  Using first-principles calculations, we study the magnetic properties of a Co
monolayer on a Pt(111) surface with a capping monolayer of selected $5d$
elements (Re, Os, Ir, Pt and Au). First we determine the tensorial exchange
interactions and magnetic anisotropies characterizing the Co monolayer for all
considered systems. We find a close relationship between the magnetic moment of
the Co atoms and the nearest-neighbor isotropic exchange interaction, which is
attributed to the electronic hybridization between the Co and the capping
layers, in spirit of the Stoner picture of ferromagnetism. The
Dzyaloshinskii-Moriya interaction is decreased for all overlayers compared to
the uncapped Co/Pt(111) system, while even the sign of the
Dzyaloshinskii-Moriya interaction changes in case of the Ir overlayer. We
conclude that the variation of the Dzyaloshinskii-Moriya interaction is well
correlated with the change of the magnetic anisotropy energy and of the orbital
moment anisotropy. The unique influence of the Ir overlayer on the
Dzyaloshinskii-Moriya interaction is traced by scaling the strength of the
spin--orbit coupling of the Ir atoms in Ir/Co/Pt(111) and by changing the Ir
concentration in the Au$_{1-x}$Ir$_{x}$/Co/Pt(111) system. Our spin dynamics
simulations indicate that the magnetic ground state of Re/Co/Pt(111) thin film
is a spin spiral with a tilted normal vector, while the other systems are
ferromagnetic.
