  The magnetic ground state of nanosized systems such as Fe double chains,
recently shown to form in the early stages of Fe deposition on Ir(100), is
generally nontrivial. Using ab initio density functional theory we find that
the straight ferromagnetic (FM) state typical of bulk Fe as well as of isolated
Fe chains and double chains is disfavored after deposition on Ir(100) for all
the experimentally relevant double chain structures considered. So long as
spin-orbit coupling (SOC) is neglected, the double chain lowest energy state is
generally antiferromagnetic (AFM), a state which appears to prevail over the FM
state due to Fe-Ir hybridization. Successive inclusion of SOC adds two further
elements, namely a magnetocrystalline anisotropy, and a Dzyaloshinskii-Moriya
(DM) spin-spin interaction, the former stabilizing the collinear AFM state, the
second favoring a long-period spin modulation. We find that anisotropy is most
important when the double chain is adsorbed on the partially deconstructed
Ir(100) -- a state which we find to be substantially lower in energy than any
reconstructed structure -- so that in this case the Fe double chain should
remain collinear AFM. Alternatively, when the same Fe double chain is adsorbed
in a metastable state onto the (5x1) fully reconstructed Ir(100) surface, the
FM-AFM energy difference is very much reduced and the DM interaction is
expected to prevail, probably yielding a helical spin structure.
