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With a view to the design of hard magnets without rare earths we explore the possibility of large magnetocrystalline anisotropy energies in Heusler compounds that are unstable with respect to a tetragonal distortion. We consider the Heusler compounds Fe(2)YZ with Y = (Ni, Co, Pt), and Co(2)YZ with Y = (Ni, Fe, Pt) where, in both cases, Z = (Al, Ga, Ge, In, Sn). We find that for the Co(2)NiZ, Co(2)PtZ, and Fe(2)PtZ families the cubic phase is always, at T = 0, unstable with respect to a tetragonal distortion, while, in contrast, for the Fe(2)NiZ and Fe(2)CoZ families this is the case for only 2 compounds-Fe2NiGe and Fe2NiSn. For all compounds in which a tetragonal distortion occurs we calculate the magnetocrystalline anisotropy energy (MAE) finding remarkably large values for the Pt containing IIeuslers, but also large values for a number of the other compounds (e.g. Co2NiGa has an MAE of -2.38 MJ m(-3)). The tendency to a tetragonal distortion we find to be strongly correlated with a high density of states (DOS) at the Fermi level in the cubic phase. As a corollary to this fact we observe that upon doping compounds for which the cubic structure is stable such that the Fermi level enters a region of high DOS, a tetragonal distortion is induced and a correspondingly large value of the MAE is then observed.
