  We investigate the origin of overshoots in the exciton spin dynamics after
resonant optical excitation. As a material system, we focus on diluted magnetic
semiconductor quantum wells as they provide a strong spin-flip scattering for
the carriers. Our study shows that overshoots can appear as a consequence of
radiative decay even on the single-particle level in a theory without any
memory. The magnitude of the overshoots in this case depends strongly on the
temperature as well as the doping fraction of the material. If many-body
effects beyond the single-particle level become important so that a
quantum-kinetic description is required, a spin overshoot appears already
without radiative decay and is much more robust against variations of system
parameters. We show that the origin of the spin overshoot can be determined
either via its temperature dependence or via its behavior for different doping
fractions. The results can be expected to apply to a wide range of
semiconductors as long as radiative decay and a spin-flip mechanism are
present.
