  We present a theoretical survey of magnetocrystalline anisotropies in
(Ga,Mn)As epilayers and compare the calculations to available experimental
data. Our model is based on an envelope function description of the valence
band holes and a spin representation for their kinetic-exchange interaction
with localised electrons on Mn ions, treated in the mean-field approximation.
For epilayers with growth induced lattice-matching strains we study in-plane to
out-of-plane easy-axis reorientations as a function of Mn local-moment
concentration, hole concentration, and temperature. Next we focus on the
competition of in-plane cubic and uniaxial anisotropies. We add an in-plane
shear strain to the effective Hamiltonian in order to capture measured data in
bare, unpatterned epilayers, and we provide microscopic justification for this
approach. The model is then extended by an in-plane uniaxial strain and used to
directly describe experiments with strains controlled by postgrowth lithography
or attaching a piezo stressor. The calculated easy-axis directions and
anisotropy fields are in semiquantitative agreement with experiment in a wide
parameter range.
