  We study theoretically the ultrafast spin dynamics of II-VI diluted magnetic
semiconductors in the presence of spin-orbit interaction. Our goal is to
explore the interplay or competition between the exchange $sd$-coupling and the
spin-orbit interaction in both bulk and quantum well systems. For bulk
materials we concentrate on Zn$_{1-x}$Mn$_x$Se and take into account the
Dresselhaus interaction, while for quantum wells we examine
Hg$_{1-x-y}$Mn$_x$Cd$_y$Te systems with a strong Rashba coupling. Our
calculations were performed with a recently developed formalism which
incorporates electronic correlations beyond mean-field theory originated from
the exchange $sd$-coupling. For both bulk and quasi-two-dimensional systems we
find that, by varying the system parameters within realistic ranges, both
interactions can be chosen to play a dominant role or to compete on an equal
footing with each other. The most notable effect of the spin-orbit interaction
in both types of systems is the appearance of strong oscillations where the
exchange $sd$-coupling by itself only causes an exponential decay of the mean
electronic spin components. The mean-field approximation is also studied and it
is interpreted analytically why it shows a strong suppression of the
spin-orbit-induced dephasing of the spin component parallel to the Mn magnetic
field.
