Origin of magnetocrystalline anisotropy in Ni-Mn-Ga-Co-Cu tetragonal martensite

We investigate the origin of magnetocrystalline anisotropy (MCA) in non-modulated martensite of Ni-Mn-Ga-Co-Cu exhibiting magnetic-field-induced strain up to 12%. Experiments as well as theoretical calculations using density functional theory show that Co and Cu doping or deviation from Ni2MnGa stoichiometry decreases the MCA. As follows from the calculations, the decrease of MCA is much stronger for Cu in Ga sublattice in comparison to Cu in Mn sublattice. The decreasing effect of Co on the MCA is only indirect caused by deficiency in Ni, which is the main element governing the MCA. For further insight, we calculated MCA and magnetic moment as a function of lattice tetragonality c/a. The MCA reaches a maximum at the same c/a where Ni magnetic moment is maximum. However, the tetragonality of equilibrium does not coincide with these maxima. Consequently, in contrast to common expectation, decreasing tetragonality from equilibrium can increase the MCA.