  We investigate the mechanism behind the breakdown of the compensation of
large magnetic moments leading to weak ferromagnetism. For this we use
first-principles calculations within density functional theory and we focus on
the weak ferromagnetic compound Mn3Sn. Our new implementation allows for an
exact treatment of the spin-density matrix and non-collinearity. In order to
gain some insight, our results are compared to the ones obtained by using the
atomic moment approximation (AMA) and its role is discussed. We find that the
appearance of the weak ferromagnetic moment in this compound originates not so
much as an effect of spin-orbit coupling as suggested previously from AMA
calculations, as from the non-collinearity of the Sn atom magnetization
density. This is confirmed by non-collinear calculations in which the SOC
effects are neglected.
