  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
function, the impurity-free surface Green function, and the tunneling matrix
elements. This generalizes Fano's analysis to the interacting case. The
differential-conductance lineshapes seen in recent STM experiments with the tip
directly over the magnetic adatom are reproduced within our model, as is the
rapid decay, \sim 10\AA, 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.
