  We investigate the structural stability and magnetic properties of cubic,
tetragonal and hexagonal phases of Mn3Z (Z=Ga, Sn and Ge) Heusler compounds
using first-principles density-functional theory. We propose that the cubic
phase plays an important role as an intermediate state in the phase transition
from the hexagonal to the tetragonal phases. Consequently, Mn3Ga and Mn3Ge
behave differently from Mn3Sn, because the relative energies of the cubic and
hexagonal phases are different. This result agrees with experimental
observations from these three compounds. The weak ferromagnetism of the
hexagonal phase and the perpendicular magnetocrystalline anisotropy of the
tetragonal phase obtained in our calculations are also consistent with
experiment.
