  Magnetic anisotropy in an antiferromagnet (AFM) with inversion symmetry
breaking (ISB) is investigated. The magnetic anisotropy energy (MAE) resulting
from the Rashba spin-orbit and s-d type exchange interactions is determined for
two different models of AFMs. The global ISB model, representing the effect of
a surface, an interface, or a gating electric field, results in an easy-plane
magnetic anisotropy. In contrast, for a local ISB model, i.e., for a
noncentrosymmetric AFM, perpendicular magnetic anisotropy (PMA) arises. Both
results differ from the ferromagnetic case, in which the result for PMA depends
on the band structure and dimensionality. These MAE contributions play a key
role in determining the direction of the Neel order parameter in
antiferromagnetic nanostructures, and reflect the possibility of
electrical-field control of the Neel vector.
