The generation and manipulation of carrier spin polarization in semiconductors solely by electric fields has garnered significant attention as both an interesting manifestation of spin-orbit physics as well as a valuable capability for potential spintronics devices. One realization of these spin-orbit phenomena, the spin Hall effect (SHE), has been studied as a means of all-electrical spin current generation and spin separation in both semiconductor and metallic systems. Previous measurements of the spin Hall effect have focused on steady-state generation and time-averaged detection, without directly addressing the accumulation dynamics on the timescale of the spin coherence time. Here, we demonstrate time-resolved measurement of the dynamics of spin accumulation generated by the extrinsic spin Hall effect in a doped GaAs semiconductor channel. Using electrically-pumped time-resolved Kerr rotation, we image the accumulation, precession, and decay dynamics near the channel boundary with spatial and temporal resolution and identify multiple evolution time constants. We model these processes using time-dependent diffusion analysis utilizing both exact and numerical solution techniques and find that the underlying physical spin coherence time differs from the dynamical rates of spin accumulation and decay observed near the sample edges.
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