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arxiv: 2509.21635 · v1 · submitted 2025-09-25 · ❄️ cond-mat.mtrl-sci

Charge, heat, and spin transport phenomena in metallic conductors

Nynke Vlietstra , Sebastian T. B. Goennenwein , Rudolf Gross , Hans Huebl This is my paper

Pith reviewed 2026-05-18 13:20 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords charge transportheat transportspin transportthermoelectric effectsgalvanomagnetic effectscollinear transporttransverse transportplanar transport
0
0 comments X

The pith

Transport phenomena in metallic conductors fall into three consistent directional categories: collinear, transverse, and planar.

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

The paper organizes the many cross-linked responses that arise when gradients in electrochemical potential, temperature, or spin-chemical potential drive flows of charge, heat, and spin in solids. It places thermoelectric, thermomagnetic, galvanomagnetic, and spin-dependent effects into collinear responses that run along the gradient, transverse responses that run perpendicular to it, and planar responses that lie in the plane spanned by multiple directions. A reader would care because this single scheme makes it possible to compare effects that are usually discussed in separate subfields and to see how primary transport and its coupled counterparts share the same directional logic.

Core claim

By structuring all transport responses according to the relative orientation between driving gradient and resulting flow, the paper shows that the full set of charge, heat, and spin phenomena—including their anomalous and spin-dependent versions—can be placed into collinear, transverse, or planar categories without remainder.

What carries the argument

The three-way division into collinear, transverse, and planar transport effects, which assigns each response to a category based on whether the measured current or voltage lies parallel, perpendicular, or coplanar with the applied gradient.

If this is right

  • Thermoelectric and thermomagnetic effects become directly comparable within the same category once their directional character is fixed.
  • Spin-dependent versions of the same effects sit alongside the charge and heat versions in the identical classification.
  • Primary flows and secondary cross-effects obey the same directional rules, so the framework treats them uniformly.
  • Galvanomagnetic and spin-galvanic responses fall naturally into the transverse or planar groups depending on sample geometry.

Where Pith is reading between the lines

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

  • Device designers could use the categories to select geometries that suppress unwanted cross-effects while preserving a desired response.
  • The scheme suggests a systematic search for missing planar spin-caloritronic effects that have not yet been reported.
  • Textbooks and courses on spintronics could adopt the same three-category map to place new phenomena next to classical ones.

Load-bearing premise

Every known thermoelectric, thermomagnetic, galvanomagnetic, and spin-dependent response can be assigned unambiguously to one of the three directional categories without forcing overlaps or leaving gaps.

What would settle it

Identification of a charge-heat-spin cross-effect in a metallic conductor whose geometry fits none of the three categories without redefinition or significant overlap with another category.

Figures

Figures reproduced from arXiv: 2509.21635 by Hans Huebl, Nynke Vlietstra, Rudolf Gross, Sebastian T. B. Goennenwein.

Figure 10
Figure 10. Figure 10: Js P'Π<0 P'Π=0 Es=-∇ɸs Jh [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 24
Figure 24. Figure 24: Here, it can be seen that each initially scalar [PITH_FULL_IMAGE:figures/full_fig_p032_24.png] view at source ↗
read the original abstract

In solid state materials, gradients of the electro-chemical potential, the temperature, or the spin-chemical potential drive the flow of charge, heat, and spin angular momentum, resulting in a net transport of energy. Beyond the primary transport processes - such as the flow of charge, heat, and spin angular momentum driven by gradients in their respective potentials - a wide range of coupled or cross-linked transport responses can occur, giving rise to a rich variety of transport phenomena. These transport phenomena are commonly categorized under (anomalous) thermoelectric, thermomagnetic, and galvanomagnetic effects, along with their spin-dependent counterparts. However, establishing a systematic classification and comparison among them remains a complex and nontrivial task. This paper attempts a didactic overview of the different transport phenomena, by categorizing and briefly discussing each of them based on charge, heat, and spin transport in conducting solids. The phenomena are structured in three categories: collinear, transverse, and so-called `planar' transport effects. The resulting overview attempts to categorize all effects in a consistent manner.

