  We study the interplay of lattice, spin and orbital degrees of freedom in a
two-dimensional model system: a flat square lattice of Te atoms on a Au(100)
surface. The atomic structure of the Te monolayer is determined by scanning
tunneling microscopy (STM) and quantitative low-energy electron diffraction
(LEED-IV). Using spin- and angle-resolved photoelectron spectroscopy (ARPES)
and density functional theory (DFT), we observe a Te-Au interface state with
highly anisotropic Rashba-type spin-orbit splitting at the X point of the
Brillouin zone. Based on a profound symmetry and tight-binding analysis, we
show how in-plane square lattice symmetry and broken inversion symmetry at the
Te-Au interface together enforce a remarkably anisotropic orbital Rashba effect
which strongly modulates the spin splitting.
