In this paper, we present the mathematical and implementation details of an ab initio method for calculating spin-polarized quantum transport properties of atomic scale spintronic devices under external bias potential. The method is based on carrying out density functional theory (DFT) within the Keldysh non-equilibrium Green's function (NEGF) formalism to calculate the self-consistent spin densities. We apply this method to investigate nonlinear and non-equilibrium spin-polarized transport in a Fe/MgO/Fe trilayer structure as a function of external bias voltage.
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