We combine Z-contrast scanning transmission electron microscopy with density-functional-theory calculations to determine the atomic structure of the interface in spin-polarized light-emitting diodes. A 44% increase in spin-injection efficiency occurs after a low-temperature anneal, which produces an ordered, coherent interface consisting of a single atomic plane of alternating Fe and As atoms. First-principles transport calculations indicate that the increase in spin-injection efficiency is due to the abruptness and coherency of the annealed interface.