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The advent of milli-kelvin scanning tunneling microscopes (STM) with inbuiltmagnetic fields has opened access to the study of magnetic phenomena withatomic resolution at surfaces. In the case of single atoms adsorbed on asurface, the existence of different magnetic energy levels localized on theadsorbate is due to the breaking of the rotational invariance of the adsorbatespin by the interaction with its environment, leading to energy terms in themeV range. These structures were revealed by STM experiments in IBM Almaden inthe early 2000's for atomic adsorbates on CuN surfaces. The experimentsconsisted in the study of the changes in conductance caused by inelastictunnelling of electrons (IETS, Inelastic Electron Tunnelling Spectroscopy).Manganese and Iron adatoms were shown to have different magnetic anisotropiesinduced by the substrate. More experiments by other groups followed up, showingthat magnetic excitations could be detected in a variety of systems: e.g.complex organic molecules showed that their magnetic anistropy was dependent onthe molecular environment, piles of magnetic molecules showed that theyinteract via intermolecular exchange interaction, spin waves were excited onferromagnetic surfaces and in Mn chains, and magnetic impurities have beenanalyzed on semiconductors. These experiments brought up some intriguingquestions: the efficiency of magnetic excitations was very high, theexcitations could or could not involve spin flip of the exciting electron andsingular-like behavior was sometimes found at the excitation thresholds. Thesefacts called for extended theoretical analysis; perturbation theories,sudden-approximation approaches and a strong coupling scheme successfullyexplained most of the magnetic inelastic processes. In addition, many-bodyapproaches were also used to decipher the interplay between inelas

Excitation of local magnetic moments by tunnelling electrons