Non-Markovian spin transfer dynamics in magnetic semiconductors despite short memory times

Abstract

A quantum kinetic theory of the spin transfer between carriers and Mn atoms in a Mn doped diluted magnetic semiconductor is presented. It turns out that the typical memory time associated with these processes is orders of magnitude shorter than the time scale of the spin transfer. Nevertheless, Markovian rate equations, which are obtained by neglecting the memory, work well only for bulk systems. For quantum wells and wires the quantum kinetic results qualitatively deviate from the Markovian limit under certain conditions. Instead of a monotonic decay of an initially prepared excess electron spin, an overshoot or even coherent oscillations are found. It is demonstrated that these features are caused by energetic redistributions of the carriers due to the energy-time uncertainty.

Influence of nonmagnetic impurity scattering on spin dynamics in diluted magnetic semiconductors

“…To this end we employ a quantum kinetic theory for carrier and impurity density matrices including the carrierimpurity correlations starting from a system Hamiltonian that comprises a kinetic energy term, the magnetic and non-magnetic carrier-impurity interactions as well as the carrier and impurity Zeeman energies. Earlier quantum kinetic studies of the spin dynamics in DMS [25][26][27]36,37 , which only considered the spin-dependent s-d interaction, predicted that in some cases, such as in narrow quantum wells optically excited very close to the band edge 38 , the spin transfer between carriers and impurities cannot be well described by rate equations. Rather, the time evolution of the carrier spin is, in these cases, nonexponential and it can exhibit non-monotonic features such as overshoots.…”

“…While some types of DMS, such as Ga 1−x Mn x As, exhibit a ferromagnetic phase 8,23 , other types of DMS, like the usually paramagnetic CdMnTe, are especially valued for the enhancement of the effective carrier g-factor by the giant Zeeman effect that can be used, e.g., to facilitate an injection of a spin-polarized current into a light-emitting diode 24 . Besides causing the giant Zeeman effect, the s-d exchange interaction between the quasi-free carriers and localized magnetic impurities also leads to other effects, such as inducing spin-flip scattering and thereby a direct transfer of spins from the carriers to the impurities and vice versa [25][26][27][28] . Typically, the s-d interaction is described by a Kondolike 29 localized spin-spin interaction between carriers and impurities.…”

Nonperturbative correlation effects in diluted magnetic semiconductors

“…We base our study on a microscopic quantum kinetic theory derived by a correlation expansion scheme 45 that is capable of a non-perturbative description of highly nonequilibrium situations. One aspect of the effects of the carrier-impurity correlations on the spin dynamics has already been found in previous works [46][47][48][49][50] : The correlations mediate the transfer of spins between the carriers and the impurities. Since in the Markovian limit, the quantum kinetic theory contains the special case of rate equations which can also be derived by a Fermi's golden rule approach 46 , this spin transfer can, in fact, be treated perturbatively 51 .…”

“…One aspect of the effects of the carrier-impurity correlations on the spin dynamics has already been found in previous works [46][47][48][49][50] : The correlations mediate the transfer of spins between the carriers and the impurities. Since in the Markovian limit, the quantum kinetic theory contains the special case of rate equations which can also be derived by a Fermi's golden rule approach 46 , this spin transfer can, in fact, be treated perturbatively 51 . Note that in some situations, e. g., for excitations close to the band edge in two-and lower-dimensional DMS 52 , the Markov limit is not a good approximation so that deviations from a golden-rule-like exponential decay are predicted.…”

“…(18) it is important to recall that the correlations typically build up on the timescale of a few fs 52 , while the spin-up and spin-down occupations change on a ps timescale 46,49 . Thus, H cor sd can be interpreted as a quasi-equilibrium value of the correlation energy for given values of adiabatically changing occupations n ↑/↓ k1 .…”