  We study the magnetic interactions in atomic layers of Fe and 5d
transition-metals such as Os, Ir, and Pt on the (001) surface of Rh using
first-principles calculations based on density functional theory. For both
stackings of the 5d-Fe bilayer on Rh(001) we observe a transition from an
antiferromagnetic to a ferromagnetic nearest-neighbor exchange interaction upon
5d band filling. In the sandwich structure 5d/Fe/Rh(001) the nearest neighbor
exchange is significantly reduced. For FeIr bilayers on Rh(001) we consider
spin spiral states in order to determine exchange constants beyond nearest
neighbors. By including spin-orbit coupling we obtain the Dzyaloshinskii-Moriya
interaction (DMI). The magnetic interactions in Fe/Ir/Rh(001) are similar to
those of Fe/Ir(001) for which an atomic scale spin lattice has been predicted.
However, small deviations between both systems remain due to the different
lattice constants and the Rh vs. Ir surface layers. This leads to slightly
different exchange constants and DMI and the easy magnetization direction
switches from out-of-plane for Fe/Ir(001) to in-plane for Fe/Ir/Rh(001).
Therefore a fine tuning of magnetic interactions is possible by using single 5d
transition-metal layers which may allow to tailor antiferromagnetic skyrmions
in this type of ultrathin films. In the sandwich structure Ir/Fe/Rh(001) we
find a strong exchange frustration due to strong hybridization of the Fe layer
with both Ir and Rh which drastically reduces the nearest-neighbor exchange.
The energy contribution from the DMI becomes extremely large and DMI beyond
nearest neighbors cannot be neglected. We attribute the large DMI to the low
coordination of the Ir layer at the surface. We demonstrate that higher- order
exchange interactions are significant in both systems which may be crucial for
the magnetic ground state.
