The doping of semiconductors with magnetic impurities gives rise not only to a spin-spin interaction between quasi-free carriers and magnetic impurities, but also to a local spin-independent disorder potential for the carriers. Based on a quantum kinetic theory for the carrier and impurity density matrices as well as the magnetic and non-magnetic carrier-impurity correlations, the influence of the non-magnetic scattering potential on the spin dynamics in DMS after optical excitation with circularly polarized light is investigated using the example of Mn-doped CdTe. It is shown that non-Markovian effects, which are predicted in calculations where only the magnetic carrier-impurity interaction is accounted for, can be strongly suppressed in the presence of non-magnetic impurity scattering. This effect can be traced back to a significant redistribution of carriers in $mathbf{k}$-space which is enabled by the build-up of large carrier-impurity correlation energies. A comparison with the Markov limit of the quantum kinetic theory shows that, in the presence of an external magnetic field parallel to the initial carrier polarization, the asymptotic value of the spin polarization at long times is significantly different in the quantum kinetic and the Markovian calculations. This effect can also be attributed to the formation of strong correlations which invalidates the semiclassical Markovian picture and it is stronger when the non-magnetic carrier-impurity interaction is accounted for. In an external magnetic field perpendicular to the initial carrier spin, the correlations are also responsible for a renormalization of the carrier spin precession frequency.
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