Abstract

We present a combined experimental and theoretical study of spin–orbit-induced spin splittings in the unoccupied surface electronic structure of the prototypical Rashba system Au(111). Spin- and angle-resolved inverse-photoemission measurements reveal a Rashba-type spin splitting in the unoccupied part of the L-gap surface state. With increasing momentum parallel to the surface, the spectral intensity is lowered and the spin splitting vanishes as the surface state approaches the band-gap boundary. Furthermore, we observe significantly spin-dependent peak positions and intensities for transitions between unoccupied sp-like bulk bands. Possible reasons for this behavior are considered: initial and final-state effects as well as the transition itself, which is controlled by selection rules depending on the symmetry of the involved states. Based on model calculations, we identify the initial states as origin of the observed Rashba-type spin effects in bulk transitions.

Highlights

  • We present a combined experimental and theoretical study of spin–orbit-induced spin splittings in the unoccupied surface electronic structure of the prototypical Rashba system Au(111)

  • Performing a simulation by use of the Pauli matrices σx and σy only (SIMxy), a corresponding in-plane or Rashba-type polarization should appear with values that are comparable to those one would expect in a full simulation. We show that this method permits a detailed analysis on the origin of Rashba-type splittings observed by our measurements of transitions between unoccupied bulk states of Au(111)

  • We studied the influence of the spin–orbit coupling on the unoccupied surface electronic structure of Au(111)

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Summary

Technique and sample preparation

Spin- and angle-resolved IPE is used to investigate the energy versus momentum dispersion as well as the spin structure of the electronic states above the Fermi level [30]. A beam of low-energy electrons with defined energy, momentum and spin from a GaAs photocathode is directed onto the surface. The photons emitted during the IPE process are detected by two energy-selective Geiger–Muller counters [32] Their energy selectivity is based on the ionization threshold of acetone used as counting gas and the transmission cut-off of a CaF2 entrance window, New Journal of Physics 15 (2013) 105001 (http://www.njp.org/). We use two counters (cf figure 1): counters C1 and C2 at fixed angles of 70◦ and 35◦ with respect to the incident electron beam are operated with window temperatures of TCaF2 = 370 and 300 K resulting in pass energies of hω = 9.8 and 9.9 eV, respectively. The sample was kept at room temperature during all measurements

Inverse-photoemission results and discussion
Computational details
One-step calculations
Conclusion
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