Magnetic Order and Lattice Instabilities in Ni$_{2}$Mn$_{1+x}$Sn$_{1-x}$ Heusler based Magnetic Shape-Memory Alloys

TL;DR

This study uses first-principles calculations to clarify magnetic order and lattice instabilities in Ni$_{2}$Mn$_{1+x}$Sn$_{1-x}$ alloys, resolving a long-standing debate and linking magnetic state to structural stability.

Contribution

It conclusively determines ferromagnetic alignment of Mn in Ni-Mn-Sn alloys and connects magnetic order with phonon instabilities, advancing understanding of their magneto-structural behavior.

Findings

FM spin alignment of Mn confirmed by phonon calculations

TA2 phonon mode instability linked to FM phase

FM phase becomes stable at 300 K, FI remains unstable

Abstract

The magnetic correlations in the austenite phase and the consequent martensitic transition in inverse magnetocaloric alloys, Ni$_{2}$Mn$_{1+x}$Sn$_{1-x}$, have been a matter of debate for decades. We conclusively establish using {\it ab initio} phonon calculations that the spin alignment of excess Mn at the Sn site (Mn$_{Sn}$) with the existing Mn in the unit cell in the high temperature cubic phase of Ni-Mn-Sn alloy is ferromagnetic (FM), and not ferrimagnetic (FI), resolving a long lasting controversy. Using first principles density functional perturbation theory (DFPT), we observe an instability of the TA$_{2}$ mode along the $\Gamma$-M direction in the FM phase, very similar to that observed in the prototypical ferromagnetic shape memory alloy (FSMA) Ni$_{2}$MnGa. This specific instability is not observed in the FI phase. Further finite temperature first principles lattice dynamics calculations reveal that at 300 K the FM phase becomes mechanically stable, while the FI phase continue to remain unstable providing credence to the fact that the high-temperature phase has FM order. These results will be primordial to understand the magneto-structural properties of this class of compounds.