Magnon-broadening of exchange-split surface states on lanthanide metals

Low-temperature scanning tunneling spectroscopy is used to study the electronic structure and the dynamics of d-like surface states on trivalent lanthanide metals from La to Lu. We find that the dynamics of these states, as revealed by their lifetime widths, is dominated by electron-phonon scattering in the occupied region and by electron-magnon scattering in the unoccupied region. We also show that the magnetic exchange splitting of these states scales with the $4f$ spin multiplied by an effective exchange-coupling constant that increases with $4f$ occupancy in an approximately linear way.