  The spin texture of the metallic two-dimensional electron system (root3 x
root3)-Au/Ge(111) is revealed by fully three-dimensional spin-resolved
photoemission, as well as by density functional calculations. The large
hexagonal Fermi surface, generated by the Au atoms, shows a significant
splitting due to spin-orbit interactions. The planar components of the spin
exhibit helical character, accompanied by a strong out-of-plane spin component
with alternating signs along the six Fermi surface sections. Moreover, in-plane
spin rotations towards a radial direction are observed close to the hexagon
corners. Such a threefold-symmetric spin pattern is not described by the
conventional Rashba model. Instead, it reveals an interplay with
Dresselhaus-like spin-orbit effects as a result of the crystalline
anisotropies.
