Ambiguity of Experimental Spin Information from States with Mixed Orbital Symmetries

The spin texture of the unoccupied bands of the surface alloy $\mathrm{Bi}/\mathrm{Ag}(111)$ is investigated with spin- and angle-resolved inverse photoemission and first-principles calculations. Surprisingly, the measured spin character does not always reflect the calculated spin texture of the bands. With the help of photoemission calculations within the one-step model, however, the discrepancy is traced back to the influence of the orbital symmetry of the respective states in combination with the experimental geometry. In particular, the calculations show that the spin texture of a surface band with mixed orbital symmetries may neither be recovered with $s$- nor $p$- nor unpolarized light. In general, spin information from direct or inverse photoemission experiments on electronic states with mixed orbital symmetries at spin-orbit-influenced surfaces has to be taken with a pinch of salt, while it remains reliable for states with pure symmetry.

Figure 1

Spin-resolved IPE spectra for various angles of electron incidence $\theta$ along $\overline{\mathrm{\Gamma }}\overline{K}$ of the alloy surface Brillouin zone. Data points represent spin-integrated (black), spin-up (red), and spin-down (blue) intensities. Solid lines serve as guide to the eye. In the inset, a sketch of the experimental setup is given, which is sensitive to the Rashba component of the spin polarization.

Figure 2

Surface electronic structure of $\mathrm{Bi}/\mathrm{Ag}(111)$. (a) Energy vs $k_{\parallel }$ dispersion as derived from the IPE data in Fig. 1. The color code is identical to that in Fig. 1. Experimental uncertainties are smaller than the symbol size. (b) Calculated spectral function $n(E,k_{\parallel })$. Surface states appear as dark features while the bulk-derived states appear as light gray regions. (c) Difference $n_{\uparrow }(E,k_{\parallel })-n_{\downarrow }(E,k_{\parallel })$ of the spin-projected spectral densities, indicated in red (blue) where spin-up (spin-down) intensity exceeds (white is for zero difference).

Figure 3

Calculated spin-integrated PE and IPE intensities (upper row) and differences of the spin-resolved intensities $I_{\uparrow }(E,k_{\parallel })-I_{\downarrow }(E,k_{\parallel })$ (lower row) for (a) $p$-polarized, (b) $s$-polarized, and (c) unpolarized light ($p\text{−}\mathrm{pol}+s\text{−}\mathrm{pol}$).

Figure 4

Orbital decomposition of the spin-integrated (upper row) and spin-projected (lower row) spectral densities from the spectral function shown in Figs. 2 and 2. $x$, $y$, and $z$ directions as defined in Fig. 1.