Theory of single spin inelastic tunneling spectroscopy

Recent work shows that inelastic electron scanning tunneling microscope (STM) probes the elementary spin excitations of a single and a few magnetic atoms in a thin insulating layer. Here I show that this new type of spectroscopy is described using a phenomenological spin-assisted tunneling Hamiltonian. Within this formalism, the inelastic $dI/dV$ lineshape is related to the spin spectral weight of the probed magnetic atom. This accounts for the spin selection rules observed experimentally. The theory agrees well with existing STM experiments for single Fe and Mn atoms as well as linear chains a few Mn atoms. The magnetic anisotropy in the inelastic $dI/dV$ and the marked odd-even $N$ effects are accounted for by the theory.