Relevance of $4f$-$3d$ exchange to finite-temperature magnetism of rare-earth permanent magnets: an ab-initio-based spin model approach for NdFe$_{12}$N

A classical spin model derived ab initio for rare-earth-based permanent magnet compounds is presented. Our target compound, NdFe$_{12}$N, is a material that goes beyond today's champion magnet compound Nd$_{2}$Fe$_{14}$B in its intrinsic magnetic properties with a simpler crystal structure. Calculated temperature dependence of the magnetization and the anisotropy field agree with the latest experimental results in the leading order. Having put the realistic observables under our numerical control, we propose that engineering $5d$-electron-mediated indirect exchange coupling between $4f$-electrons in Nd and $3d$-electrons from Fe would most critically help to enhance the material's utility over the operation-temperature range.