Effective Equations for the Precession Dynamics of Electron Spins and Electron-Impurity Correlations in Diluted Magnetic Semiconductors

TL;DR

This paper derives simplified effective equations for electron spin precession and impurity correlations in diluted magnetic semiconductors, demonstrating their accuracy and analytical tractability compared to full quantum kinetic models.

Contribution

The authors develop a Markov limit of quantum kinetic equations that accurately describes spin dynamics, including higher order correlation effects, improving upon standard rate models.

Findings

Markov limit reproduces full quantum kinetic results accurately

Effective equations include higher order correlation precession effects

Analytical solutions provide clear physical interpretation

Abstract

Starting from a quantum kinetic theory for the spin dynamics in diluted magnetic semiconductors, we derive simplified equations that effectively describe the spin transfer between carriers and magnetic impurities for an arbitrary initial impurity magnetization. Taking the Markov limit of these effective equations, we obtain good quantitative agreement with the full quantum kinetic theory for the spin dynamics in bulk systems at high magnetic doping. In contrast, the standard rate description where the carrier-dopant interaction is treated according to Fermi's golden rule, which involves the assumption of a short memory as well as a perturbative argument, has been shown previously to fail if the impurity magnetization is non-zero. The Markov limit of the effective equations is derived, assuming only a short memory, while higher order terms are still accounted for. These higher order terms represent the precession of the carrier-dopant correlations in the effective magnetic field due to the impurity spins. Numerical calculations show that the Markov limit of our effective equations reproduces the results of the full quantum kinetic theory very well. Furthermore, this limit allows for analytical solutions and for a physically transparent interpretation.