  Quantum kinetic equations of motion for carrier and impurity spins in
paramagnetic II-VI diluted magnetic semiconductors in a $\mathbf{k}$-dependent
effective magnetic field are derived, where the carrier-impurity correlations
are taken into account. In the Markov limit, rates for the electron-impurity
spin transfer can be derived for electron spins parallel and perpendicular to
the impurity spins corresponding to measurable decay rates in Kerr experiments
in Faraday and Voigt geometry. Our rigorous microscopic quantum kinetic
treatment automatically accounts for the fact that, in an individual spin
flip-flop scattering process, a spin flip of an electron is necessarily
accompanied by a flop of an impurity spin in the opposite direction and the
corresponding change of the impurity Zeeman energy influences the final energy
of the electron after the scattering event. This shift in the electron energies
after a spin flip-flop scattering processes, which usually has been overlooked
in the literature, turns out to be especially important in the case of
extremely diluted magnetic semiconductors in an external magnetic field. As a
specific example for a $\mathbf{k}$-dependent effective magnetic field the
effects of a Rashba field on the dynamics of the carrier-impurity correlations
in a Hg$_{1-x-y}$Cd$_y$Mn$_x$Te quantum well are described. It is found that,
although accounting for the Rashba interaction in the dynamics of the
correlations leads to a modified $\mathbf{k}$-space dynamics, the time
evolution of the total carrier spin is not significantly influenced.
Furthermore, a connection between the present theory and the description of
collective carrier-impurity precession modes is presented.

Mesoscale and Nanoscale Physics