Spin-spiral structures in a free-standing Fe(110) monolayer are determined by the first-principles film full-potential linearized augmented plane wave method with intra-atomic noncollinear magnetism. The results obtained predict that the spin-spiral structures are energetically favourable over the collinear ferromagnetic state. The interatomic exchange parameters, which are evaluated from the formation energy of the spin-spiral structures, indicate that a competition between the nearest-neighbour ferromagnetic interaction and the long-distant antiferromagnetic interactions leads to the stabilization of the spin-spiral structures. In addition, the spin-orbit coupling is found to play an important role in determining the magnetic ground state.
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