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 external magnetic field. In the absence of magnetic field, we find a spin-spiral ground state, while applying 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 wave length 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-neighbor Dzyaloshinskii-Moriya interaction and the isotropic exchange coupling, $D/J$. Our results also indicate that the applied field needed to stabilize the skyrmion lattice increases when the diameter of individual skyrmions decreases. Based on our observations, we suggest that the formation of the skyrmion lattice can be tuned by small structural modification of the thin film.
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