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International audienceThe magnetic properties of iron (spin and orbital magnetic moments, magnetocrystalline anisotropy energy) in various geometries and dimensionalities are investigated by using a parametrized tight-binding model in an $s$, $p$ and $d$ atomic orbital basis set including spin polarization and the effect of spin-orbit coupling. The validity of this model is well established by comparing the results with those obtained by using an ab-initio code. This model is applied to the study of iron in bulk bcc and fcc phases, $(110)$ and $(001)$ surfaces and to the monatomic wire, at several interatomic distances. New results are derived. The variation of the component of the orbital magnetic moment on the spin quantization axis has been studied as a function of depth, revealing a significant enhancement in the first two layers, especially for the $(001)$ surface. It is found that the magnetic anisotropy energy is drastically increased in the wire and can reach several meV. This is also true for the orbital moment, which in addition is highly anisotropic. Furthermore it is shown that when the spin quantization axis is neither parallel nor perpendicular to the wire the average orbital moment is not aligned with the spin quantization axis. At equilibrium distance the easy magnetization axis is along the wire but switches to the perpendicular direction under compression. The success of this model opens up the possibility of obtaining accurate results on other elements and systems with much more complex geometries

Magnetism of iron: from the bulk to the monatomic wire