Rashba-type splitting of the Au(110) surface state: A combined inverse and direct photoemission study

The Shockley surface state located at $\overline{\mathrm{Y}}$ on the $(1\times 2)$-reconstructed Au(110) surface is predicted to exhibit a Rashba-type spin splitting. Previous photoemission experiments searched for this splitting but it could not be resolved yet. In order to uncover a possible splitting, the unoccupied surface state on Au(110) is examined with spin- and angle-resolved inverse photoemission, whereas Na-covered Au(110) allows for investigation of the now occupied surface state by means of spin- and angle-resolved direct photoemission. Our data show clear spin splittings in the order of $100\mathrm{meV}$ with a sign reversal at $\overline{\mathrm{Y}}$ in the surface state's in-plane spin components which is characteristic for a Rashba-type behavior. Furthermore, we deduce an effective mass of $m^{*}=(0.27\pm 0.02)m_e$ and a Rashba parameter of ${\alpha }_R=(0.46\pm 0.04)\mathrm{eV}\AA$ from direct photoemission measurements.

Figure 1

LEED patterns of the Au(110) (a) and Na/Au(110) (b) surfaces show the $(1\times 2)$ superstructure caused by a “missing-row” reconstruction. The surface Brillouin zone of the $(1\times 2)$ surface is marked with solid lines, the $(1\times 1)$ in dashed lines.

Figure 2

Spin- and angle-resolved inverse photoemission data around $\overline{\mathrm{Y}}$ on $(1\times 2)$-Au(110): (a) Spin-integrated spectra exhibit the dispersing Rashba-type surface state (black tick marks) and a bulk transition (dashed tick mark). (b) Dispersion $E\left(k_{\parallel }\right)$ of the surface state as derived from peak positions in (a) located in the band gap around $\overline{\mathrm{Y}}$. Blue lines resemble the dispersions published in Refs. [14] (dashed) and [16] (dotted-dashed). Surface-projected band structure (light gray area) taken from Ref. [15]. Spin-resolved spectra were measured for $\theta ={38}^{\circ },{43}^{\circ }$ (green solid lines). (c) Reversal of sign in the spin signal for spectra taken left and right of $\overline{\mathrm{Y}}$ (${\theta }_{\overline{\mathrm{Y}},E_f=0.35\mathrm{eV}}=42.3^{\circ }$) confirms the Rashba splitting of the surface state. Spectra for spin up (spin down) of the $P_y$ component are plotted in red (blue).

Figure 3

Spin- and angle-resolved photoemission around $\overline{\mathrm{Y}}$ of Na-covered $(1\times 2)$-Au(110) measured with $p$-polarized light ($\hslash \omega =21\mathrm{eV}$): (a) The intensity of the Rashba-type surface state mapped with ARPES is displayed as a contour plot (linear gray scale). Its dispersion is sketched by the blue solid line. (b) ARPES EDCs show the dispersion of the surface state (tick marks). Its Rashba-type spin splitting results in an asymmetric line shape away from $\overline{\mathrm{Y}}$. An example of the two-line-decomposition fit procedure is shown as gray lines for $\theta =-23.2^{\circ }$. (c) Dispersion $E\left(k_{\parallel }\right)$ deduced from curve fitting the EDCs with two Lorentzian functions (open circles). The dispersion is fitted by two parabolas (blue dashed lines). (d) SARPES data confirm the sign reversal of the $P_y$ spin component. Spectra for spin up (spin down) of the $P_y$ component are plotted in red (blue). Peak positions are marked for two exemplary angles. The black solid line depicts the spin-averaged spectrum for $-21.7^{\circ }$.