First-principles study of the structural stability of cubic, tetragonal and hexagonal phases in Mn₃Z (Z=Ga, Sn and Ge) Heusler compounds

We investigate the structural stability and magnetic properties of the 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 for 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.