We have studied the perpendicular magnetic anisotropy of Co/Pt multilayers and the electron spin injection efficiency by optical spectroscopy from a [Co(0.6 nm)/Pt(1 nm)] 4 /Fe(0.3 nm)/MgO perpendicular tunnel spin injector grown on AlGaAs/GaAs semiconductor light-emitting diodes. We observe a 2.5% circular polarization at low temperature close to the magnetic remanence when the 0.3 nm Fe film of the ferromagnetic injector is sufficiently thin to maintain the magnetization out of plane. The acquired squared magnetization cycle is explained by the remaining interlayer exchange coupling existing between Fe and the (Co/Pt) multilayer through Pt or possible perpendicular magnetic anisotropy at the MgO/Fe interface. The corresponding spin polarization of the current is then estimated as 7%, measured by photoluminescence techniques, after the necessary uprenormalization, taking into account the electron spin-flip rate in the quantum well. In contrast, no circular polarization is observed when the thin Fe layer is removed and despite the rather high magnetic polarizability of the 5d 9 electronic open shell of Pt at the interface with MgO. This emphasizes the reduced size of tunneling branching of wave functions at the interface, of the order of the atomic plane unit.