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In the modern world there is an ever growing demand for new electronic devices that need to be smaller, faster and at the same time consume less energy. The silicon technology, however, reached a level of miniaturization that is difficult to overcome. In the last years, this fueled the research towards alternatives, and spintronics is a very promising one. In spintronics the charge is replaced by the spin as main quantity of interest in the functioning of devices. The electronic spin can be controlled in Multiferroic Tunnel Junctions, devices in which the tunneling properties are tuned through the manipulation of magnetism and ferroelectricity. In order to design efficient spintronic memories and transistors, the physical processes taking place at the microscopical level must be fully understood. Theoretical investigations can at the same help unraveling experimental findings and lead the research towards the most promising systems.In this thesis, Density Functional Theory as the main tool for theoretical investigations of multiferroic tunnel junctions. Three systems, consisting of different materials and possessing different properties, have been investigated with two main goals.\\The first is to show how a combined methods approach can lead to a description of a tunnel junction obtained completely ab-initio, and therefore not biased by empirical findings. To achieve this goal several codes has been used in parallel. Beside the "standard" DFT, employed in the determination of the electronic properties, cRPA was used to correct the description of correlations, and a Green function based embedding technique has been used to calculate transport properties.\\Second, this thesis aims at showing that theoretical investigations can be used to achieve a full description of a spintronic device, starting from the basic properties of the constituents of the junction, to arrive at the proposal of new mechanisms to exploit in novel devices.\\The properties of the compounds constituting the metallic leads, as well as the one constituting the tunnel barrier, have been studied in details. Particular focus received perovskite materials, such as the ferroelectric BaTiO$_3$ employed as a tunnel barrier and the double perovskite Sr$_2$FeMoO$_6$ used as a magnetic lead. Three different junctions have been investigated. The first, based on the ferromagnet/ferroelectric Fe/BaTiO$_3$ interface, is considered a prototypical junction for the study of magnetoelectric coupling in spintronic devices. The importance of the ferromagnet/ferroelectric Sr$_2$FeMoO$_6$/BaTiO$_6$ interface of the second investigated junction, lies in the full spin polarization achievable due to the half-metallicity of the double perovskite. The third studied system is a ferroelectric junction based on GeTe, in which the ferroelectric polarization can be used as the handle to control the emergence of a spin current due to a Rashba splitting in GeTe bulk bands.

Effective low-energy Hamiltonians for several different families of iron-based superconductors are compared after deriving them from the downfolding scheme based on first-principles calculations. Systematic dependences of the derived model parameters on the families are elucidated, many of which are understood from the systematic variation of the covalency between Fe-3d and pnictogen-/chalcogen-p orbitals., Comment: 23 pages, 7 figures and 12 tables. To appear in J. Phys. Soc. Jpn. The revised version contains a comment on the transfer integrals in the caption of Table |V. Table |V-V|| have been revised accordingly.