Figure 1

(a) Principle of the formation of standing electron waves in the quantum film represented by a potential box. (b) Thickness dependence of quantum-well states. Photoelectron spectra in normal emission at 62.5 eV photon energy. Au and Ag coverage on W(110) increases from bottom to top. In addition to $sp$-type quantum-well states (downward triangles), a $d$-type quantum-well state (square) and a surface state of the W (upward triangles) are shown. (c) Two-dimensional Brillouin zones of bcc (110) substrate and fcc (111) quantum film. Present measurements follow the $\overline{\Gamma S}$ direction of the substrate. (d) Schematic for the case of two occupied quantum-well states. The spin-orbit interaction splits the free-electron-like dispersions leading to a spin-orbit splitting proportional to $k_{\parallel }$ and a spin-polarized “Russian nested doll” Fermi surface. No splitting occurs in normal emission ($k_{\parallel }=0$). For a given ${\mathbf{k}}_{\parallel }\ne \mathbf{0}$ (vertical line), four peaks are expected for the two quantum-well states with two spin orientations each.Reuse & Permissions

Figure 2

Spin-resolved photoemission at 50 eV photon energy and $k_{\parallel }(E_{\mathrm{F}})=-0.43{\AA }^{-1}$ for (a) Au and (b) Ag showing spin-orbit split quantum-well states which cause the spin-polarized Fermi surface. Upward triangles for spin-up and downward triangles for spin-down.Reuse & Permissions

Figure 3

Angle-dependendent photoemission representing $E(k_{\parallel })$ for 4 ML Au (a) spin averaged and (b) spin resolved. The first derivative of the photoemission intensity is shown, and the surface-projected band gap of W is marked (hatching outside of the gap). Crosses mark spin-resolved data from (b). (c) Ratio of the spin-orbit splitting ${\Delta }_{\mathrm{so}}$ in Ag and Au for comparable quantum-well states (quantum number $n$) from Fig. 2. The ratio is $\approx 1$. (d) ${\Delta }_{\mathrm{so}}$ vs $k_{\parallel }$ for the Au monolayer state and Au quantum-well states at different thicknesses. In strong contrast to the Au monolayer state which is hybridized with the W substrate, ${\Delta }_{\mathrm{so}}$ of the 5 ML quantum-well state is proportional to $k_{\parallel }$ in full agreement with the Rashba model. Squares and triangles denote spin-resolved measurements, and circles denote spin-averaged data.Reuse & Permissions