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

The hyperfine field from dynamically polarized nuclei in n-GaAs is very spatially inhomogeneous, as the nu- clear polarization process is most efficient near the randomly-distributed donors. Electrons with polarized spins traversing the bulk semiconductor will experience this inhomogeneous hyperfine field as an effective fluctuating spin precession rate, and thus the spin polarization of an electron ensemble will relax. A theory of spin relaxation based on the theory of random walks is applied to such an ensemble precessing in an oblique magnetic field, and the precise form of the (unequal) longitudinal and transverse spin relaxation analytically derived. To investigate this mechanism, electrical three-terminal Hanle measurements were performed on epitaxially grown Co$_2$MnSi/$n$-GaAs heterostructures fabricated into electrical spin injection devices. The proposed anisotropic spin relaxation mechanism is required to satisfactorily describe the Hanle lineshapes when the applied field is oriented at large oblique angles.