  We consider inelastic scattering of localized magnetic moments coupled with
the electrons on the surface. We argue that spin-inelastic transitions of the
magnetic impurities generate oscillations at a momentum $k$, corresponding to
the inelastic mode, in the second derivative of the current with respect to
voltage $d^2I/dV^2$. These oscillations are similar in nature to Friedel
oscillations. Inelastic Friedel oscillations, which were previously proposed
for spin-unpolarized set-up, is here extended for spin-polarized systems. We
propose to use scanning tunneling microscope to measure spin-inelastic
scattering generated at the impurity spin by imaging the $d^2I/dV^2$
oscillations on the metal surface.
