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We investigate the spin relaxation length in GaAs spin light-emitting diode devices under drift transport at room temperature. The spin-polarised electrons are injected through a MgO tunnel barrier from a Fe/Tb multilayer in magnetic remanence. The decrease in circular polarization with increasing injection path length is investigated and found to be exponential, supporting drift-based transport. The spin relaxation length in our samples is 26 nm, and a lower bound for the spin injection efficiency at the spin injector/GaAs interface is estimated to be 25 ± 2%.