Figure 1

Surface state wave functions for two extreme cases of step densities on vicinal Au(111): (a) the electrons are confined within each terrace and (b) they are delocalized on the average surface. (c) Graphical representation, for case (a), of the main Fermi surfaces (solid circles) and the umklapp states (dotted circles) induced by the step superlattice. Directions of the tangential in-plane spin polarization vectors are included. The sample coordinate system and the experimental setup are schematically represented in (d) and (e), respectively. $\alpha$ is the miscut angle and $d$ is the distance between steps. A slight sample tilt around the $x$-axis could not be corrected, therefore momentum scans along $k_x$ follow the green dashed line in (c) rather than the high symmetry gray line.Reuse & Permissions

Figure 2

Spin-integrated ARPES data from Au(11 12 12), Au(7 8 8) and Au(2 2 3), representing Fermi surface maps (a)–(c) and band dispersions perpendicular to the steps (d)–(f), taken with 21 eV photon energy. The surface state bands are broadened due to the terrace width distribution, completely masking the spin splitting. For Au(11 12 12) and Au(7 8 8) weak replica due to umklapp scattering are observed.Reuse & Permissions

Figure 3

Spin-resolved MDCs from the three investigated vicinal surfaces taken with 23 eV photon energy [binding energies: 0.10 eV for Au(11 12 12) and Au(7 8 8), 0.05 eV for Au(2 2 3)] obtained by rotation of ${\Theta }_s$ in Fig. 1e. The top graphs (a)–(c) give the spin-integrated intensities, showing also the fitted peak profiles used for the two-step fitting routine described in the text. In the graphs (d)–(f), the corresponding spin polarization curves and errors for the $x$ (green open circles), $y$ (magenta open squares), and $z$ (black triangles) components are represented. The polarization fits (see text) are shown as continuous lines in the corresponding color. The discontinuous line in (f) corresponds to the $y$ polarization fit when fixing the splitting to the flat Au(111) value. The bottom panels (g)–(i) show the resulting polarization vectors for the individual peaks. In the top and bottom graphs the components from the main (umklapp) states are indicated as continuous (discontinuous) lines using the same color codes. Each of the bottom panels gives the in-plane (left) and the out-of-plane (right) orientation of the spin polarization vectors.Reuse & Permissions