We have performed single-atom magnetization curve (SAMC) measurements and inelastic scanning tunneling spectroscopy (ISTS) on individual Fe atoms on a Cu(111) surface. The SAMCs show a broad distribution of magnetic moments with 3.5 mu(B) being the mean value. ISTS reveals a magnetization excitation with a lifetime of 200 fsec which decreases by a factor of 2 upon application of a magnetic field of 12 T. The experimental observations are quantitatively explained by the decay of the magnetization excitation into Stoner modes of the itinerant electron system as shown by newly developed theoretical modeling.