Electronic Stopping of Slow Protons in Transition and Rare Earth Metals: Breakdown of the Free Electron Gas Concept

The electronic stopping cross sections (SCS) of Ta and Gd for slow protons have been investigated experimentally. The data are compared to the results for Pt and Au to learn how electronic stopping in transition and rare earth metals correlates with features of the electronic band structures. The extraordinarily high SCS observed for protons in Ta and Gd cannot be understood in terms of a free electron gas model, but are related to the high densities of both occupied and unoccupied electronic states in these metals.

Figure 1

Experimental and simulated energy spectra of 10 keV ${\mathrm{D}}^{+}$ scattered from Au and Gd are shown. trbs simulations (solid lines) and experimental spectra (open symbols) coincide when experimentally deduced SCS are employed. Dashed lines represent the energy interval used in the evaluation, short-dashed spectra refer to simulations in which ${ϵ}_{\mathrm{Gd}}$ was varied by $\pm 20\%$.

Figure 2

Electronic SCS of Gd for H ions (protons and deuterons) are shown as function of the proton energy in the range 0.5 keV–10 MeV (LEIS data: full circles, RBS data: full triangles). Also displayed is a fit to the complete data set. Open symbols refer to data from Refs. [33, 34, 35, 36].

Figure 3

Electronic SCS of Au, Pt, Ta, and Gd for protons are displayed as function of the ion velocity in atomic units. The upper abscissa denotes the corresponding proton energies.

Figure 4

Electronic densities of states (DOS) are shown for the conduction bands of Au, Pt, Ta, and Gd, as function of $E\text{−}{E}_F$. The filled part of the DOS corresponds to the occupied states. For the DOS of Gd dotted lines indicate below and above $E_F$ the energy intervals, in which the high features due to the $f$ band were scaled down by factors of 30 and 4, respectively.