Low-energy collective electronic excitations in Pd metal

Abstract

A theoretical study of collective electronic excitations in Pd at low-energy (from 0 to $\ensuremath{\sim}3\text{ }\text{eV}$) domain is reported. The calculations were performed with full inclusion of the electron band structure obtained within self-consistent pseudopotential approach. We show that the presence in Pd of two kinds of carriers (in $s\text{\penalty1000-\hskip0pt}p$ and $d$ bands) at the Fermi level produces dramatic modification of the excitation spectra in this energy range in comparison with free-electron-like model prediction. In particular, at small momenta a peculiar plasmon mode with characteristic sound-like dispersion---an acoustic plasmon---is predicted to exist in this material. This mode has strong directional dependence on the momentum transfer: whereas for momenta along the $⟨100⟩$ and $⟨111⟩$ symmetry directions it arises as a single mode up to $\ensuremath{\sim}1\text{ }\text{eV}$, along the $⟨110⟩$ direction two acoustic modes (one of which disperses up to $\ensuremath{\sim}2.5\text{ }\text{eV}$) with different slope exist. As in many metallic systems, e.g., in transition metals, there are energy bands with large difference in the Fermi velocities, we expect that the existence of such plasmon mode must be a rather general phenomenon. Additionally, present calculations reveal other well-defined features in the energy-loss spectra in this low-energy range due to numerous interband transitions.