  The dynamical behavior of the magnetism of diluted magnetic semiconductors
(DMS) has been investigated by means of atomistic spin dynamics simulations.
The conclusions drawn from the study are argued to be general for DMS systems
in the low concentration limit, although all simulations are done for 5%
Mn-doped GaAs with various concentrations of As antisite defects. The
magnetization curve, $M(T)$, and the Curie temperature $T_C$ have been
calculated, and are found to be in good correspondence to results from Monte
Carlo simulations and experiments. Furthermore, equilibrium and non-equilibrium
behavior of the magnetic pair correlation function have been extracted. The
dynamics of DMS systems reveals a substantial short ranged magnetic order even
at temperatures at or above the ordering temperature, with a non-vanishing pair
correlation function extending up to several atomic shells. For the high As
antisite concentrations the simulations show a short ranged anti-ferromagnetic
coupling, and a weakened long ranged ferromagnetic coupling. For sufficiently
large concentrations we do not observe any long ranged ferromagnetic
correlation. A typical dynamical response shows that starting from a random
orientation of moments, the spin-correlation develops very fast ($\sim$ 1ps)
extending up to 15 atomic shells. Above $\sim$ 10 ps in the simulations, the
pair correlation is observed to extend over some 40 atomic shells. The
autocorrelation function has been calculated and compared with ferromagnets
like bcc Fe and spin-glass materials. We find no evidence in our simulations
for a spin-glass behaviour, for any concentration of As antisites. Instead the
magnetic response is better described as slow dynamics, at least when compared
to that of a regular ferromagnet like bcc Fe.
