Spin diffusion in GaAs quantum wells

The diffusion coefficient of spin in semiconductors is often estimated using the Einstein relation,$D=\chi ^{-1}\mu $, relating diffusion and mobility. However, direct measurements of spin diffusion coefficient $D_{s}$ and the mobility \textit{$\mu $} in an n-GaAs quantum well sample with carrier density $n=7\times 10^{11}$cm$^{-2}$ have revealed that spin diffusion is substantially suppressed [1] relative to $\chi ^{-1}\mu $ because of the ``spin-Coulomb drag'' effect [2]. In this talk we present data that illustrate the behavior of D$_{s}$, \textit{$\mu $}, and the spin relaxation time as $n$ is lowered towards the metal to insulator transition. Spin transport is characterized by the transient spin grating technique [3], which is based on optical injection of an electron-spin polarization wave with variable wavevector. Spin relaxation is measured by polarization-resolved transient absorption and \textit{$\mu $} is obtained from 4-contact transport measurements. We discuss the evolution of spin Coulomb drag and D'yakanov-Perel spin relaxation from the degenerate to nondegenerate regimes. [1] J. Orenstein, APS invited talk, this session. [2] I. D'Amico and G. Vignale, Phys. Rev. B 62, 4853 (2000). [3] A.R. Cameron, et al., Phys. Rev. Lett., 4793 (1996).