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We investigate the dynamics of Fe adatoms and dimers deposited on the Cu(111)metallic surface in the presence of spin-orbit coupling, within time-dependentdensity functional theory. The \textit{ab initio} results providematerial-dependent parameters that can be used in semiclassical approaches,which are used for insightful interpretations of the excitation modes. Bymanipulating the surroundings of the magnetic elements, we show that ellipticalprecessional motion may be induced through the modification of the magneticanisotropy energy. We also demonstrate how different kinds of spin precessionare realized, considering the symmetry of the magnetic anisotropy energy, theferro- or antiferromagnetic nature of the exchange coupling between theimpurities, and the strength of the magnetic damping. In particular, the normalmodes of a dimer depend on the initial magnetic configuration, changingdrastically by going from a ferromagnetic metastable state to theantiferromagnetic ground state. By taking into account the effect of thedamping into their resonant frequencies, we reveal that an importantcontribution arises for strongly biaxial systems and specially for theantiferromagnetic dimers with large exchange couplings. Counter intuitively,our results indicate that the magnetic damping influences the quantumfluctuations by decreasing the zero-point energy of the system.

Engineering elliptical spin-excitations by complex anisotropy fields in Fe adatoms and dimers on Cu(111)