  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.
