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 [3]. 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) [4]. 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).

References :

[1] 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).

[2] J. E. Hirsch, « Spin Hall effect » Phys. Rev. Lett **83**, 1834 (1999).

[3] J.-E. Wegrowe, « Twofold stationary states in the classical spin-Hall effect » J. Phys.: Cond Matter **29**, 485801 (2017).

[4] 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).