  The 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.
