  In this paper we present results of our calculations of the non-collinear
spin density distribution in the systems with frustrated triangular magnetic
structure (Mn-based antiperovskite compounds, Mn_{3}AN (A=Ga, Zn)) in the
ground state and under external mechanical strain. We show that the spin
density in the (111)-plane of the unit cell forms a "domain" structure around
each atomic site but it has a more complex structure than the uniform
distribution of the rigid spin model, i.e. Mn atoms in the (111)-plane form
non-uniform "spin clouds", with the shape and size of these "domains" being
function of strain. We show that both magnitude and direction of the spin
density change under compressive and tensile strains, and the orientation of
"spin domains" correlates with the reversal of the strain, i.e. switching
compressive to tensile strain (and vice versa) results in "reversal" of the
domains. We present analysis for the intra-atomic spin-exchange interaction and
the way it affects the spin density distribution. In particular, we show that
the spin density inside the atomic sphere in the system under mechanical stress
depends on the degree of localization of electronic states.
