Influence of d electrons on the dispersion relation of Ag surface plasmons for different single-crystal faces

The surface plasmon dispersion relation of Ag is calculated for different single-crystal orientations. To describe the dynamical response properties of both delocalized 5s electrons and more tightly bound 4d electrons, the jellium model is combined with the so-called dipolium model, in which the occupied Ag d bands are represented in terms of polarizable spheres located at the sites of a semi-infinite fee lattice. The nonlocal susceptibility characterizing the s electron response in the surface region is derived using density functional theory. The screening of the Coulomb interaction between conduction electrons via the lattice of dipoles, and of the dipole interaction via the surrounding sea of conduction electrons, is treated self-consistently. Electron energy loss spectra are calculated for all three low-index faces. The surface plasmon energy is found to increase with parallel wave vector for all cases. The magnitude of the positive slope depends on the crystal orientation and, for Ag(110), on the propagation direction. These results are in qualitative agreement with electron energy loss measurements.