Giant Spin Splitting through Surface Alloying

The long-range ordered surface alloy $\mathrm{Bi}/\mathrm{Ag}(111)$ is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane.

Figure 1

(a) Schematic top view of the $(\sqrt{3}\times \sqrt{3})R30°$ $\mathrm{Bi}/\mathrm{Ag}(111)$ surface alloy [Bi, light gray (orange); Ag, dark gray (blue)]. (b) Side view of the schematic, illustrating the outward relaxation of Bi in the surface layer. (c) Experimental band structure obtained by ARPES. The abscissa is the wave vector $k_x$ along the $\overline{M}\mathrm{\text{−}}\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ line in the vicinity of the center of the surface alloy Brillouin zone ($\overline{\Gamma }$, i.e., ${\mathit{k}}_{\parallel }=0$). The ordinate gives the energy below the Fermi level (0 eV).

Figure 2

Band structure measurements by ARPES (left-hand panels) and calculations (right-hand panels) in the vicinity of the $\overline{\Gamma }$ point. Note the different horizontal scales.

Figure 3

(a)–(c) Constant energy contour of the spin polarization $\mathit{P}$ in $x$, $y$, and $z$ direction, respectively, at an energy of $-0.55\mathrm{eV}$. The projection in $x$, $y$, and $z$ direction is shown in (a)–(c), respectively. The intensity scale is linear with red and blue coloring corresponding to positive and negative values, respectively. White areas indicate sign changes, where the projection is zero. The constant energy contours of the band dispersion are shown as black lines, where the two inner contours correspond to the first set of bands in Fig. 1c, while the two outer contours correspond to the second set of bands. (d) Constant energy map by ARPES at an energy of $-0.17\mathrm{eV}$.