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Šipr, O.; Minár, J.; Ebert, H. (2016): Influence of spin-orbit coupling on the magnetic dipole term T-alpha. In: Physical Review B, Vol. 94, No. 14, 144406
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Abstract

The influence of the spin-orbit coupling (SOC) on the magnetic dipole term T-alpha is studied across a range of systems in order to check whether the T-alpha term can be eliminated from analysis of x-ray magnetic circular dichroism spectra performed via the spin moment sum rule. Fully relativistic Korringa-Kohn-Rostoker Green's function calculations for Co monolayers and adatoms on Cu, Pd, Ag, Pt, and Au (111) surfaces were performed to verify whether the sum over magnetic dipole terms T-x + T-y + T-z is zero and whether the angular dependence of the T-alpha term goes as 3 cos(2) theta - 1. It follows that there are circumstances when the influence of the SOC on T-alpha cannot be neglected even for 3d atoms where the SOC is nominally small. The crucial factor appears to be the dimensionality of the system: For 3d adatoms, the influence of SOC on T-alpha can be significant whereas for monolayers it is always practically negligible. Apart from the dimensionality, hybridization between adatom and substrate states is also important: Small hybridization enhances the importance of the SOC and vice versa.