Microscopic theory of spin relaxation of a single Fe adatom coupled to substrate vibrations

Understanding the spin-relaxation mechanism of single adatoms is an essential step towards creating atomic magnetic memory bits or even qubits. Here we present essentially parameter-free theory by combining \textit{ab-initio} electronic and vibrational properties with many-body nature states. Our calculations account for millisecond spin lifetime measured recently on Fe MgO/Ag(100) reproduce dependence number decoupling layers external field. We show how interaction environment should be tuned in order to enhance stability, propose a clear fingerprint experimentally detecting localized spin-phonon excitation.