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arxiv: 2604.08989 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mes-hall

Reciprocity of Charge-Orbital-Spin Transport in Normal-Metal/Ferromagnet Heterostructures

Abhishek Erram , Akanksha Chouhan , Ashwin A. Tulapurkar This is my paper

Pith reviewed 2026-05-10 17:56 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords orbital Hall effectOnsager reciprocityorbital torqueorbital pumpingheterostructurestransmission coefficientsspin-orbitronics
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The pith

Orbital torque and orbital pumping obey Onsager reciprocity in metal-ferromagnet stacks

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

The paper measures both orbital torque acting on magnetization and the reciprocal orbital pumping in the same normal-metal/ferromagnet devices. Two-port scattering-parameter data on Ru/Ni, Ru/Pt/CoFeB and Co/Cu/SiO2 stacks show that the transmission coefficients obey the symmetry relations demanded by Onsager reciprocity. This directly links charge-to-orbital, orbital-to-spin and their inverse conversions. A reader cares because the result places orbital angular momentum transport on the same reciprocal footing as conventional spin transport, suggesting symmetric device operation is possible.

Core claim

Using two-port scattering parameter measurements on Ru/Ni, Ru/Pt/CoFeB and Co/Cu/SiO2 devices, the transmission coefficients satisfy the symmetry relations required by Onsager reciprocity, demonstrating reciprocal conversion between charge, orbital and spin angular momenta. The results establish orbital pumping as the reciprocal counterpart of orbital torque and supply a unified framework for orbital transport phenomena.

What carries the argument

Onsager reciprocity relations among transmission coefficients extracted from two-port scattering-parameter measurements, which enforce bidirectional equivalence between orbital torque generation and orbital pumping.

If this is right

  • Orbital pumping can be used as the direct reciprocal readout of orbital torque within one device platform.
  • Charge, orbital and spin angular momenta convert into one another with symmetric efficiencies.
  • A single framework now covers both orbital and spin transport in the same heterostructures.
  • The reciprocity holds across several material combinations, indicating it is not limited to one interface.

Where Pith is reading between the lines

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

  • Device geometries could exploit the reciprocity to make the same stack function as both generator and detector of orbital currents.
  • Varying normal-metal thickness would map the orbital diffusion length while the reciprocity relation remains the test of consistency.
  • The same measurement protocol could be applied to other candidate orbital materials to check whether reciprocity is universal.

Load-bearing premise

The measured transmission signals arise predominantly from the orbital Hall effect and its inverse rather than from spin Hall effects, anomalous Hall effects or interface contributions that could produce the same symmetry by coincidence.

What would settle it

Independent control experiments that suppress orbital contributions while preserving spin contributions yet still find the transmission symmetries intact, or vice versa.

Figures

Figures reproduced from arXiv: 2604.08989 by Abhishek Erram, Akanksha Chouhan, Ashwin A. Tulapurkar.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration (a) Orbital current injec [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The device schematic used to show the reciprocity [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The real and imaginary parts of the transmission [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. ∆ [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

Orbital angular momentum has recently emerged as an important carrier of angular momentum in solids, offering new pathways for spin orbitronic functionality beyond conventional spin transport. Here, we investigate the orbital Hall effect which generates orbital torques and their reciprocal process viz orbital pumping and the inverse orbital Hall effect (iOHE) in non-magnet/ferromagnet heterostructures. Using two port scattering parameter measurements on Ru/Ni, Ru/Pt/CoFeB and Co/Cu/SiO2 devices, we directly probe both orbital torque driven magnetization dynamics and orbital pumping within the same device platform. We observe that the transmission coefficients satisfy the symmetry relations required by Onsager reciprocity, demonstrating reciprocal conversion between charge, orbital and spin angular momenta. Our results establish orbital pumping as the reciprocal counterpart of orbital torque. Our experimental findings provide a unified framework for orbital transport phenomena.

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 / 2 minor

Summary. The manuscript reports two-port scattering parameter measurements on Ru/Ni, Ru/Pt/CoFeB, and Co/Cu/SiO2 heterostructures to probe orbital torque and its reciprocal process, orbital pumping combined with the inverse orbital Hall effect. The central claim is that the measured transmission coefficients satisfy the symmetry relations required by Onsager reciprocity, thereby demonstrating reciprocal conversion among charge, orbital, and spin angular momenta within a single device platform.

