  The magnetic properties of Nd${}_2$Fe${}_{14}$B (NFB)/transition metal (TM =
Fe, Co) multilayer systems are studied on the basis of first-principles density
functional calculations. We optimize the model structure under a variety of
crystallographic alignments of the NFB layer, and analyze the mechanism of
interface magnetic coupling. Improvements in remanent magnetization compared to
that of single NFB are observed in NFB(001)/Fe, NFB(110)/Fe, and NFB(100)/Co.
On the other hand, in NFB(100)/Fe, remanence degradation due to the
anti-parallel magnetization alignment between NFB and Fe layers is observed. In
this system, which has the shortest optimized interlayer distance among all
considered systems, an itinerant electron magnetism is required around the
interface to lower the total energy, and accordingly, anti-ferromagnetic
coupling is preferred. The significant difference in property between
NFB(100)/Fe and NFB(100)/Co is attributed to the difference between their
interface structures, optimized interlayer distances, and magnetic stiffness of
TM layers.
