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

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-dependent density functional theory. The ab initio results provide material-dependent parameters that can be used in semiclassical approaches, which are used for insightful interpretations of the excitation modes. By manipulating the surroundings of the magnetic elements, we show that elliptical precessional motion may be induced through the modification of the magnetic anisotropy energy. We also demonstrate how different kinds of spin precession are realized, considering the symmetry of the magnetic anisotropy energy, the ferro- or antiferromagnetic nature of the exchange coupling between the impurities, and the strength of the magnetic damping. In particular, the normal modes of a dimer depend on the initial magnetic configuration, changing drastically by going from a ferromagnetic metastable state to the antiferromagnetic ground state. By taking into account the effect of the damping into their resonant frequencies, we reveal that an important contribution arises for strongly biaxial systems and specially for the antiferromagnetic dimers with large exchange couplings. Counterintuitively, our results indicate that the magnetic damping influences the quantum fluctuations by decreasing the zero-point energy of the system