Abstract
We study the non-equilibrium dynamics of a spinful single-orbital quantum dot with an incorporated quantum mechanical spin-1/2 magnetic impurity. Due to the spin degeneracy, double occupancy is allowed, and Coulomb interaction together with the exchange coupling of the magnetic impurity influence the dynamics. By extending the iterative summation of real-time path integrals (ISPI) to this coupled system, we monitor the time-dependent non-equilibrium current and the impurity spin polarization to determine features of the time-dependent non-equilibrium dynamics. We particulary focus on the deep quantum regime, where all time and energy scales are of the same order of magnitude and no small parameter is available. We observe a significant influence of the non-equilibrium decay of the impurity spin polarization both in the presence and in the absence of Coulomb interaction. The exponential relaxation is faster for larger bias voltages, electron–impurity interactions and temperatures. We show that the exact relaxation rate deviates from the corresponding perturbative result. In addition, we study in detail the impurity's back action on the charge current and find a reduction of the stationary current for increasing coupling to the impurity. Moreover, our approach allows us to systematically distinguish mean-field Coulomb and impurity effects from the influence of quantum fluctuations and flip-flop scattering, respectively. In fact, we find a local maximum of the current for a finite Coulomb interaction due to the presence of the impurity.
Highlights
Diluted magnetic semiconductors [1, 2, 3, 4] are an important class of materials for the spintronics community since they combine properties ofmagnets and semiconductors
We study the nonequilibrium dynamics of a spinful single-orbital quantum dot with an incorporated quantum mechanical spin-1/2 magnetic impurity
An ideal candidate for such a model system is a small quantum dot which connects metallic leads and carries a magnetic degree of freedom described by a quantum mechanical spin
Summary
Diluted magnetic semiconductors [1, 2, 3, 4] are an important class of materials for the spintronics community since they combine properties of (ferro-)magnets and semiconductors. We mention the switching of the spin state of the central iron ion in a single molecular complex in a double layer on gold by a low temperature scanning tunnelling microscope [19] for which our model is applicable It mimics features of the dynamics of electrons in quantum dots that are subject to hyperfine interactions with the nuclei of the host material. [48] to the magnetic Anderson model This approach evaluates a real time path integral expression for the Keldysh partition function in a numerically exact manner and is suitable for nonlinear transport. This scheme has been carefully verified by a comparison to existing approximations in the appropriate parameter regimes for the single-impurity Anderson model [48]. The dependence of the relaxation rate on various model parameters is presented
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