Microscopic theory of the martensitic transition inFe1−xNix

Fixed-spin-moment band-structure calculations of ${\mathrm{Fe}}_3$Ni show that the face-centered-cubic structure is unstable with respect to small tetragonal distortions. Using the Bain transformation for the crossover from the fcc to the bcc structure, we show that the ground state of ${\mathrm{Fe}}_3$Ni corresponds, in agreement with experiment, to the bcc structure, which is by 1.75 mRy/atom lower in energy than the fcc structure. The band structure of the nonmagnetic phase of fcc ${\mathrm{Fe}}_3$Ni reveals Fermi-surface nesting, which can give rise to Kohn-like anomalies. This nesting behavior is very similar to what has recently been found in the nonmagnetic ${\mathrm{Ni}}_{\mathit{x}}$ ${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$ compound [G. L. Zhao and B. N. Harmon, Phys. Rev. B 45, 2818 (1992)]. We argue that this nesting behavior is one of the causes for the martensitic transition in ${\mathrm{Fe}}_3$Ni. The change in the phonon-dispersion curves, which is connected with the formation of martensite, is evaluated by using the method of Varma and Weber [C. M. Varma and W. Weber, Phys. Rev. Lett. 39, 1094 (1977)]. We find pronounced softening of the ${\mathrm{TA}}_2$ shear mode for q in the [110] direction and a polarization vector along the [001] direction. The search for Invar anomalies in fcc ${\mathrm{Fe}}_3$Ni has shown that there are two competing effects, of which one is connected with the structural change from the fcc to the bcc structure, and the other with the magnetovolume instability in the fcc structure, involving a transition from the low-moment (LM) to the high-moment (HM) state in a critical range of volumes. It is argued that in ${\mathrm{Fe}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ni}}_{\mathit{x}}$ and for x>0.65 the gain in energy due to the formation of martensite is more favorable as compared to the gain in exchange energy from the LM→HM transition, whereas for x<0.65 is it more favorable to form Invar.