Significance. If the signals can be unambiguously attributed to orbital transport, the work would supply a direct experimental test of reciprocity between orbital torque and orbital pumping, providing a unified framework for charge-orbital-spin phenomena that extends conventional spin-orbitronics. The use of the same device for both forward and reverse processes is a methodological strength that avoids cross-experiment comparisons.

major comments (2)
  1. [Abstract and Results] Abstract and Results section: The claim that observed S-parameter symmetry 'demonstrates reciprocal conversion between charge, orbital and spin angular momenta' is not supported by the data alone, because Onsager reciprocity holds for any linear reciprocal process; the manuscript provides no thickness-dependent scaling, control samples (e.g., spin-Hall-dominant stacks), or quantitative decomposition that isolates the orbital Hall / iOHE contribution from possible spin-Hall or interface spin-orbit torque signals in the chosen heterostructures.
  2. [Experimental Methods and transmission data figure] Experimental Methods and Fig. 3 (or equivalent transmission data figure): Raw S21 and S12 traces are presented without reported uncertainties, fitting procedures, or explicit checks for parasitic effects such as electromagnetic crosstalk or contact resistance; without these, it is impossible to determine whether the reported equality is quantitative or merely qualitative within experimental noise.
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction could more clearly distinguish the present reciprocity test from prior orbital Hall torque measurements in the literature.
  2. [Main text] Notation for the transmission coefficients (S21 vs. S12) should be defined explicitly in the main text rather than only in a supplementary note.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript arXiv:2604.08989. We address each of the major comments in detail below and indicate the revisions we plan to make to strengthen the paper.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results section: The claim that observed S-parameter symmetry 'demonstrates reciprocal conversion between charge, orbital and spin angular momenta' is not supported by the data alone, because Onsager reciprocity holds for any linear reciprocal process; the manuscript provides no thickness-dependent scaling, control samples (e.g., spin-Hall-dominant stacks), or quantitative decomposition that isolates the orbital Hall / iOHE contribution from possible spin-Hall or interface spin-orbit torque signals in the chosen heterostructures.

    Authors: We agree that Onsager reciprocity is a general property and does not by itself prove the involvement of orbital degrees of freedom. Our manuscript selects specific heterostructures (Ru/Ni, Ru/Pt/CoFeB, Co/Cu/SiO2) where orbital transport is expected to play a significant role based on established material properties and previous studies on orbital Hall effects in these systems. The key strength is demonstrating the reciprocity within the same device for torque and pumping processes. To better support the claim, we will revise the Abstract and Results to include a more detailed justification of material choice and add references to works showing orbital dominance in similar stacks. However, we do not have thickness-dependent data or additional control samples in the current dataset, as the focus was on demonstrating the reciprocity principle. We believe the observed symmetry in these platforms provides evidence within the context of orbital spintronics. revision: partial

  2. Referee: [Experimental Methods and transmission data figure] Experimental Methods and Fig. 3 (or equivalent transmission data figure): Raw S21 and S12 traces are presented without reported uncertainties, fitting procedures, or explicit checks for parasitic effects such as electromagnetic crosstalk or contact resistance; without these, it is impossible to determine whether the reported equality is quantitative or merely qualitative within experimental noise.

    Authors: We thank the referee for pointing this out. In the revised version, we will update the Experimental Methods section to include a description of the data acquisition and analysis procedures, including how uncertainties were estimated from multiple measurements. We will add error bars to the S21 and S12 data in the relevant figure. Additionally, we will include explicit checks for parasitic effects by reporting measurements on reference samples without the ferromagnetic layer or with different geometries to assess crosstalk and contact resistance contributions. This will allow readers to evaluate the quantitative agreement with Onsager symmetry. revision: yes

standing simulated objections not resolved
  • The lack of thickness-dependent scaling, control samples (e.g., spin-Hall-dominant stacks), and quantitative decomposition to isolate orbital contributions, which would require additional experiments beyond the current manuscript.

Circularity Check

0 steps flagged

No circularity: experimental observation of external Onsager symmetry

full rationale

The paper reports two-port scattering measurements on Ru/Ni, Ru/Pt/CoFeB and Co/Cu/SiO2 devices and states that the observed transmission coefficients obey the symmetry relations required by Onsager reciprocity. Onsager reciprocity is an external, established theorem invoked only as an interpretive benchmark; the paper does not derive the symmetry from its own data or equations, nor does it fit parameters and then relabel the fit as a prediction. No self-citations, ansatzes, or uniqueness theorems are used to close any derivation loop. The central claim therefore remains an empirical finding interpreted through independent physics and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Onsager reciprocity theorem applied to transport coefficients; no free parameters, ad-hoc axioms, or new postulated entities are introduced in the abstract.

axioms (1)
  • standard math Onsager reciprocity relations hold for the charge-orbital-spin transport coefficients in the heterostructures
    Invoked to interpret the observed symmetry between transmission coefficients as evidence of reciprocal orbital conversion.

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Reference graph

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