The physical properties of the Hall current

Abstract

We study the stationary state of Hall 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. 128, 054501 (2020)] in which the stationary state of an 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 transverse currents are derived. It is shown that the efficiency of the power injection into the lateral circuit is quadratic in the Hall angle and obeys to the maximum transfer theorem. For usual values of the Hall angle, the main contribution of this power injection provides from the longitudinal current flowing along the edges instead of the transverse current crossing the Hall bar.

Screening effect in spin Hall devices

“…However, this current is weighted by the factor α/(1 + α) [Eq. (35)], where α ≈ (2 /l sf ) 2 [Eq. (36)].…”

“…1 and 2). The typical behavior due to the screening observed in the usual Hall bar [33][34][35] could then be extrapolated also for the spin Hall bar (with the presence of longitudinal pure spin current near the edges). However, the coupling between the two channels due to both the electrostatic interaction [see Eq.…”

“…In other terms, the distribution of charge densities and currents is determined by the state of minimum power production, taking into account the global constraints applied to the system. These constraints are due to the presence of the electric generator, the electrostatic boundary conditions, and the symmetries of the device [30,31,[33][34][35].…”

“…It is, however, possible to take into account the nonequilibrium nature of the electric screening in the case of a ideal Hall bar [30][31][32][33][34][35] on the basis of the least dissipation principle [36][37][38]. The global constraints applied to the system (current injection, global charge conservation, and geometry) are used instead of the local boundary conditions.…”

“…Physically, this surface current is responsible for the well-known * jean-eric.wegrowe@polytechnique.edu robustness of the Hall voltage, which can be measured while using a good or a bad voltmeter (i.e., with huge variations of the electric leakage at the edges [39]), because the electric charges accumulated are renewed permanently despite the zero transverse current. Furthermore, if a secondary passive circuit is contacted at the two edges of the Hall bar, the variational method shows that the electric current injected is mainly carried by the longitudinal surface currents δJ x (y) instead of the transverse current J y [35].…”