Driving force for martensitic transformation in ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$

The martensitic transformation in ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$ alloys has been investigated within ab initio density functional theory. The experimental trend of a martensitic transition happening beyond $x=0.36$ is captured within these calculations. The microscopic considerations leading to this are traced to increased Ni-Mn hybridization which results from the Ni atom experiencing a resultant force along a lattice vector and moving towards the Mn atoms above a critical concentration. The presence of the lone pair electrons on Sn forces the movement of Ni atoms away from Sn. While band Jahn Teller effects have been associated with this transition, we show quantitatively that at least in this class of compounds they have a minor role.

Figure 1

Atom and angular momentum projected partial density of states for (a) Ni $3d$, (b)Mn $3d$, (c) Sn $5p$, and (d) Sn $5s$ in the parent compound ${\mathrm{Ni}}_2\mathrm{MnSn}$. The Fermi energy ${\mathrm{E}}_F$ is at 0 eV.

Figure 2

Ni-Mn1 and Ni-Mn2 bond distances in Å units, after full relaxation of the cubic structure of composition $x=0.25$, 0.375, and 0.50 of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1+x}{\mathrm{Sn}}_{1-x}$. The direction of magnetic moment on each atom has been indicated by an arrow.

Figure 3

Line charge density of the Sn $5s$ states along the Sn-Mn and Sn-Ni bond. The respective bond lengths are indicated in parentheses.

Figure 4

The tight-binding (circles) as well as the ab initio band structure (solid line) of ${\mathrm{Ni}}_2{\mathrm{Mn}}_{1.5}{\mathrm{Sn}}_{0.5}$ in the (a) cubic and the (b) fully relaxed tetragonal phase.