Experimental energy dispersions for valence and conduction bands of palladium

Abstract

Using angle-resolved photoemission with synchrotron radiation, we have determined accurate energy-versus-momentum dispersion relations along the $〈111〉$ direction using a Pd(111) crystal. The energy $E$ (\ensuremath{\lesssim} 0.1 eV accuracy) and the momentum parallel to the surface ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$ are measured directly. The perpendicular component of the momentum ${k}_{\ensuremath{\perp}}$ is obtained from the measured final energy via a calculated free-electron-like final band that is found to be accurate within \ifmmode\pm\else\textpm\fi{}5% of the zone-boundary momentum by comparison with certain critical points that have been measured directly (${L}_{1}$, ${{\ensuremath{\Gamma}}^{\ensuremath{'}}}_{2}$, and ${\ensuremath{\Gamma}}_{15}$). For the initial bands, we find the dispersions of the two $d$-like ${\ensuremath{\Lambda}}_{3}$ bands and of the $\mathrm{sp}$-type ${\ensuremath{\Lambda}}_{1}$ band. Measured critical points (in eV) for bands numbered with increasing energy are: ${\ensuremath{\Gamma}}_{2,3,4}=\ensuremath{-}2.55\ifmmode\pm\else\textpm\fi{}0.15$, ${\ensuremath{\Gamma}}_{5,6}=\ensuremath{-}1.15\ifmmode\pm\else\textpm\fi{}0.1$, ${\ensuremath{\Gamma}}_{7}=18.4\ifmmode\pm\else\textpm\fi{}0.5$, ${\ensuremath{\Gamma}}_{8}=21.7\ifmmode\pm\else\textpm\fi{}0.5$, ${L}_{4}=\ensuremath{-}0.4\ifmmode\pm\else\textpm\fi{}0.2$, ${L}_{5}\ensuremath{-}0.1\ifmmode\pm\else\textpm\fi{}0.1$, and ${L}_{7}=7.7\ifmmode\pm\else\textpm\fi{}0.3$. Spin-orbit splitting (\ensuremath{\sim} 0.4 eV maximum) is observed for the upper ${\ensuremath{\Lambda}}_{3}$ band.