We study the dynamics of carrier-spin injection in a diluted magnetic semiconductor double quantum well (DMS-DQW) of CdMnTe/CdTe by means of pump-probe absorption spectroscopy. The time dependences of the absorption saturation intensity show the injection dynamics of spin-polarized electrons and heavy holes (hhs) from the DMS-CdMnTe into the non-magnetic CdTe wells, where separate tunneling of the electron and the hh is directly elucidated with time constants of 150 ps and 1 ns, respectively. The degree of circular polarization P of the absorption saturation increases from 0 to 70 ps after pumping in the non-magnetic CdTe well, which is caused by the injection of polarized electron spins in the DMS well. We observe a systematic dependence of the rise time of P on the magnetic field. The faster polarization of the electron spin in the DMS well results in a faster electron-spin injection. The electron's spin polarization is accelerated in the DMS well by LO-phonon scattering at 6 T, where the electron spin splitting is close to the one-LO-phonon energy, which enables us to demonstrate a fast electron-spin injection with a time constant of 10 ps.
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