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Schematic graph of the model setup. The layers are labeled with l, such that l < 0 corresponds to the left, and l > 0 to the right lead. The central layer is l ¼ 0. In the present setup, the z-direction, here labeled by l, is the direction of transport. The transverse (w.r.t. the transport direction) wave vector, k k ¼ ðk x , k y Þ, is a good quantum number.
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The transmission through a magnetic layer of correlated electrons sandwiched between non-interacting normal-metal leads is studied within model calculations. We consider the linear regime in the framework of the Meir–Wingreen formalism, according to which the transmission can be interpreted as the overlap of the spectral function of the surface lay...
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... the contrary, for two or more interacting layers, the lesser Green's function will be needed. Figure 1 shows the geometry of the system: noninteracting leads, left (L) and right (R), separated by the central region (C). Both leads consist of a semiinfinite stack of square-lattice planes. ...
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Citations
Many fascinating features in condensed matter systems emerge due to the interaction between electrons. Magnetism is such a paramount consequence, which is explained in terms of the exchange interaction of electrons. Another prime example is the metal-to-Mott-insulator transition, where the energy cost of Coulomb repulsion competes against the kinetic energy, the latter favoring delocalization. While systems of correlated electrons are exciting and show remarkable and technologically promising physical properties, they are difficult to treat theoretically. A single-particle description is insufficient; the quantum many-body problem of interacting electrons has to be solved. In the present thesis, we study physical properties of half-metallic ferromagnets which are used in spintronic devices. Half-metals exhibit a metallic spin channel, while the other spin channel is insulating; they are characterized by a high spin polarization. This thesis contributes to the development of numerical methods and applies them to models of half-metallic ferromagnets. Throughout this work, the single-band Hubbard Hamiltonian is considered, and electronic correlations are treated within dynamical mean-field theory. Instead of directly solving the lattice model, the dynamical mean-field theory amounts to solving a local, effective impurity problem that is determined self-consistently. At finite temperatures, this impurity problem is solved employing continuous-time quantum Monte Carlo algorithms formulated in the action formalism. As these algorithms are formulated in imaginary time, an analytic continuation is required to obtain spectral functions. We formulate a version of the N-point Padé algorithm that calculates the location of the poles in a least-squares sense. To directly obtain spectra for real frequencies, we employ Hamiltonian-based tensor network methods at zero temperature. We also summarize the ideas of the density matrix renormalization group algorithm, and of the time evolution using the time-dependent variational principle, employing a diagrammatic notation. Real materials never display perfect translational symmetry. Thus, realistic models require the inclusion of disorder effects. In this work, we discuss these within a single-site approximation, the coherent potential approximation, and combine it with the dynamical mean-field theory, allowing to treat interacting electrons in multicomponent alloys on a local level. We extend this combined scheme to off-diagonal disorder, that is, disorder in the hopping amplitudes, by employing the Blackman–Esterling–Berk formalism. For this purpose, we illustrate the ideas of this formalism using tensor diagrams and provide an efficient implementation. The structure of the effective medium is discussed, and a concentration scaling is proposed that resolves some of its peculiarities. The limit of vanishing hopping between different components is discussed and solved analytically for the Bethe lattice with a general coordination number. We exemplify the combined algorithm for a Bethe lattice, showing results that exhibit alloy-band-insulator to correlated-metal to Mott-insulator transitions. We study models of half-metallic ferromagnets to elucidate the effects of local electronic correlations on the spectral function. To model half-metallicity, a static spin splitting is used to produce the half-metallic density of states. Applying the Padé analytic continuation to the self-energy instead of the Green’s function produces reliable spectral functions agreeing with the zero-temperature results obtained for real frequencies. To address transport properties, we investigate the interface of a half-metallic layer and a metallic, band insulating, or Mott insulating layer. We observe charge reconstruction which induces metallicity at the interface; quasiparticle states are present in the Mott insulating layer even for a large Hubbard interaction. The transmission through a barrier made of such a single interacting half-metallic layer sandwiched by metallic leads is studied employing the Meir–Wingreen formalism. This allows for a transparent calculation of the transmission in the presence of the Hubbard interaction. For a strong coupling of the central layer to the leads, we identify high intensity bound states which do not contribute to the transmission. For small coupling, on the other hand, we find resonant states which enhance the transmission. In particular, we demonstrate that even for a single half-metallic layer, highly polarized transmissions are achievable.
We present a combination of density functional theory and dynamical mean-field theory (DMFT) for computing the electron transmission through two-terminal nanoscale devices. The method is then applied to metallic junctions presenting alternating Cu and Co layers, which exhibit spin-dependent charge transport and the giant magnetoresistance (GMR) effect. The calculations show that the coherent transmission through the 3d states is greatly suppressed by electron correlations. This is mainly due to the finite lifetime induced by the electron-electron interaction and is directly related to the imaginary part of the computed many-body DMFT self-energy. At the Fermi energy, where in accordance with the Fermi-liquid behavior the imaginary part of the self-energy vanishes, the suppression of the transmission is entirely due to the shifts of the energy spectrum induced by electron correlations. Based on our results, we finally suggest that the GMR measured in Cu/Co heterostructures for electrons with energies about 1 eV above the Fermi energy is a manifestation of dynamical correlation effects.
