In latter years, a new field has emerged from the understanding, control and manipulation of objects at nanoscale level (nano-objects). It is commonly known as nanoscience. This field addresses a huge number of important issues starting from basic science and ending in a large variety of technological applications. Among the nano-objects, the small clusters or nanoclusters play a very important role, since they are the bricks of nanoscience. Therefore, the study of small clusters deserves a special attention. On the side of the technological applications in nanoscience, the study of the microscopic details of multilayer transition-metal systems is also very important because in this systems was discovered the giant magnetoresistance (GMR) effect. In this thesis we deal with transition-metal clusters and magnetic multilayers, both from a theoretical point of view, in such a way that the calculated atomic properties have been performed in the framework of the density functional theory. Thus, in the first part, we first studied the electronic structure, geometry, and magnetic properties of cobalt clusters ranging in size from the isolated atom up to a maximum of 13 cobalt atoms. After that, we concentrate our efforts in the study of small silver clusters with a number of atoms less or equal than 23 of which we have calculated the structure, static response to an external electric field, and the magnetic properties. Based on the magnetic properties we have found for these silver clusters, we have suggested a possible application of these clusters in biomedicine as magnetic drug delivery. We have also performed calculations of the electronic structure of the oxidized neutral and charged silver clusters. Eventually, we discussed the magnetic properties of cobalt-manganese alloy clusters, and in particular, the surprising enhancement of the magnetic moment recently observed in dilute CoMn alloy clusters was explained using ab initio methods.
On the other hand, in the second part of this thesis, we studied from ab initio methods the electronic structure and the magnetic properties of the Fe/Cr trilayer system. After the Fe/Cr system was well characterized from first principles calculations and the layer potentials were calculated, we used the theoretical models that we have developed to calculate the conductivity properties of the Fe/Cr system. We concentrate our efforts in the study of the GMR as a function of the interfacial scattering and the surface roughness. The importance of the ab initio monolayer potentials was also stressed in the thesis in order to confirm that the interface monolayers play a dominant role in the intrinsic GMR.
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