Surface electronic structure of Re(0001): A spin-resolved photoemission study

Abstract

The surface electronic structure of Re(0001) has been investigated in a combined experimental and theoretical study. Spin- and angle-resolved photoemission was employed to unravel the spin-dependent $E({\mathbf{k}}_{\ensuremath{\parallel}})$ dispersion of electronic states along the $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{M}}$ and $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{K}}$ directions. The results are compared with band-structure calculations based on density-functional theory. Additional calculations include transitions into final states by taking into account the corresponding matrix elements. Recently, Shockley- and Tamm-type surface states close to ${E}_{\mathrm{F}}$ were identified, which were found to be mixed by spin-orbit coupling. Here, we determined the Rashba parameter ${\ensuremath{\alpha}}_{\mathrm{R}}$ of the surface state around $\overline{\mathrm{\ensuremath{\Gamma}}}$ to 0.32 and $0.34\phantom{\rule{4pt}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\stackrel{\ifmmode \mathring{}\else \r{}\fi{}}{\mathrm{A}}$ along $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{M}}$ and $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.16em}{0ex}}\overline{\mathrm{K}}$, respectively. Furthermore, we extend our analysis to a wider $E({\mathbf{k}}_{\ensuremath{\parallel}})$ range revealing a multitude of electronic states along both high-symmetry directions. In particular, Rashba-type spin splittings are observed around the high-symmetry $\overline{\mathrm{\ensuremath{\Gamma}}}$ and $\overline{\mathrm{M}}$ points. At variance with theoretical predictions for a perfect hcp(0001) surface, we do not find any out-of-plane spin polarization. This is caused by monatomic steps of a real Re(0001) surface with alternating terminations, leading on average to an effective sixfold surface symmetry and vanishing net out-of-plane spin polarization.