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Magnetic anisotropy energy in disordered Ge_{1-x}Mn_{x}Te

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.