Inherent orbital spin textures in Rashba effect and their implications in spin–orbitronics

Abstract

The Rashba effect gives rise to the key feature of chiral spin texture. Recently it was demonstrated that the orbital angular momentum (OAM) texture forms the underlying basis for Rashba spin texture. Here we solve a model Hamiltonian of a generic p-orbital system in the presence of crystal field, internal spin–orbit coupling (SOC) and inversion symmetry breaking (ISB), and demonstrate, in addition to OAM and spin texture, the existence of orbital projection (OP) of the spin texture in a general Rashba system. The unique form of the OP pattern follows from the same condition for the existence of chirality of the spin texture. From the analytical results, we obtained the spin polarization as a function of parameters such as the SOC strength, crystal field splitting and degree of ISB, and compare them with those from numerical solutions and ab initio calculations. All three methods yield highly consistent results. Our results suggest means of external modulation, and elucidate the multi-orbital nature of the Rashba effect and the underlying OP of the spin texture. The understanding has potential applications in fields such as spin–orbitronics that requires delicate control between orbital occupancy and spin momentum.