# First principles study of the structural phase stability and magnetic order in various structural phases of Mn$_2$FeGa

## TL;DR

This study uses density functional theory to analyze the structural stability and magnetic order of Mn$_2$FeGa across different phases, revealing phase transformation mechanisms and magnetic interactions.

## Contribution

It provides a detailed first-principles analysis of phase stability, transformation pathways, and magnetic structures in Mn$_2$FeGa, highlighting the Jahn-Teller effect and magnetic interactions.

## Key findings

- Hexagonal to tetragonal transformation involves a Heusler-like phase.
- Tetragonal phase exhibits collinear ferromagnetic order due to exchange interactions.
- Hexagonal phase has in-plane magnetic moments with no frustration.

## Abstract

We investigate the structural and magnetic properties of Mn$_{2}$FeGa for different phases(cubic, hexagonal and tetragonal) reported experimentally using density functional theory. The relative structural stabilities, and the possible phase transformation mechanisms are discussed using results for total energy, electronic structure and elastic constants. We find that the phase transformation form hexagonal to ground state tetragonal structure would take place through a Heusler-like phase which has a pronounced electronic instability. The electronic structures, the elastic constants and the supplementary phonon dispersions indicate that the transition from the Heusler-like to the tetragonal phase is of pure Jahn-Teller origin. We also describe the ground state magentic structures in each phase by computations of the exchange interactions. For Heusler-like and tetragonal phases, the ferromagnetic exchange interactions associated with the Fe atoms balance the dominating antiferromagnetic interactions between the Mn atoms leading to collinear magnetic structures. In the hexagonal phase, the direction of atomic moment are completely in the planes with a collinear like structure, in stark contrast to the well known non-collinear magnetic structure in the hexagonal phase of Mn$_{3}$Ga, another material with similar structural properties. The overwhelmingly large exchange interactions of Fe with other magnetic atoms destroy the possibility of magnetic frustration in the hexagonal phase of Mn$_{2}$FeGa. This comprehensive study provides significant insights into the microscopic physics associated with the structural and magnetic orders in this compound.