Lifetime of surface states on (0001) surfaces of lanthanide metals

We have studied the electronic structure of surface states on (0001) surfaces of Gd, Ho, and Lu films with scanning-tunneling spectroscopy at low temperature (10 K). The ${5d}_{z^2}$-like surface states have a small dispersion and exhibit magnetic exchange splittings that are proportional to the $4f$-spin moment, being largest for Gd and zero for Lu. The surface state in Lu lies directly at the Fermi energy, resulting in a sharp peak in the tunneling spectrum. A line-shape analysis of the tunneling spectra reveals linewidths and, hence, lifetimes of surface-state electrons governed by electron-phonon and electron-electron scattering.