Probing Magnetism at the Atomic Scale:  Non-Equilibrium Statistical Mechanics Theoretical Treatise

Sammanfattning: Here, I present a theoretical study, based on non-equilibrium quantum statistical mechanics and on the non-equilibrium extension to the RKKY intveraction,where I investigate the emergence of magnetism at the atomic scale in adsorbed molecular complexes hosting localized spin moments, at the stake of being probed with scanning tunneling microscopy tip, and being driven by a temperature gradient and gated by an electric field. The scanning tunneling microscopy set up is modeled as a molecular junction with a magnetic molecule embedded within it, where the molecule consists in a set of electronic levels resembling the typical s-p orbitals of a metal hydride or an organometal, and a localized spin moment resembling the magnetic unit hosted by the latter and former type of molecules mentioned. The electronic levels and the magnetic units are coupled via the Kondo interaction. One of the electrodes in the junction plays the role of an scanning tunneling microscopy tip, and the other one, does it for the metal in which the molecule is adsorbed, and a bias voltage and a temperature gradient is applied across both metals, giving rise to the effect of the above mentioned experimental set up and producing electrical, spin, energy and heat currents as a response, providing the possibility to predict experimentally observed quantities such as differential conductivities. Throughout the thesis, I present first a comprehensive introduction to the topic pointing out its relevance, the experimental context in which the work I append lies and I as well present the formal structure of the work I present. The upcoming chapters, lead the audience to the discussion of the non-equilibrium formalism in atomic, molecular and condensed matter physics, paying special attention on the subject on magnetism, and putting in to context the molecular system where the interplay, among electrons, spins and phonons is relevant. To wrap up the theoretical discussion I described the state of the art progress on quantum coherence and interferometry in molecular junctions and locate my contribution into this context. Then I conclude and summarize. My contribution promises to pave the way to more robust spin based quantum engineered technology.