Relativistic spin-polarised scattering theory-solution of the single-site problem

Relativistic spin-polarised scattering theory is discussed and the relevant radial Dirac equations for an electron in a potential with a magnetic component are derived. The solutions to these equations, when expanded to lowest order in l/c‘ (cis the velocity of light), thus treat spin-orbit coupling and spin-polarisation effects on an equal footing. By matching to free-particle solutions at the boundary of the potential, expressions for the scattering amplitudes are given. We perform explicit calculations for the example of an electron scattering from a single Pt atom in an external magnetic field. The interpretation of the results gives a clear and useful picture of the interplay between spin-orbit coupling and spin polarisation. A scattering analogue to a generalised ‘Zeeman effect’ is described.