We show by spatially and time-resolved photoluminescence that the application of an electric field transverse to the plane of an intrinsic GaAs (111) quantum well (QW) allows the transport of photogenerated electron spins polarized along the direction perpendicular to the QW plane over distances exceeding 10~$mu$m. We attribute the long spin transport lengths to the compensation of the in-plane effective magnetic field related to the intrinsic spin-orbit (SO) interaction by means of the electrically generated SO-field. Away from SO-compensation, the precession of the spin vector around the SO-field decreases the out-of-plane polarization of the spin ensemble as the electrons move away from the laser generation spot. The results are reproduced by a model for two-dimensional drift-diffusion of spin polarized charge carriers under weak SO-interaction.
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