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Spin Hall Effect and Irreversible Thermodynamics; Center-to-Edge Transverse Current-Induced Voltage



Wayne M. Saslow


We examine the Dyakonov and Perel theory of the Spin Hall Effect from the viewpoint of irreversible thermodynamics. As thermodynamic driving forces we include the effect of the thermal gradient, the gradient of the electrochemical potential (rather than the potential gradient and density gradient separately), and the gradient of 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 the original work of Dyakonov and Perel, in addition to the new terms due to thermal gradients, the Onsager relations require three new (non-linear) terms in the current density, and minor revisions in the current density and spin current density. The center-to-edge transverse voltage difference due both to the $\beta\vec{P}\times\vec{E}$ term of Dyakonov and Perel and one of these new current density terms is calculated for the first time. A capacitative probe likely would not significantly disturb this effect. %We also consider the boundary conditions on the fluxes and the surface transport coefficients that relate the fluxes crossing a surface to the differences in the thermodynamic driving forces across that surface.
Physical Review B


spintronics, spin-orbit scattering, irreversible thermodynamics


Saslow, W. (2015), Spin Hall Effect and Irreversible Thermodynamics; Center-to-Edge Transverse Current-Induced Voltage, Physical Review B, [online], (Accessed June 12, 2024)


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Created January 5, 2015, Updated November 10, 2018