Carrier-impurity spin transfer dynamics in paramagnetic II-VI diluted magnetic semiconductors in the presence of a wave-vector-dependent magnetic field

摘要

Quantum kinetic equations of motion for carrier and impurity spins inparamagnetic II-VI diluted magnetic semiconductors in a $\mathbf{k}$-dependenteffective magnetic field are derived, where the carrier-impurity correlationsare taken into account. In the Markov limit, rates for the electron-impurityspin transfer can be derived for electron spins parallel and perpendicular tothe impurity spins corresponding to measurable decay rates in Kerr experimentsin Faraday and Voigt geometry. Our rigorous microscopic quantum kinetictreatment automatically accounts for the fact that, in an individual spinflip-flop scattering process, a spin flip of an electron is necessarilyaccompanied by a flop of an impurity spin in the opposite direction and thecorresponding change of the impurity Zeeman energy influences the final energyof the electron after the scattering event. This shift in the electron energiesafter a spin flip-flop scattering processes, which usually has been overlookedin the literature, turns out to be especially important in the case ofextremely diluted magnetic semiconductors in an external magnetic field. As aspecific example for a $\mathbf{k}$-dependent effective magnetic field theeffects of a Rashba field on the dynamics of the carrier-impurity correlationsin 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 thecorrelations leads to a modified $\mathbf{k}$-space dynamics, the timeevolution of the total carrier spin is not significantly influenced.Furthermore, a connection between the present theory and the description ofcollective carrier-impurity precession modes is presented.