Abrupt Rotation of the Rashba Spin to the Direction Perpendicular to the Surface

The polarization vector of the Rashba spin, which must be parallel to the two-dimensional (2D) plane in an ideal system, is found to change abruptly and definitely to the direction perpendicular to the surface at the $\overline{K}$ point of the Brillouin zone of a real hexagonal system, the $\mathrm{Tl}/\mathrm{Si}(111)\mathrm{\text{−}}(1\times 1)$ surface. This finding obtained experimentally by angle-resolved and spin-resolved photoemission measurements is fully confirmed by a first-principles theoretical calculation. We found that the abrupt rotation of the Rashba spin is simply understood by the 2D symmetry of the hexagonal structure.