  The ab initio electronic structure calculations of the Ni$_{2}$MnGa The 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.
