First-principles study of lattice instabilities in ferromagnetic Ni₂MnGa

The phonon-dispersion relations and elastic constants for ferromagnetic Ni₂MnGa in the cubic and tetragonally distorted Heusler structures are computed using density-functional and density-functional-perturbation theory within the spin-polarized generalized-gradient approximation. For 0.9<c/a<1.06, the TA₂ transverse- acoustic branch along [110] and the symmetry-related directions exhibit a dynamical instability at a wave vector that depends on c/a. Through examination of the Fermi-surface nesting and electron-phonon coupling, this is identified as a Kohn anomaly. In the parent cubic phase the computed tetragonal shear elastic constant, C^′=(C₁₁-C₁₂)/2, is close to zero, indicating a marginal elastic instability towards a uniform tetragonal distortion. We conclude that the cubic Heusler structure is unstable against a family of energy-lowering distortions produced by the coupling between a uniform tetragonal distortion and the corresponding [110] modulation. The computed relation between the c/a ratio and the modulation wave vector is in excellent agreement with structural data on the premartensitic (c/a=1) and martensitic (c/a=0.94) phases of Ni₂MnGa.