Tilmann Hickel

Determination of symmetry reduced structures by a soft-phonon analysis in magnetic shape memory alloys

Max-Planck-Institut für Eisenforschung GmbH, Postfach 140444, 40074 Düsseldorf, German

Wednesday, 30 May 2007, 14.00, W2.19

Ni₂MnGa is a typical example of a Heusler alloy that undergoes a martensitic transformation. In the high-temperature austenitic phase it has a cubic L2₁ structure, whereas below 200 K the symmetry is reduced by an orthorhombic distortion. Despite lattice deformations of more than 6% and large strains connected to this change, it is completely reversible. Therefore, Ni₂MnGa serves as a shape memory compound. The fact that Ni₂MnGa additionally orders ferromagnetically below 360 K makes the material particularly attractive for applications as actuators and sensors. Nevertheless, its structural details in the martensitic phase are still a subject of much debate. Several shuffling structures have been observed experimentally. The temperature and magnetic field dependent transformations between these structures need to be understood for an improvement of the magnetic switching (e.g. operation with higher reliability and smaller magnetic fields). Our tool to identify the stable structures and the low energy transition paths is the calculation of free energy surfaces as function of key reaction coordinates (e.g. c/a- ratio) in DFT. (The GGA xc-functional and the PAW approach implemented in VASP were used in these investigations.) The different variants of the low symmetry orthorhombic structures lead to characteristic minima at this surface. However, the ab initio determination of the experimentally observed shuffling structures is challenging, due to the large phase space of possible atomic positions and the small shuffling formation energies of only a few meV per unit cell. Hence, we used the quasiharmonic approximation in order to compute and analyze phonon spectra. Starting with the symmetric structure of the austenite, the TA₂ phonon dispersion shows a phonon softening along the [110] direction. We were able to extract detailed information about the kind of this lattice instability from the eigenvectors of the unstable phonon modes. By setting up the corresponding modulated harmonics in supercell calculations, we systematically and efficiently identified stable shuffling structures. The resulting structural phases (austenite, martensite, pre-martensite) allow to assign and to interpret the experimental observations.