K -asymmetric spin splitting at the interface between transition metal ferromagnets and heavy metals

We systematically investigate the spin-orbit coupling-induced band splitting originating from inversion symmetry breaking at the interface between a Co monolayer and 4d (Tc, Ru, Rh, Pd, and Ag) or 5d (Re, Os, Ir, Pt, and Au) transition metals. In spite of the complex band structure of these systems, the odd-in-k spin splitting of the bands displays striking similarities with the much simpler Rashba spin-orbit coupling picture. We establish a clear connection between the overall strength of the odd-in-k spin splitting of the bands and the charge transfer between the d orbitals at the interface. Furthermore, we show that the spin splitting of the Fermi surface scales with the induced orbital moment, weighted by the spin-orbit coupling.