Effect of the spin-orbit interaction on the surface electronic structure of Gd<i>X</i><sub>2</sub>Si<sub>2</sub> (<i>X =</i> Cu, Ag, Au)
Within the framework of the density functional theory we study the magnetic and electronic structure of Gd X <sub>2</sub>Si<sub>2</sub> ( X = Cu, Ag, Au). We focus on the influence of spin-orbit effects on the electronic structure of the (001) surface. The compounds under consideration were found to exhibit intralayer antiferromagnetism, which, however, does not significantly affect the surface electronic structure of the Gd X <sub>2</sub>Si<sub>2</sub>(001) near the Fermi level. We show that the spin-orbit splitting of two-dimensional states into Gd X <sub>2</sub>Si<sub>2</sub>(001), characterized by a combination of intrinsic spin-orbit splitting with Bychkov-Rashba splitting, increases with the atomic number of the noble metal element. Based on the analysis of the spatial extent of d orbitals and their interaction with silicon orbitals, we discuss the change in the strength of the spin-orbit interaction in compounds with noble metals. The effect of the d shell filling on the spin-orbit interaction is discovered by comparing intermetallic compounds based on rare-earth and noble metals and isostructural intermetallic compounds with transition metals.