On december 11, we have the pleasure to welcome in Spintec Jean-Eric Wegrowe from Ecole Polytechnique. At 11h, he will give a seminar on “Spin-Hall stationarity conditions in the light of the second law of thermodynamics” in room 434A.
The determination of the stationary states for the bulk spin-Hall effect [1,2] are discussed in the context of the two spin-channel model. It is shown that the usual stationarity condition (no explicite time-dependence of the densities) leads to an indeterminacy : different stationary states can equally be defined . A first state is characterized by a transverse pure spin current while a second stationary state is characterized by a spin-dependent electric field. The two states have the same properties with respect to spin-accumulation and spin-Hall angle, but not with respect to the dissipated power.
However, the application of the second law of thermodynamics allows the formulation of the stationarity condition to be re-considered in form of a variational principle (the Kirchhoff-Helmholtz principle) . The stationary state is then defined univocally : the first state is typically found in the case of the Corbino disk (Fig.1), while the second state is found in the case of the Hall bar (Fig.2).
 M. I. Dyakonov and V. I. Perel « Possibility of orienting electron spins with current » JETP Lett. 13, 467 (1971) and « Current induced spin orientation in semiconductors » Phys. Lett A 35, 459 (1971).
 J. E. Hirsch, « Spin Hall effect » Phys. Rev. Lett 83, 1834 (1999).
 J.-E. Wegrowe, « Twofold stationary states in the classical spin-Hall effect » J. Phys.: Cond Matter 29, 485801 (2017).
 J.-E. Wegrowe, R. Benda, M. J. Rubì. « Conditions for the generation of spin and charge currents in spin-Hall devices » Europhys. Lett. 18, 67005 (2017).