Imaging Electron Spin Flows in Semiconductors in the Presence of Electric, Magnetic, and Strain Fields

Using methods for scanning Kerr microscopy, we directly acquire two-dimensional images of spin-polarized electrons flowing laterally in bulk epilayers of n:GaAs [1]. Optical injection provides a local dc source of polarized electrons, whose subsequent drift and/or diffusion is controlled with electric, magnetic, and -in particular- strain fields. The acquired spatial maps directly reveal how flows of polarized electron spins respond to these three fields when applied individually or in combination. Spin precession induced by controlled uniaxial stress along the $\langle$110$\rangle$ axes demonstrates the direct $|\vec{k}|$-linear spin-orbit coupling of electron spin to the shear (off-diagonal) components of the strain tensor $\epsilon$, through a Hamiltonian of the form $c_3 (\sigma_x \epsilon_{xy}k_y - \sigma_y \epsilon_{yx}k_x)$. The $|\vec{k}|$- linear nature of the strain-induced ``internal" magnetic field ($\vec{B}_\epsilon$) leads to a spatial coherence of dc spin flows that is preserved over much greater distances as compared with spin flows manipulated by external magnetic fields. $\vec{B}_\epsilon$ is shown to be in-plane and orthogonal to $\vec{k}$, and therefore chiral for radially- diffusing spins. Lastly, the spatial period of strain-induced spin precession is explicitly shown to be independent of applied electrical bias, of possible benefit to future spintronic devices. [1] S. A. Crooker and D. L. Smith, cond-mat/0411461