Title: Competing Ferromagnetic and Anti-Ferromagnetic interactions in Iron Nitride $ζ$-Fe$_2$N,
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.