  Using first-principles calculations, we elucidate microscopic mechanisms of
perpendicular magnetic anisotropy (PMA)in Fe/MgO magnetic tunnel junctions
through evaluation of orbital and layer resolved contributions into the total
anisotropy value. It is demonstrated that the origin of the large PMA values is
far beyond simply considering the hybridization between Fe-3d$ and O-2p
orbitals at the interface between the metal and the insulator. On-site
projected analysis show that the anisotropy energy is not localized at the
interface but it rather propagates into the bulk showing an attenuating
oscillatory behavior which depends on orbital character of contributing states
and interfacial conditions. Furthermore, it is found in most situations that
states with $d_{yz(xz)}$ and $d_{z^2}$ character tend always to maintain the
PMA while those with $d_{xy}$ and $d_{x^2-y^2}$ character tend to favor the
in-plane anisotropy. It is also found that while MgO thickness has no influence
on PMA, the calculated perpendicular magnetic anisotropy oscillates as a
function of Fe thickness with a period of 2ML and reaches a maximum value of
3.6 mJ/m$^2$.
