  High fraction of the surface atoms considerably enhances the influence of
size and shape on the magnetic and electronic properties of nanoparticles.
Shape effects in ferromagnetic nanoparticles are well understood and allow to
set and control the parameters of a sample that affect its magnetic anisotropy
during production. In the present paper we study the shape effects in the other
widely used magnetic materials -- antiferromagnets, -- which possess
vanishingly small or zero macroscopic magnetization. We take into account the
difference between the surface and bulk magnetic anisotropy of a nanoparticle
and show that the effective magnetic anisotropy depends on the particle shape
and crystallographic orientation of its faces. Corresponding shape-induced
contribution to the magnetic anisotropy energy is proportional to the particle
volume, depends on magnetostriction, and can cause formation of equilibrium
domain structure. Crystallographic orientation of the nanoparticle surface
determines the type of domain structure. The proposed model allows to predict
the magnetic properties of antiferromagnetic nanoparticles depending on their
shape and treatment.
