Strong Linear Dichroism in Spin-Polarized Photoemission from Spin-Orbit-Coupled Surface States

A comprehensive understanding of spin-polarized photoemission is crucial for accessing the electronic structure of spin-orbit coupled materials. Yet, the impact of the final state in the photoemission process on the photoelectron spin has been difficult to assess in these systems. We present experiments for the spin-orbit split states in a Bi-Ag surface alloy showing that the alteration of the final state with energy may cause a complete reversal of the photoelectron spin polarization. We explain the effect on the basis of ab initio one-step photoemission theory and describe how it originates from linear dichroism in the angular distribution of photoelectrons. Our analysis shows that the modulated photoelectron spin polarization reflects the intrinsic spin density of the surface state being sampled differently depending on the final state, and it indicates linear dichroism as a natural probe of spin-orbit coupling at surfaces.

Figure 1

Angle-resolved photoemission data of the spin-orbit split surface states in ${\mathrm{BiAg}}_2/\mathrm{Ag}(111)$ taken along the $\overline{\mathrm{\Gamma }}\overline{M}$ direction ($k_x$) using $p$-polarized in (a)–(c) and $s$-polarized light in (d). (e) Schematic of the spin-orbit split branches ${\mathrm{\Psi }}_{+}$ and ${\mathrm{\Psi }}_{-}$. (f) Sketch of the experimental geometry.

Figure 2

Modulation of the photoemission intensity of the spin-orbit split branches ${\mathrm{\Psi }}_{+}$ and ${\mathrm{\Psi }}_{-}$ in ${\mathrm{BiAg}}_2/\mathrm{Ag}(111)$ with photon energy (cf. Fig. 1). (a) energy distribution curves (EDC) at negative wave vectors $k_x$. The spectra were normalized to the background intensity at binding energies below 1.5 eV. The two peaks in each EDC are assigned to the branches ${\mathrm{\Psi }}_{+}$ and ${\mathrm{\Psi }}_{-}$. Calculated and measured intensities for ${\mathrm{\Psi }}_{+}$ depending on photon energy are shown in (b) and (c). (d) Calculated intensities $I_z$ and $I_x$ for the light electric field along $z$ and along $x$, respectively, for the branch ${\mathrm{\Psi }}_{+}$ at negative $k_x$. (e) Probability density $\rho (z)$ of the photoelectron final state $|\mathrm{\Phi }⟩$ as a function of the surface-normal coordinate $z$ and $\hslash \omega$. (f) Line profiles of $\rho (z)$ in (e) at selected photon energies.

Figure 3

Modulation of the photoelectron spin polarization in ${\mathrm{BiAg}}_2/\mathrm{Ag}(111)$ with excitation energy $\hslash \omega$. (a),(b) Spin-resolved EDC at positive (a) and negative (b) wave vectors along $k_y$ [cf. Figs. 1 and 1]. The spin-quantization axis of the measurement is aligned with the $x$ axis. (c) One-step photoemission calculation of the photoelectron spin polarization for the branch at lower energy along $k_y$ assuming $p$-polarized light and an angle of incidence $\theta =45°$. (d) Calculated net-spin photocurrents of the branch at lower energy at $k_y=\pm 0.1{\AA }^{-1}$ for $\theta =45°$ and $\theta =73°$ (e) Measured photoelectron spin polarization for the spin-orbit split branches depending on $\hslash \omega$, as extracted from the data in (a).