Theory of screening of the phonon-modulated spin-orbit interaction in metals

We investigate the long-wavelength limit of the phonon-modulated spin-orbit interaction in the self-consistent Hartree approximation. Within the jellium model we show that the screening is provided by the spin-other-orbits term in the electron-electron interaction. In the case bf a discrete-lattice model, the modifications in the electronic wave functions induced by the spin-orbit coupling of the electrons to the ions give rise to spin-mixed matrix elements of the Coulomb electron-electron interaction. This is able to provide a further screening mechanism to the phonon-modulated spin-orbit interaction. Our self-consistent treatment of the screening justifies a posteriori the results of previous theories based on an already screened lattice potential.