We study the magnetic behavior of a 4d transition-metal Ru monolayer (ML) on different substrates and orientations. In the ground state, an ideal Ru-ML is expected to be ferromagnetic on Ag(001) and Au(001) with a magnetic moment, µ, around 1.7 µB (Bohr magnetons) in both cases. On Cu(001), a Ru-ML is not magnetic. In this paper, we study the magnetic behavior of a Ru-ML at other orientations, i.e., (110) and (111), and analyze the phenomenon as a whole. We find magnetism on Au(111), and Ag(111) (µ ≈ 1 µB for both) but no magnetic activity on a Cu substrate in any orientation. This gives the first impression that the lattice parameter of the substrate is the one that governs the switching on of magnetism in the Ru-ML. But then, we find that on both Ag(110) and Au(110), an ideal Ru-ML is not magnetic. For that reason, we have tried to find another geometric parameter that would correlate better with the magnetic moment. We find that neither the total number of first nearest neighbors for each orientation, nor the number of them on the ML, or the number of them in the substrate, or the area per atom on the ML, correlate. We find a correlation with a parameter, Ω0, that represents the volume per atom in the monolayersubstrate interface region. But this parameter seems to have the wrong trend according to intuition. Further analysis shows that the details of the interaction are important, and that the physics underlying the switching on of magnetism in a Ru-ML on noble metal substrates, is determined by an intraband transfer of d-electronic states, from lower and higher energies to the Fermi level, that enhances the density of states at that energy, in an important way. This depends on specificities of the interaction between the ML and the substrate that are hardly taken into account by a single parameter that is merely geometric. PACS Nos.: 75.10b, 75.30m, 75.70.Ak, 73.20.At
Disturbance Observer-Based Nonsingular Terminal Sliding Mode Control for Spacecraft Electromagnetic Docking