Electronic transport and correlations in single magnetic molecule devices

In this dissertation, we study the most important microscopic aspects that grant molecules such as Single Molecule Magnets (SMMs) their preferential spin direction. We do so by proposing and solving a model that includes correlations between electrons occupying atomic orbitals. In addition, we study the relation between the non-equilibrium electronic transport signatures in a SMM model weakly coupled to a three-terminal single electron transistor device, and the interference features of the SMM model in the presence of a magnetic field. Finally, we investigate the equilibrium transport features in a giant-spin model of a SMM in the Kondo regime. We study how the magnetic field modulation of the energy in a highly anisotropic molecule can affect the conductance of the molecule in the Kondo regime