  CrSb is a layered antiferromagnet (AFM) with perpendicular magnetic
anisotropy, a high N\'{e}el temperature, and large spin-orbit coupling (SOC),
which makes it interesting for AFM spintronic applications. To elucidate the
various mechanisms of N\'{e}el vector control, the effects of strain, band
filling, and electric field on the magnetic anisotropy energy (MAE) of bulk and
thin-film CrSb are determined and analysed using density functional theory. The
MAE of the bulk crystal is large (1.2 meV per unit cell). Due to the
significant ionic nature of the Cr-Sb bond, finite slabs are strongly affected
by end termination. Truncation of the bulk crystal to a thin film with one
surface terminated with Cr and the other surface terminated with Sb breaks
inversion symmetry, creates a large charge dipole and average electric field
across the film, and breaks spin degeneracy, such that the thin film becomes a
ferrimagnet. The MAE is reduced such that its sign can be switched with
realistic strain, and the large SOC gives rise to an intrinsic voltage
controlled magnetic anisotropy (VCMA). A slab terminated on both faces with Cr
remains a compensated AFM, but with the compensation occurring nonlocally
between mirror symmetric Cr pairs. In-plane alignment of the moments is
preferred, the magnitude of the MAE remains large, similar to that of the bulk,
and it is relatively insensitive to filling.
