Electric potential difference → Electrical work

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.06 × C.01 · Electric potential difference × Thermoelectricfamily: ThermoelectricD.06 × C.17 · Electric potential difference × Spin caloritronicfamily: Spin caloritronic

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Carnot limit · formula-bound · hard, applies to this route
  η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c
• Onsager–Casimir reciprocity · constitutive-relation · listed, never decisive
  L_ij(B) = ε_i ε_j L_ji(−B): the cross-coefficients of coupled linear transport are equal up to the time-reversal parities ε of the variables and reversal of the magnetic field; L_ij = L_ji is the zero-field, even-parity case

Steps

1. 01
   Electric potential difference —drives→ Ettingshausen effectestablishedclaim record

   electrical → thermal

   • a current in a conductor with a perpendicular magnetic field

   solid · conductor required · magnetic field required

   refs [1] [2]
2. 02
   Ettingshausen effect —produces→ Temperature gradientestablishedclaim record

   thermal → thermal

   refs [2] [3]
3. 03
   Temperature gradient —drives→ Spin Seebeck effectreplicatedclaim record

   thermal → spin · loss to thermal

   • a magnetised ferromagnet, metallic or insulating (YIG), under a temperature gradient
   • an adjacent spin sink (heavy-metal layer) is needed for the usual electrical detection through inverse spin Hall conversion, not for the spin-Seebeck response itself

   solid · ferromagnet required · temperature gradient required

   refs [4] [5] [6] [7]
4. 04
   Spin Seebeck effect —produces→ Spin currentreplicatedclaim record

   spin → spin · loss to thermal

   • magnon current pumps a spin current into the adjacent metal across the interface

   refs [5] [7]
5. 05
   Spin current —drives→ Inverse spin Hall effectestablishedclaim record

   spin → electrical · loss to thermal

   • a heavy metal with strong spin–orbit coupling (Pt, Ta, W); works at room temperature

   solid · conductor required · room temperature

   refs [8] [9]
6. 06
   Inverse spin Hall effect —produces→ Charge carriersestablishedclaim record

   electrical → electrical

   refs [8] [9]
7. 07
   Charge carriers —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • carriers driven through an external load at the potential difference the source maintains

   refs [10]

Evidence for the complete composition · 0

No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.

Evidence for the constituent relations · 10

1. [1]
   A. von Ettingshausen, W. Nernst. Ueber das Auftreten electromotorischer Kräfte in Metallplatten, welche von einem Wärmestrome durchflossen werden und sich im magnetischen Felde befinden (1886)

   Annalen der Physik 265, 343–347 · doi:10.1002/andp.18862651010 · crossref ✓ 2026-09-19 · record
2. [2]
   H. B. Callen. The application of Onsager's reciprocal relations to thermoelectric, thermomagnetic, and galvanomagnetic effects (1948)

   Physical Review 73, 1349 · doi:10.1103/PhysRev.73.1349 · crossref ✓ 2026-09-19 · record
3. [3]
   H. J. Goldsmid. Introduction to Thermoelectricity (2nd ed.) (2016)

   Springer Series in Materials Science 121 · doi:10.1007/978-3-662-49256-7 · crossref ✓ 2026-09-19 · record
4. [4]
   K. Uchida, et al.. Observation of the spin Seebeck effect (2008)

   Nature 455, 778–781 · doi:10.1038/nature07321 · crossref ✓ 2026-09-19 · record
5. [5]
   K. Uchida, et al.. Spin Seebeck insulator (2010)

   Nature Materials 9, 894–897 · doi:10.1038/nmat2856 · crossref ✓ 2026-09-19 · record
6. [6]
   G. E. W. Bauer, E. Saitoh, B. J. van Wees. Spin caloritronics (2012)

   Nature Materials 11, 391–399 · doi:10.1038/nmat3301 · crossref ✓ 2026-09-19 · record
7. [7]
   M. Weiler et al.. Experimental test of the spin mixing interface conductivity concept (2013)

   Physical Review Letters 111, 176601 · doi:10.1103/PhysRevLett.111.176601 · crossref ✓ 2026-09-19 · record
8. [8]
   E. Saitoh et al.. Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect (2006)

   Applied Physics Letters 88, 182509 · doi:10.1063/1.2199473 · crossref ✓ 2026-09-19 · record
9. [9]
   J. Sinova et al.. Spin Hall effects (2015)

   Reviews of Modern Physics 87, 1213 · doi:10.1103/RevModPhys.87.1213 · crossref ✓ 2026-09-19 · record
10. [10]
    N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

    Holt, Rinehart and Winston · book, no DOI · record