  We theoretically analyze the influence of chemical disorder on magnetic
anisotropy in Ge_{1-x}Mn_{x}Te semiconductor layers known to exhibit
carrier-induced ferromagnetism and ferroelectric distortion of rhombohedral
crystal lattice. Using DFT method we determine the local changes in the crystal
structure due to Mn ions substitution for Ge and due to the presence in
Ge_{1-x}Mn_{x}Te of very high concentration of cation vacancies. We calculate
the effect of this structural and chemical disorder on single ion magnetic
anisotropy mechanism and show that its contribution is order of magnitude
smaller as compared to magnetic anisotropy mechanism originating from the spin
polarization induced by Mn ions into neighboring Te and Ge ions. We also
discuss magnetic anisotropy effects due to pairs of Mn ions differently
allocated in the lattice. The spatial averaging over chemical disorder strongly
reduces the strength of this magnetic anisotropy mechanism and restores the
global rhombohedral symmetry of magnetic system.
