Photoemission of a Quantum Cavity with a Nonmagnetic Spin Separator

Quantum well states are a consequence of confinement in a quantum cavity. In this study we investigate with photoemission the influence of the interface electronic structure on the quantum well state energy dispersion in ultrathin Mg(0001) films on $W(110)$. Coupling between the $sp$-derived quantum well states and the substrate across the interface becomes manifest in a deviation from free electronlike dispersion behavior. Most importantly, we observe a marked level splitting, which is interpreted as due to the Rashba effect at the interface. Such an interfacial electron beam splitting on materials with strong spin-orbit coupling is an essential ingredient for novel spintronic devices. The combination of a quantum cavity with a heavy, electron reflecting substrate reveals spin-splitting effects in ultrathin films without conventional magnetism being involved.

Figure 1

(a) Quantum well states as seen by ultraviolet photoemission [modified VG Escalab MkII with a monochromatized hydrogen $L{y}_{\alpha }(h\nu =10.2\mathrm{eV})$ photon source] in normal emission geometry at $T=300\mathrm{K}$. States above the surface state energy at $-1.7\mathrm{eV}$ are QWS. The film thickness for the spectra is given in units of unit cells (5.21 Å), comprising two atomic layers. (b) Experimental cavity with surface and interface boundary and three cavity modes. An off-normal quantum well state, characterized by a wave vector component parallel to the surface, $k_{\parallel }$, indicating a sidewards displacement. (c) Ideal cavity with infinitely high walls. (d) Difference between a confined quantum well state and a leaky quantum well resonance with a corresponding change in wavelength. (e) Vectorial representation of the effective in-plane magnetic field, $B_{\mathrm{eff}}$, at the Rashba interface. (f) Brillouin zones with high symmetry points for the epitaxial relationship between the sixfold symmetric (${\mathrm{C}}_6$) Mg(0001) thin film and the twofold symmetric (${\mathrm{C}}_2$) $W(110)$ substrate.

Figure 2

Fermi surface contours displayed as a function of $k_{\parallel }$. Marked is the hexagonal Mg Brillouin zone with high symmetry points $\overline{\Gamma }$, $\overline{M}$, $\overline{K}$; SS labels free electronlike surface state and $n=1$, 2 successive QWS; symbols are identical to the ones in Fig. 3. (a) Theoretical Fermi surface for a 3 unit cell thick slab, obtained with the $\mathrm{\text{APW}}+\mathrm{\text{lo}}$ code wien2k [19]. (b) and (c) Experimental Fermi surface map for a three and eight unit cell thick film, respectively; experimental raw data are plotted in the lower left part (i.e., below the 135° diagonal line) and asymmetry plots [11] in the upper part; the curved black line marks the border between the surface projected bulk states and surface projected bulk gap; it falls together with strong deviations from the circular symmetry, highlighted in the asymmetry plots (see upper part). The color bar (right side) indicates the intensity scale.

Figure 3

$E(k_{\parallel })$ dispersion plots for 4, 6, 8, and 11 unit cell thick films taken along the 135° diagonal line (Fig. 2) are displayed in (a), (b), (c), and (d), respectively. Consecutive QWS $n=1$, 2, 3 and the surface state (SS) are labeled. The second derivative of the measurements is shown to highlight the different features. The surface projected band structure of $W(110)$ appears as an overlay of white dots. Empty and filled circles mark the surface state and its splitting; empty and filled triangles label the $n=1$ QWS and its splitting.