  Microscopic properties of low-energy spin dynamics in diluted magnetic
semiconductor are addressed in a framework of the Kondo lattice model including
random distribution of magnetic dopants. Based on the fluctuation-dissipation
theorem, we derive an explicit dependence of the spin diffusion coefficient on
the single-particle Green function which is directly evaluated by dynamical
mean-field theory. In the paramagnetic state, the magnetic scattering has been
manifested to suppress spin diffusion. In agreement with other ferromagnet
systems, we also point out that the spin diffusion in diluted magnetic
semiconductors at small carrier concentration displays a monotonic $1/T$-like
temperature dependence. By investigating the spin diffusion coefficient on a
wide range of the model parameters, the obtained results have provided a
significant scenario to understand the spin dynamics in the paramagnetic
diluted magnetic semiconductors.
