A First-Principles Investigation of Phonon Softenings and Lattice Instabilities in the Shape-Memory System Ni$_{2}$MnGa

Ferromagnetic mg has unique magnetoelastic properties. These are investigated by detailed computational studies of the phonon dispersion curves for the non-modulated cubic Ltw and tetragonal structures. For the Ltw structure, a complete softening of the transverse acoustic mode has been found around the wave vector $mathbf{q}=[1/3,1/3,0](2 pi/a)$. The softening of this TA{2} phonon mode leads to the premartensitic modulated super-structure observed experimentally. Further phonon anomalies, related to other structural transformations in mg, have also been found and examined. These anomalies appear to be due to the coupling of particular acoustic phonon modes and optical modes derived from Ni.