Manipulation of the spin-orbit coupling using the Dirac equation for spin-dependent potentials

A scheme is presented that allows one to decompose the spin-orbit coupling operator into two parts within calculations based on the Dirac equation for spin-dependent potentials. The first term lifts energetic degeneracies but leaves the spin as a good quantum number, while the second term causes hybridization of states with a different spin character. To investigate the importance of these terms and of the mechanism connected to them a number of model calculations for the dispersion relation, the spin-orbit-induced orbital magnetic moment, and the magneto-optical Kerr effect in several transition metal systems have been performed by retaining just one of them. In all cases studied it was found that the first term is by far the most important source for spin-orbit-induced phenomena.