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 provides a didactic overview of charge, heat, and spin transport in metallic conductors. It groups thermoelectric, thermomagnetic, galvanomagnetic, and spin-dependent phenomena into three directional categories—collinear, transverse, and planar—based on the relative orientations of driving gradients (electrochemical potential, temperature, spin-chemical potential) and the resulting currents, with the goal of a consistent taxonomy covering all such effects.

Significance. If the proposed taxonomy proves mutually exclusive and exhaustive, the work could serve as a useful organizing framework for the literature on coupled transport responses. As a synthesis without new derivations or predictions, its primary value would lie in clarity of presentation and the absence of post-hoc exceptions in the mapping.

major comments (2)
  1. [Abstract] Abstract: the assertion that the three categories 'categorize all effects in a consistent manner' is load-bearing for the central claim, yet the manuscript supplies neither an explicit decision tree nor an exhaustive mapping table. Without these, it remains unclear whether every cited response (e.g., planar Hall, spin Nernst, anisotropic magnetothermopower) can be assigned unambiguously.
  2. [Introduction] Introduction / section introducing the planar category: the geometric criterion that distinguishes 'planar' from transverse effects is not stated with sufficient precision when both charge and spin currents lie in the same plane. This risks overlap and therefore undermines mutual exclusivity of the bins.
minor comments (2)
  1. Add a summary table that lists each discussed effect together with its assigned category and the vector directions of gradient and current; this would make the consistency claim directly verifiable.
  2. Ensure every named effect is accompanied by at least one primary reference so readers can check the assignment independently.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below and will revise the manuscript to improve the precision and transparency of the taxonomy.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the three categories 'categorize all effects in a consistent manner' is load-bearing for the central claim, yet the manuscript supplies neither an explicit decision tree nor an exhaustive mapping table. Without these, it remains unclear whether every cited response (e.g., planar Hall, spin Nernst, anisotropic magnetothermopower) can be assigned unambiguously.

    Authors: We agree that an explicit decision tree and mapping table would make the central claim more verifiable. In the revised manuscript we will insert a comprehensive table that enumerates every phenomenon discussed (including planar Hall, spin Nernst, and anisotropic magnetothermopower) together with the vector orientations of the driving gradient and response current that determine its category. We will also add a short decision flowchart in the introduction that formalizes the assignment rules. These additions will demonstrate that the three bins remain mutually exclusive and exhaustive for the cited effects. revision: yes

  2. Referee: [Introduction] Introduction / section introducing the planar category: the geometric criterion that distinguishes 'planar' from transverse effects is not stated with sufficient precision when both charge and spin currents lie in the same plane. This risks overlap and therefore undermines mutual exclusivity of the bins.

    Authors: We acknowledge that the geometric definition of the planar category requires sharper wording to avoid ambiguity when currents are coplanar. In the revision we will replace the current description with an explicit vector criterion: planar effects are those in which the driving gradient and the induced current both lie in the plane normal to the magnetization (or analogous vector), with the current component parallel to the gradient being allowed only when it is modulated by the in-plane anisotropy; transverse effects are those in which the current is strictly perpendicular to both the gradient and the magnetization. A new figure with labeled vector diagrams will illustrate the distinction and confirm the absence of overlap. revision: yes

Circularity Check

0 steps flagged

No circularity: literature synthesis with proposed taxonomy but no derivations or self-referential reductions

full rationale

The paper is a didactic overview and literature synthesis that proposes structuring known transport phenomena into collinear, transverse, and planar categories based on charge, heat, and spin transport. No equations, first-principles derivations, predictions, or fitted parameters are presented that could reduce to inputs by construction. The central claim is an organizational attempt to categorize effects consistently, without self-definitional loops, self-citation load-bearing arguments, or renaming of results as new derivations. The classification is offered as a consistent framework for existing phenomena rather than a derived result equivalent to its own premises.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

As a review the central claim rests on the correctness and completeness of the prior literature on thermoelectric, thermomagnetic, and spin-transport effects; no new free parameters or entities are introduced.

axioms (1)
  • domain assumption Standard linear-response transport relations (Onsager reciprocity, Fourier's law, Ohm's law) remain valid in metallic conductors under the conditions considered.
    Invoked implicitly when discussing coupled responses.

pith-pipeline@v0.9.0 · 5724 in / 1206 out tokens · 38606 ms · 2026-05-18T13:20:31.183927+00:00 · methodology

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Reference graph

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