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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 circulardichroism spectra done via the spin moment sum rule. Fully relativisticKorringa-Kohn-Rostoker (KKR) Green function calculations for Co monolayers andadatoms on Cu, Pd, Ag, Pt, and Au (111) surfaces were performed to verifywhether the sum over magnetic dipole terms $T_{x}+T_{y}+T_{z}$ is zero andwhether the angular dependence of the \ta\ term goes as $3\cos^{2}\theta-1$. Itfollows that there are circumstances when the influence of the SOC on$T_{\alpha}$ cannot be neglected even for 3$d$ atoms, where the SOC isnominally small. The crucial factor appears to be the dimensionality of thesystem: for 3$d$ adatoms, the influence of SOC on $T_{\alpha}$ can besignificant while for monolayers it is always practically negligible. Apartfrom the dimensionality, hybridization between adatom and substrate states isalso important: small hybridization enhances the importance of the SOC and viceversa.

Influence of spin-orbit coupling on the magnetic dipole term $T_{\alpha}$