Origins of Rashba spin textures in iridium (111) surface bands far above the Fermi energy

Recent advances in low-energy electron microscopy have enabled high-resolution, spin-sensitive measurements of electronic bands at higher energies than previously explored (so-called SPLEEM). For example, measurements of the unoccupied electronic bands of iridium revealed Rashba spin textures around 15 eV above the Fermi energy. Here, we provide a theoretical description of these observations and explain their origin. We use density functional theory to calculate the electronic band structure of the iridium (111) surface, finding an in-plane two-fold symmetric spin texture and an out-of-plane three-fold symmetric spin texture at similar energies to those found in experiment. Interestingly, these spin textures come from bands with dominantly f-orbital character. Based on our DFT results, we construct a minimal tight-binding model that explains the origins of the observed two-fold symmetric and three-fold symmetric spin textures. Our findings explain how the symmetry of unoccupied f-electrons, symmetry of the iridium surface, and strong spin-orbit coupling give rise to Rashba spin textures, consistent with recent SPLEEM measurements.