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The hyperfine field from dynamically polarized nuclei in n-GaAs is veryspatially inhomogeneous, as the nu- clear polarization process is mostefficient near the randomly-distributed donors. Electrons with polarized spinstraversing the bulk semiconductor will experience this inhomogeneous hyperfinefield as an effective fluctuating spin precession rate, and thus the spinpolarization of an electron ensemble will relax. A theory of spin relaxationbased on the theory of random walks is applied to such an ensemble precessingin an oblique magnetic field, and the precise form of the (unequal)longitudinal and transverse spin relaxation analytically derived. Toinvestigate this mechanism, electrical three-terminal Hanle measurements wereperformed on epitaxially grown Co$_2$MnSi/$n$-GaAs heterostructures fabricatedinto electrical spin injection devices. The proposed anisotropic spinrelaxation mechanism is required to satisfactorily describe the Hanlelineshapes when the applied field is oriented at large oblique angles.

Anisotropic spin relaxation in $n$-GaAs from strong inhomogeneous hyperfine fields produced by the dynamical polarization of nuclei