Spin Hall effect and irreversible thermodynamics: Center-to-edge transverse current-induced voltage

We examine the Dyakonov and Perel theory of the Spin Hall effect (SHE) from the viewpoint of irreversible thermodynamics, which is more constraining than the symmetry arguments of pure phenomenology. As thermodynamic driving forces we include the thermal gradient, the gradient of the electrochemical...

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Bibliographic Details
Published in:Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2015-01, Vol.91 (1), Article 014401
Main Author: Saslow, Wayne M.
Format: Article
Language:English
Subjects:
Condensed matter
Current density
Density
Electric potential
Fluxes
Hall effect
Mathematical analysis
Thermodynamics
Voltage
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Summary:We examine the Dyakonov and Perel theory of the Spin Hall effect (SHE) from the viewpoint of irreversible thermodynamics, which is more constraining than the symmetry arguments of pure phenomenology. As thermodynamic driving forces we include the thermal gradient, the gradient of the electrochemical potential (rather than the potential gradient and density gradient separately), and the "internal" magnetic field that is thermodynamically conjugate to the magnetization. In turn, we obtain the form of bulk transport coefficients relating the fluxes to the thermodynamic forces. Relative to Dyakonov and Perel, in addition to the new terms due to thermal gradients, the Onsager relations require three new (nonlinear) terms in the current density, and minor revisions in the current density and spin current density. For a longitudinal current along a strip, the center-to-edge transverse voltage difference, due both to the - beta P x E term of of the number current density q and to one of the new current density terms, is calculated. An ac capacitative probe likely would not significantly disturb this effect. An appendix explicitly relates the anomalous Hall Effect to the term in the (vector) number flux that is Onsager related to the SHE term in the (tensor) spin flux.
ISSN:1098-0121
1550-235X
DOI:10.1103/PhysRevB.91.014401