We have investigated the atomic and electronic structure of the ($sqrt{3}times sqrt{3}$)$R30^{circ}$ SnAu$_2$/Au(111) surface alloy. Low energy electron diffraction and scanning tunneling microscopy measurements show that the native herringbone reconstruction of bare Au(111) surface remains intact after formation of a long range ordered ($sqrt{3}times sqrt{3}$)$R30^{circ}$ SnAu$_2$2/Au(111) surface alloy. Angle-resolved photoemission and two-photon photoemission spectroscopy techniques reveal Rashba-type spin-split bands in the occupied valence band with comparable momentum space splitting as observed for the Au(111) surface state, but with a hole-like parabolic dispersion. Our experimental findings are compared with density functional theory (DFT) calculation that fully support our experimental findings. Taking advantage of the good agreement between our DFT calculations and the experimental results, we are able to extract that the occupied Sn-Au hybrid band is of (s, d)-orbital character while the unoccupied Sn-Au hybrid bands are of (p, d)-orbital character. Hence, we can conclude that the Rashba-type spin splitting of the hole-like Sn-Au hybrid surface state is caused by the significant mixing of Au d- to Sn s-states in conjunction with the strong atomic spin-orbit coupling of Au, i.e., of the substrate.
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