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.