Ab initio calculations of the magnetic shape-memory alloy ${\mathrm{Ni}}_{50}{\mathrm{Mn}}_x{\mathrm{Al}}_{50-x}$ with $0⩽x⩽50$ were carried out using density functional theory and PAW potentials. The alloy is ferromagnetic in the range from 14 to 31 at.$\%$ $\mathrm{Mn}$. The magnetic moment and structural properties are discussed in terms of the density of states. Furthermore martensitic phases with long-periodic shuffling structure were calculated: $2\mathrm{M}$, $10\mathrm{M}$, and $14\mathrm{M}$. Their stability is discussed in respect to the electronic structure and the lattice dynamics, whereby phonon dispersion relations in [110] direction for the cubic ${\mathrm{L}2}_1$ Heusler structure have been calculated. The transverse-acoustic phonon mode is shown to soften at the wave vector $\zeta =[1∕\mathrm{3\hspace{0.17em}}1∕3\mathrm{\hspace{0.17em}0}]$ which confirms the tendency of ${\mathrm{Ni}}_2\mathrm{MnAl}$ to form modulated structures at low temperatures. The theoretical results of the modulated martensitic phases correspond to experimental data, obtained from thin films near the stoichiometric composition.

• Received 27 November 2003

DOI:https://doi.org/10.1103/PhysRevB.70.014111