The authors discuss here a theory of the inelastic electron tunneling spectra of a magnetic nanosystem (an atom or a molecule) adsorbed on a solid surface measured in a scanning tunneling microscope. They study scenarios when the tunneling electrons sequentially interact with several magnetic centers or when the magnetic centers are made out of heavy atoms with a strong spin-orbit coupling. They discuss how the exchange interaction between the nanosystem and the tunneling electrons changes when orbital moments enter the picture.
Kolorenč et al. (Fri,) studied this question.