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.
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