We study the stationary state of Hall-bar devices composed of a load circuit connected to the lateral edges of a Hall-bar. We follow the approach developed in a previous work (Creff et al. J. Appl. Phys 2020) in which the stationary state of a ideal Hall bar is defined by the minimum power dissipation principle. The presence of both the lateral circuit and the magnetic field induces the injection of a current: the so-called Hall current. Analytical expressions for the longitudinal and the transverse currents are derived. The same analysis is performed on the spin-Hall effect, in the framework of the two spin-channel model.
The Hall effect occurring in a Hall bar is revisited on the basis on non-equilibrium thermodynamics principles. Following the approach developed in a previous work (Creff et al. J. Appl. Phys 2020), the stationary state is defined by the minimum power dissipation principle, and the well-known results about the charge accumulation at the lateral edges and the corresponding Hall voltage are recovered. Beyond, the effect of a sizable current leakage occurring at the edges is investigated. An analytical expression of this output current - proportional to the magnetic field and the leakage resistance - is derived.
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