Ab initio total energy calculations show that the antiferromagnetic (111) order is not the ground state for the ideal CuMnSb Heusler alloy in contrast to the results of neutron diffraction experiments. It is known, that Heusler alloys usually contain various defects depending on the sample preparation. We have therefore investigated magnetic phases of CuMnSb assuming the most common defects which exist in real experimental conditions. The full-potential supercell approach and a Heisenberg model approach using the coherent potential approximation are adopted. The results of the total energy supercell calculations indicate that defects that bring Mn atoms close together promote the antiferromagnetic (111) structure already for a low critical defect concentrations ($approx$ 3%). A detailed study of exchange interactions between Mn-moments further supports the above stabilization mechanism. Finally, the stability of the antiferromagnetic (111) order is enhanced by inclusion of electron correlations in narrow Mn-bands. The present refinement structure analysis of neutron scattering experiment supports theoretical conclusions.
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