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We present a detailed first principles study on the magnetic structure of an Fe monolayer on different surfaces of 5d transition metals. We use the spin-cluster expansion technique to obtain parameters of a spin model, and predict the possible magnetic ground state of the studied systems by employing the mean field approach and, in certain cases, by spin dynamics calculations. We point out that the number of shells considered for the isotropic exchange interactions plays a crucial role in the determination of the magnetic ground state. In the case of Ta substrate we demonstrate that the out-of-plane relaxation of the Fe monolayer causes a transition from ferromagnetic to antiferromagnetic ground state. We examine the relative magnitude of nearest neighbour Dzyaloshinskii–Moriya (D) and isotropic (J) exchange interactions in order to get insight into the nature of magnetic pattern formations. For the Fe/Os (0 0 0 1 …