Spin orientation and spin-Hall effect induced by tunneling electrons

It is shown that a flux of unpolarized electrons across a symmetric double barrier quantum well induces a spin polarization inside the well. Besides, the transmitted current acquires a spin polarized component and the spin-Hall current flows in the planar direction. These phenomena are due to a combined effect of Dresselhaus interaction and the spin-orbit interaction induced by gradients of heterostructure material parameters. In contrast to previous studies of the spin filtering effect, we predict that it can be observed in the case of an isotropic distribution of incident electrons.