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The ab initio electronic structure calculations of the Ni2MnGa alloy indicate that the orthorhombic 4O structure exhibits the lowest energy compared to all known martensitic structures. The 4O structure is formed by nanotwin double layers, i.e., oppositely oriented nanotwins consisting of two (101) lattice planes of nonmodulated martensitic structure. It exhibits the lowest occupation of density of states at the Fermi level. The total energy 1.98 meV/atom below the energy of nonmodulated martensite is achieved within structural relaxation by shifting Mn and Ga atoms at the nanotwin boundaries. The same atomic shift can also be found in other martensitic nanotwinned or modulated structures such as 10M and 14M, which indicates the importance of the nanotwin double layer for the stability of these structures. Our discovery shows that the nanotwinning or modulation is a natural property of low-temperature martensitic phases in Ni-Mn-Ga alloys.PACS numbers: 81.30. Kf, 71.15.Nc, 64.60.My Among Heusler alloys, the Ni 2 MnGa is one of the few, which exhibit the unique properties resulting in a giant magnetic field-induced strain (MFIS) in their lowtemperature martensitic phase 1 . The MFIS can reach up to 12 % in case of Co-and Cu-doped Ni 2 MnGa 2 . Important factors enabling the MFIS are large magnetocrystalline anisotropy and extraordinarily high mobility of martensite twin boundaries 3-6 that primarily depends on martensite structure. While at elevated temperature there is a single austenitic phase of Ni 2 MnGa with cubic L2 1 structure, several low-temperature martensitic phases have been observed depending on composition, temperature and applied stress 7-9 . Martensitic phases with orthorhombic or monoclinic structures exhibit modulation of (110) planes in [110] direction with the periodicity of ten or fourteen lattice planes (10M or 14M). The third martensitic phase with nonmodulated (NM) tetragonally distorted L2 1 structure is typical for larger deviation from stoichiometry. In addition, above the martensitic transformation temperature there is a cubic premartensite with the periodicity of six lattice planes (6M) in alloys with small deviation from stoichiometry 10 .Low-temperature instability of L2 1 austenite can be explained by a strong Fermi surface nesting responsible for the phonon softening in [110] direction, which explains structural modulation of 6M premartensite 11-14 . In addition there is also a large Ni-e g peak corresponding to antibonding states right below the Fermi level, E f , in the minority density of states (DOS) channel. Due to the band Jahn-Teller effect the L2 1 cubic structure lowers its symmetry, which pushes the peak above E f resulting in lower energy [15][16][17] . Nonetheless, the precise causes of the variety of observed low temperature martensitic phases and mechanism of intermartensitic transformations between them have not been fully explained yet.Ab initio calculations have been employed to understand modulations in Ni 2 MnGa. Early works used description of 10M and 14M m...

The influence of Co and Cu doping on Ni-Mn-Ga Heusler alloy is investigated using the first-principles exact muffin-tin orbital method in combination with the coherent-potential approximation. Single-element doping and simultaneous doping by both elements are investigated in Ni 50−x Co x Mn 25−y Ga 25−z Cu y+z alloys, with dopant concentrations x, y, and z up to 7.5 at. %. Doping with Co in the Ni sublattice decreases the (c/a) NM ratio of the nonmodulated (NM) martensite, but it simultaneously increases the cubic phase stability with respect to the NM phase. Doping with Cu in the Mn or in Ga sublattices does not change the (c/a) NM ratio significantly and it decreases the cubic phase stability. For simultaneous doping by Co in the Ni sublattice and Cu in the Mn or Ga sublattices, the effects of the individual dopants are independent and about the same as for the single-element doping. Thus, the (c/a) NM ratio can be adjusted by Co doping while the phase stability can be balanced by Cu doping, resulting in stable martensite with a reduced (c/a) NM. The local stability of the cubic phase with respect to the tetragonal deformation can be understood on the basis of a density-of-states analysis.

In order to explain the formation of low-temperature phases in stoichiometric Ni2MnGa magnetic shape memory alloy, we investigate the phase transformation paths from cubic austenite with Heusler structure to low-symmetry martensitic structures. We used ab initio calculations combined with the generalized solid state nudged elastic band method to determine the minimum energy path and corresponding changes in crystal lattice. The four-, five-, and seven-layered modulated phases of martensite (4O, 10M, and 14M) are built as the relaxed nanotwinned non-modulated (NM) phase. Despite having a total energy larger than the other martensitic phases, the 10M phase will spontaneously form at 0 K, because there is no energy barrier on the path and the energy decreases with a large negative slope. Moreover, a similar negative slope in the beginning of path is found also for the transformation to the 6M premartensite, which appears as a local minimum on the path leading further to 10M martensite. Transformation paths to other structures exhibit more or less significant barriers in the beginning hindering such a transformation from austenite. These findings correspond to experiment and demonstrates that the kinetics of the transformation is decisive for the selection of the particular low-symmetry structure.

Resonant ultrasound spectroscopy measurements and density functional theory calculations were used to analyze the effect of Co and Cu doping (3-6 at. %) on elastic constants of non-modulated martensite of the Ni-Mn-Ga ferromagnetic shape memory alloy. Due to the doping, the studied alloys exhibited decreased tetragonal ratios c/a≈1.14. Both the experiments and the calculations revealed that the lowering of the c/a ratio resulted in a change of the orientation of the softest shearing modes of the tetragonal lattice. The newly appearing softest shearing modes for the doped materials have approximatelyorientations and indicate a lattice instability directly related to the particularly low twinning stress for compound á ñ 101 101 { } ¯twins, needed for the magnetically induced reorientation.

We have found low temperature a/b nanotwins having (110) twinning plane in a five-layered modulated martensite phase of Ni50Mn25+xGa25−x (at. %) Heusler alloys and identified the particular region in phase diagram where the nanotwinning occurs. Evolution of the structure with decreasing temperature was studied by X-ray diffraction using single crystals exhibiting magnetic shape memory effect. The merging of (400) and (040) lines upon cooling for 2.6 < x < 3.5 indicated a/b nanotwinning originating from the refinement of initially coarse a/b twins. Refinement of the twins with decreasing temperature was observed directly using scanning electron microscopy. The prerequisite for nanotwinning is an extremely low twin boundary energy, which we estimated using first-principles calculations to be 0.16 meV/Å2. As the nanotwinning distorts the relation between the crystal lattice and the X-ray diffraction pattern, it should be taken into consideration in structural studies of Ni-Mn-Ga Heusler alloys.

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