Determining the spin-orbit coupling via spin-polarized spectroscopy of magnetic impurities

We study the spin-resolved spectral properties of the impurity states associated to the presence of magnetic impurities in two-dimensional as well as one-dimensional systems with Rashba spin-orbit coupling. We focus on Shiba bound states in superconducting materials, as well as on impurity states in metallic systems. Using a combination of a numerical T-matrix approximation and a direct analytical calculation of the bound-state wave function, we compute the local density of states (LDOS) together with its Fourier transform (FT). We find that the FT of the spin-polarized LDOS, a quantity accessible via spin-polarized scanning tunneling microscopy, allows to accurately extract the strength of the spin-orbit coupling. Also, we confirm that the presence of magnetic impurities is strictly necessary for such measurement, and that non-spin-polarized experiments cannot have access to the value of the spin-orbit coupling.