Collective Spin-Hall Effect for Electron-Hole Gratings

We show that an electric field parallel to the wavefronts of an electron-hole grating in a GaAs quantum well generates, via the electronic spin Hall effect, a spin grating of the same wave vector and with an amplitude that can exceed 1% of the amplitude of the initial density grating. We refer to this phenomenon as "collective spin Hall effect". A detailed study of the coupled-spin charge dynamics for quantum wells grown in different directions reveals rich features in the time evolution of the induced spin density, including the possibility of generating a helical spin grating.