Quantum kinetic theory of ultrafast phenomena in diluted magnetic semiconductors
Final Report Abstract
We have studied theoretically the ultrafast spin dynamics in diluted magnetic semiconductors (DMS), which are semiconductor materials with a low concentration of magnetic impurities. We considered samples of the II-VI family, like ZnSe and HgTe, in the often encountered regime where the concentration of electrons in the conduction band stemming from weak optical excitation is a low. Typically, the magnetic impurities are Mn atoms and the relevant spin dynamics takes place on time scales of tens or hundreds of picoseconds. A first result was that the widely used description of the spin transfer between conduction band carriers and magnetic impurities based on Fermi’s golden rule fails qualitatively to reproduce the predictions of an advanced quantum kinetic theory when applied to bulk DMS with a non-zero initial impurity magnetization. This result is remarkable because for zero initial impurity magnetization the golden rule treatment worked excellent in bulk DMS. We could show that this failure results from a precession-type time evolution of carrier-impurity correlations which is discarded in the golden rule limit. The prime methodical achievement of the project was the development of a reduced description for the dynamics in DMS driven by the exchange interaction between carriers and magnetic impurities. A key feature of this approach is to account for precessions of both the electronic spins as well as of the carrier-impurity correlations. We thus coined the name “Precession of Electron Spins and Correlations” (PESC) for this level of theory. The PESC equations have the advantage of an enormously reduced numerical load compared with the full quantum kinetic theory while keeping the accuracy of the full theory over a wide parameter range. Furthermore, the simplicity of the PESC equations allows for intuitive interpretations that are hard to reach in the full theory due to its complexity. The application of the PESC equations led to a wealth of new insights ranging from finding a deeper understanding under which conditions correlation induced memory effects may become important via enabling studies of the competition between exchange and spin orbit interactions to investigations of correlation induced divergences. In particular, we analyzed the interplay between the usually prevalent interaction in II-VI DMS, that is, the exchange sd-coupling, and the spin-orbit interaction, both in bulk and in quantum wells. Our main conclusion is that, far from being always a small perturbation, the spin-orbit interaction can affect qualitatively the ultrafast spin dynamics in realistic DMS. Here, it is important to note that in certain materials like Hg1−x−y Mnx Cdy Te the relative strength of the spin-orbit coupling compared with the exchange interaction can be tuned in a wide range by changing the doping fraction. We predict that reaching a regime of comparable spin-orbit and exchange interactions leads to experimentally observable strong modifications of the spin relaxation times and to strong oscillations in the spin evolution which are completely absent without the spin-orbit interaction. Thus, tailoring the relative importance of spin orbit and exchange interactions can lead to new spin control scenarios that cannot be envisioned when one of these interactions dominates. Our study initiates a subfield of study which may have implications in future technologies involving the control of the state of magnetic impurities in semiconductors, like data storage and quantum information processing. A further highlight of the present project is the derivation of analytical expressions for shifts of the precession frequency of the carrier spins and the carrier-impurity correlation energy in DMS using the PESC equations. In quasi-two-dimensional systems like quantum wells these quantities are shown to exhibit logarithmic divergences indicating the formation of strongly correlated carrier-impurity states. We also presented a comprehensive study of the sensitivity of the spin dynamics of electrons after photoexcitation with twisted light (light with orbital angular momentum) in the presence of spinorbit interactions in regular (non-magnetic) semiconductors. This study unveiled a surprising aspect of the spin-orbit interaction in extended semiconductor systems: The spin dynamics is for the most part insensitive to the orbital angular momentum state of the electrons (in our study, induced by the twisted light) when the electronic states merge into a continuum as is the case, e.g., in extended semiconductors for excitations above the band edge. This finding should be taken into consideration in the search for mechanisms to control the angular momentum transfer from orbital to spin degrees of freedom. Our work suggests that this search has the best perspectives for success in systems supporting discrete electronic states which applies, e.g., to strongly confined quantum structure.
Publications
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Insensitivity of spin dynamics to the orbital angular momentum transferred from twisted light to extended semiconductors. Phys. Rev. B. 92, 115301 (2015)
M. Cygorek, P. I. Tamborenea, and V. M. Axt
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Ultrafast spin dynamics in II-VI diluted magnetic semiconductors with spin-orbit interaction. Phys. Rev. B 91, 195201 (2015)
F. Ungar, M. Cygorek, P. I. Tamborenea, and V. M. Axt
