion (ST-FMR analysis)] The mapping from measured torque efficiency to bulk SHC would be strengthened by explicit demonstration that the signal scales with BiSb thickness rather than saturating at the interface (e.g., via a thickness series or control samples with fixed interface but varying bulk thickness); without such data the numerical agreement with bulk calculations alone does not rule out dominant interfacial contributions.

    Authors: A thickness series would indeed provide further support. However, all films in the present study were grown at the fixed thickness required for high structural quality and in-vacuo ARPES verification of the band structure across the full composition range. The parameter-free agreement between the measured effective SHC and the bulk tight-binding calculations, which follows the bulk band inversion, is difficult to reconcile with a dominant interface contribution that would not be expected to exhibit the same composition dependence. We will expand the discussion section to make this reasoning explicit. revision: no

standing simulated objections not resolved
  • Provision of a thickness series demonstrating that the ST-FMR signal scales with BiSb thickness, as this would require new experimental samples and measurements beyond the scope of the current study.

Circularity Check

0 steps flagged

No circularity: experiment compared to independent bulk tight-binding calculations

full rationale

The paper extracts effective SHC from ST-FMR measurements on epitaxial films and reports numerical agreement with separate tight-binding computations of intrinsic bulk SHC. No step reduces a claimed prediction to a fitted parameter, self-citation, or definitional identity within the paper's own equations; the tight-binding results are presented as external first-principles input. The central claim therefore remains an empirical comparison rather than a self-referential derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the accuracy of the tight-binding model for bulk SHC and the assumption that ST-FMR isolates bulk intrinsic contribution.

axioms (1)
  • domain assumption Tight-binding calculations accurately capture the intrinsic spin Hall conductivity of the bulk bands
    Used as the benchmark for experimental comparison across compositions.

pith-pipeline@v0.9.0 · 5832 in / 1070 out tokens · 28418 ms · 2026-05-24T06:09:15.084389+00:00 · methodology

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Reference graph

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