We study the behaviour of the magnetization in a half-metallic ferromagnet/nonmagnetic insulator/ferromagnetic metal/paramagnetic metal (FM1/NI/FM2/PM) tunnel junction. It is calculated self-consistently within the nonequilibrium Keldysh formalism. T
he magnetic regions are treated as band ferromagnets and are described by the single-band Hubbard model. We developed a nonequilibrium spectral density approach to solve the Hubbard model approximately in the switching magnet. By applying a voltage to the junction it is possible to switch between antiparallel (AP) and parallel (P) alignment of the magnetizations of the two ferromagnets. The transition from AP to P occurs for positive voltages while the inverse transition from P to AP can be induced by negative voltages only. This behaviour is in agreement with the Slonczewski model of current-induced switching and appears self-consistently within the model, i.e. without using half-classical methods like the Landau-Lifshitz-Gilbert equation.
Using the Keldysh formalism the tunneling current through a hybrid structure where a confined magnetic insulator (I) is sandwiched between two non-magnetic leads is calculated. The leads can be either normal metals (M) or superconductors (S). Each re
gion is modelled as a single band in tight-binding approximation in order to understand the formation of the tunneling current as clearly as possible. The tunneling process itself is simulated by a hybridization between the lead and insulator conduction bands. The insulator is assumed to have localized moments which can interact with the tunneling electrons. This is described by the Kondo Lattice Model (KLM) and treated within an interpolating self-energy approach. For the superconductor the mean-field BCS theory is used. The spin polarization of the current shows a strong dependence both on the applied voltage and the properties of the materials. Even for this idealized three band model there is a qualitative agreement with experiment.
