Theory of scanning tunneling spectroscopy of a magnetic adatom on a metallic surface

A comprehensive theory is presented for the voltage, temperature, and spatial dependence of the tunneling current between a scanning tunneling microscope (STM) tip and a metallic surface with an individual magnetic adatom. Modeling the adatom by a nondegenerate Anderson impurity, a general expression is derived for a weak tunneling current in terms of the dressed impurity Green's function, the impurity-free surface Green's function, and the tunneling matrix elements. This generalizes Fano's analysis to the interacting case. The differential-conductance line shapes seen in recent STM experiments with the tip directly over the magnetic adatom are reproduced within our model, as is the rapid decay, similar to 10 Angstrom, of the low-bias structure as one moves the tip away from the adatom. With our simple model for the electronic structure of the surface, there is no dip in the differential conductance at approximately one lattice spacing from the magnetic adatom, but rather we see a resonant enhancement. The formalism for tunneling into small clusters of magnetic adatoms is developed.