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Comparison between a quantum kinetic theory of spin transfer dynamics in Mn doped bulk semiconductors and its Markov limit for non-zero Mn magnetization

We investigate the transfer between carrier and Mn spins due to the s-d-exchange interaction in a Mn doped bulk semiconductor within a microscopic quantum kinetic theory. We demonstrate that the spin transfer dynamics is qualitatively different for components of the carrier spin parallel and perpendicular to the Mn magnetization. From our quantum kinetic equations we have worked out the corresponding Markov limit which is equivalent to rate equations based on Fermi's golden rule. The resulting equations resemble the widely used Landau-Lifshitz-Gilbert-equations, but also describe genuine spin transfer due to quantum corrections. Although it is known that the Markovian rate description works well for bulk systems when the initial Mn magnetization is zero, we find large qualitative deviations from the full quantum kinetic theory for finite initial Mn magnetizations. These deviations mainly reflect corrections of higher than leading order in the interaction which are not accounted for in golden rule-type rates.