Electronic and magnetic structures of the rare-earth permanent magnet ${\mathrm{Nd}}_2$${\mathrm{Fe}}_{14}$B

Electronic and magnetic structures of ${\mathrm{Nd}}_2$${\mathrm{Fe}}_{14}$B are investigated by performing self-consistent local-density-approximation band-structure calculations and photoemission-spectroscopy (PES) measurements. Employing the linear muffin-tin-orbital band method, we have obtained electronic band structures for both paramagnetic and ferromagnetic phases of ${\mathrm{Nd}}_2$${\mathrm{Fe}}_{14}$B, and compared the calculated density of states (DOS) with the experimental data obtained from PES measurements. It is found that B atoms contribute to the stabilization of the structure and substantially reduce the magnetic moment of neighboring Fe atoms through a hybridization interaction. The average magnetic moment of Fe atoms in the ferromagnetic phase is estimated to be 2.15${\mathrm{\mu }}_{\mathit{B}}$. Depending on the distances from B atoms, Fe atoms at the ${\mathit{j}}_2$ site and those at the e site have the largest and smallest magnetic moments, respectively, in qualitative agreement with the experimental trend. The valence-band PES measurements for Nd 4f states indicate that the Nd valence is close to trivalent, with negligible Nd 4f spectral intensity close to ${\mathit{E}}_{\mathit{F}}$, which is consistent with the observed trivalent Nd 4f magnetic moments in this compound. The line shape of the Nd 4f PES is broader than that of pure Nd metal, reflecting effects of the hybridization between Nd 4f and Fe 3d electrons. The Fe 3d PES spectrum shows that the Fe 3d electrons mainly determine the DOS near ${\mathit{E}}_{\mathit{F}}$. The calculated Fe 3d projected local density of states agrees reasonably well with the Fe 3d PES spectrum, which implies that the Fe 3d magnetism in ${\mathrm{Nd}}_2$${\mathrm{Fe}}_{14}$B may well be understood in terms of the itinerant magnetism of Fe 3d electrons.