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Theoretical probing of inelastic spin-excitations in adatoms on surfaces

We review our recent work on the simulation, description and prediction of spin-excitations in adatoms and dimers deposited on metallic surfaces. This work done together with Douglas L. Mills, is an extension of his seminal contribution (with Pascal Lederer) published 50 years ago on the spin-dynamics of transition metal impurities embedded in transition metal hosts [P. Lederer, D.L. Mills, Phys. Rev. {\bf 160}, 590 (1967)]. The main predictions of his model were verified experimentally with state of the art inelastic scanning tunneling spectroscopy on adatoms. Our formalism, presented in this review, is based on time-dependent density functional theory, combined with the Korringa-Kohn-Rostoker Green function method. Comparison to experiments is shown and discussed in detail. Our scheme enables the description and prediction of the main characteristics of these excitations, \emph{i.e.} their resonance frequency, their lifetime and their behavior upon application of external perturbations such as a magnetic field.