Phase stability and magnetic properties of ThMn$_{12}$ type rare-earth materials*

We investigate the chemical and the dynamical stabilities, and magnetic properties of Ce-based ThMn$_{12}$ materials with the {\it ab initio} calculations that use the $4f$ electrons. Phonon calculations predict positive frequencies in CeFe$_{12}$ and CeFe$_{12}$N suggesting that both compounds are dynamically stable. The calculated formation energy is positive for CeFe$_{12}$, confirming that it cannot be synthesized experimentally in bulk. The formation energy is improved significantly by the addition of nitrogens to the interstitial sites. We also computed the phonon frequencies and found all positive in the substituted compounds. Electronic structure results indicate composition-dependent Ce mixed-valence behavior, which modifies magnetocrystalline anisotropy (MCA). The calculations yield a large MCA constant, $K_1$, in all compositions, especially in CeZrFe$_{11}$. While nitrogen improves the magnetic moment, it has the opposite effect in $K_1$.