  We study magnetic properties of NdFe$_{11}$Ti$X$, where $X$=B, C, N, O, and
F, by using the first-principles calculation based on the density functional
theory. Its parent compound NdFe$_{11}$Ti has the ThMn$_{12}$ structure, which
has the symmetry of space group $I4/mmm$, No. 139. The magnetization increases
by doping B, C, N, O, and F at the $2b$ site of the ThMn$_{12}$ structure. The
amount of the increase is larger for $X$=N, O, F than for $X$=B, C. On the
other hand, the crystal field parameter $\langle r^{2} \rangle A_{0}^{2}$,
which controls the axial magnetic anisotropy of the Nd $4f$ magnetic moment,
depends differently on the dopant. With increase of the atomic number from
$X$=B, $\langle r^{2} \rangle A_{0}^{2}$ increases, takes a maximum value for
$X$=N, and then turns to decrease. This suggests that in NdFe$_{11}$Ti$X$,
nitrogen is the most appropriate dopant among B, C, N, O, and F for permanent
magnets in terms of magnetization and anisotropy. The above calculated
properties are explained based on the detailed analysis of the electronic
structures of NdFe$_{11}$Ti$X$.
