  We present results of tight-binding spin-dynamics simulations of individual
and pairs of substitutional Mn impurities in GaAs. Our approach is based on the
mixed quantum-classical scheme for spin dynamics, with coupled equations of
motions for the quantum subsystem, representing the host, and the localized
spins of magnetic dopants, which are treated classically. In the case of a
single Mn impurity, we calculate explicitly the time evolution of the Mn spin
and the spins of nearest-neighbors As atoms, where the acceptor (hole) state
introduced by the Mn dopant resides. We relate the characteristic frequencies
in the dynamical spectra to the two dominant energy scales of the system,
namely the spin-orbit interaction strength and the value of the p-d exchange
coupling between the impurity spin and the host carriers. For a pair of Mn
impurities, we find signatures of the indirect (carrier-mediated) exchange
interaction in the time evolution of the impurity spins. Finally, we examine
temporal correlations between the two Mn spins and their dependence on the
exchange coupling and spin-orbit interaction strength, as well as on the
initial spin-configuration and separation between the impurities. Our results
provide insight into the dynamic interaction between localized magnetic
impurities in a nano-scaled magnetic-semiconductor sample, in the extremely
dilute (solotronics) regime.
