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We perform an extensive study of the spin-configurations in a PdFe bilayer on Ir (111) in terms of ab initio and spin-model calculations. We use the spin-cluster expansion technique to obtain spin model parameters, and solve the Landau-Lifshitz-Gilbert equations at zero temperature. In particular, we focus on effects of layer relaxations and the evolution of the magnetic ground state in an external magnetic field. In the absence of a magnetic field, we find a spin-spiral ground state; while applying an external magnetic field, skyrmions are generated in the system. Based on energy calculations of frozen spin configurations with varying magnetic field we obtain excellent agreement for the phase boundaries with available experiments. We find that the wavelength of spin-spirals and the diameter of skyrmions decrease with increasing inward Fe layer relaxation, which is correlated with the increasing ratio of the nearest …