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.
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