  We present a detailed ab initio study of the electronic structure and
magnetic order of an Fe monolayer on the Ir(001) surface covered by adsorbed
oxygen and hydrogen. The results are compared to the clean Fe/Ir(001) system,
where recent intensive studies indicated a strong tendency towards an
antiferromagnetic order and complex magnetic structures. The adsorption of an
oxygen overlayer significantly increases interlayer distance between the Fe
layer and the Ir substrate, while the effect of hydrogen is much weaker. We
show that the adsorption of oxygen (and also of hydrogen) leads to a p(2$\times
$1) antiferromagnetic order of the Fe moments, which is also supported by an
investigation based on a disordered local moment state. Simulated scanning
tunneling images using the simple Tersoff-Hamann model hint that the proposed
p(2$\times $1) antiferromagnetic order could be detected even by non-magnetic
tips.
