The spatial distribution of dynamic nuclear spin polarization (DNP) has been investigated in a lateral all-semiconductor spin-injection device based on a (Ga,Mn)As/n+-GaAs spin-Esaki diode. The DNP induced by the hyperfine interaction has been probed via satellite peaks in non-local Hanle-type spin precession signals, indicating the recovery of electron spin polarization. A quantitative analysis using the self-consistent calculation reproduces the magnetic field position of the satellite peaks as a function of spin injection bias and injector-detector separation. The distance dependence of the Hanle curves reveals that the spin-lattice relaxation rather than the hyperfine interaction is the dominant mechanism of nuclear spin relaxation in the non-local region.

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