Dynamics of excited electrons in copper and ferromagnetic transition metals: Theory and experiment

Both theoretical and experimental results for the dynamics of photoexcited electrons at surfaces of Cu and the ferromagnetic transition metals Fe, Co, and Ni are presented. A model for the dynamics of excited electrons is developed, which is based on the Boltzmann equation and includes effects of photoexcitation, electron-electron scattering, secondary electrons (cascade and Auger electrons), and transport of excited carriers out of the detection region. From this we determine the time-resolved two-photon photoemission (TR-2PPE). Thus a direct comparison of calculated relaxation times with experimental results by means of TR-2PPE becomes possible. The comparison indicates that the magnitudes of the spin-averaged relaxation time $\tau$ and of the ratio ${\tau }_{\uparrow }/{\tau }_{\downarrow }$ of majority and minority relaxation times for the different ferromagnetic transition metals result not only from density-of-states effects, but also from different Coulomb matrix elements M. Taking $M_{\mathrm{Fe}}>M_{\mathrm{Cu}}>M_{\mathrm{Ni}}{=M}_{\mathrm{Co}}$ we get reasonable agreement with experiments.