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.
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