Large magnetic anisotropy predicted for metastable structures of rare-earth free Co-Fe-N compounds

Metastable structures of cobalt nitrides and Fe-substituted cobalt nitrides are explored as promising candidates for rare-earth free permanent magnets. Through crystal structure searches using adaptive genetic algorithm, new structures of Co$_{\mathrm{n}}$N (n $=$ 3\textellipsis 8) are found to have lower energies than those previously discovered by experiments. Substituting a fraction of Co with Fe helps to stabilize the new structures and at the same time further improve the magnetic properties. Based on first-principles density functional calculation, large magnetic anisotropy energy is predicted in this system, reaching as high as 3.18 MJ/m$^{\mathrm{3}}$ (245.6 $\mu $eV per transition metal atom). In addition, for the extensively studied Fe$_{\mathrm{16}}$N$_{\mathrm{2}}$ magnets, we discuss a tetragonal to cubic structure transition as replacing Fe with Co, which can be well explained by electron counting analysis. Different magnetic properties in Co$_{\mathrm{16-x}}$Fe$_{\mathrm{x}}$N$_{\mathrm{2}}$ between the Co-rich side (x $\le $ 8) and Fe-rich side (x \textgreater 8) is closely related to the structural transition.