  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.
