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

TL;DR

This paper develops a quantum kinetic framework to analyze carrier-impurity spin transfer in paramagnetic II-VI diluted magnetic semiconductors, highlighting the importance of energy shifts during spin-flip processes and exploring effects of a wave-vector-dependent magnetic field like Rashba.

Contribution

It introduces a rigorous microscopic quantum kinetic model that includes energy shifts in spin-flip scattering and applies it to systems with k-dependent magnetic fields, such as Rashba interactions.

Findings

Energy shifts significantly affect spin transfer dynamics in dilute magnetic semiconductors.

Rashba field modifies k-space dynamics but does not greatly alter total carrier spin evolution.

The theory connects microscopic spin transfer processes with collective precession modes.

Abstract

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.