# Competing Ferromagnetic and Anti-Ferromagnetic interactions in Iron Nitride $\zeta$-Fe$_2$N

## TL;DR

This study uses first-principles calculations to determine that the ground state of zeta-Fe₂N is ferromagnetic, with competing magnetic interactions and implications for experimental magnetic transition observations.

## Contribution

It provides a detailed first-principles analysis revealing the ferromagnetic ground state and competing interactions in zeta-Fe₂N, clarifying previous experimental ambiguities.

## Key findings

- Ground state of zeta-Fe₂N is ferromagnetic with a magnetic moment of 1.528 μ_B.
- FM state is lower in energy than AFM and NM states by 8.44 meV and 191 meV per formula unit.
- Presence of competing FM and AFM interactions mediated by nitrogen atoms.

## Abstract

The paper discusses the magnetic state of zeta phase of iron nitride viz. $\zeta$-Fe$_2$N on the basis of spin polarized first principles electronic structure calculations together with a review of already published data. Results of our first principles study suggest that the ground state of $\zeta$-Fe$_2$N is ferromagnetic (FM) with a magnetic moment of 1.528 $\mu_\text{B}$ on the Fe site. The FM ground state is lower than the anti-ferromagnetic (AFM) state by 8.44 meV and non-magnetic(NM) state by 191 meV per formula unit. These results are important in view of reports which claim that $\zeta$-Fe$_2$N undergoes an AFM transition below 10K and others which do not observe any magnetic transition up to 4.2K. We argue that the experimental results of AFM transition below 10K are inconclusive and we propose the presence of competing FM and AFM superexchange interactions between Fe sites mediated by nitrogen atoms, which are consistent with Goodenough-Kanamori-Anderson rules. We find that the anti-ferromagnetically coupled Fe sites are outnumbered by ferromagnetically coupled Fe sites leading to a stable FM ground state. A Stoner analysis of the results also supports our claim of a FM ground state.