Role of typical elements in Nd${}_2$Fe${}_{14}$$X$ ($X$ = B, C, N, O, F)

The magnetic properties and structural stability of Nd${}_2$Fe${}_{14}X$ ($X$ = B, C, N, O, F) are theoretically studied by first-principles calculations focusing on the role of $X$. We find that B reduces the magnetic moment (per formula unit) and magnetization (per volume) in Nd${}_2$Fe${}_{14}$B. The crystal-field parameter $A_2^0⟨r^2⟩$ of Nd is not enhanced either, suggesting that B has minor roles in the uniaxial magnetocrystalline anisotropy of Nd. These findings are in contrast to the long-held belief that B works positively for the magnetic properties of Nd${}_2$Fe${}_{14}$B. As $X$ changes from B to C, N, O and F, both the magnetic properties and stability vary significantly. The formation energies of Nd${}_2$Fe${}_{14}X$ and $\alpha$-Fe relative to that of Nd${}_2$Fe${}_{17}X$ are negative for $X$ = B and C, whereas they are positive when $X$ = N, O and F. This indicates that B plays an important role in stabilizing the Nd${}_2$Fe${}_{14}$B phase.