First principles study of doping effects in NdFe$_{11}$Ti permanent magnet compound

Permanent magnet compounds are required to have large magnetization and strong uniaxial magnetocrystalline anisotropy. NdFe$_{11}$Ti which is one of the ThMn$_{12}$-type rare-earth 3d-transition metal compounds has large magnetic moment due to its high content of Fe. The magnetization and magnetocrystalline anisotropy of the compound can be tuned by nitrogen doping at interstitial sites. NdFe$_{11}$TiN is a good candidate for a permanent magnet compound. Then, it is interesting whether there is another dopant that enhances the magnetic properties. We have investigated doping effects of NdFe$_{11}$TiX where X$=$B, C, N, O, and F by using first principles calculation. These dopants increase the magnetization, and the increase is especially large for N, O, and F doping. The magnetocrystalline anisotropy is estimated from the crystalline electric field parameter \textless r$^{2}$\textgreater A$_{2}^{0}$. NdFe$_{\mathrm{11}}$TiB has negative value of \textless r$^{2}$\textgreater A$_{2}^{0}$ that implies the compound has in-plane anisotropy. As the atomic number of the dopant increases from B to N, \textless r$^{2}$\textgreater A$_{2}^{0}$ is increased, and NdFe$_{11}$TiN has a large positive value, suggesting strong uniaxial anisotropy. Then, \textless r$^{2}$\textgreater A$_{2}^{0}$ turns to decrease as the dopant is changed from N to O to F, and NdFe$_{11}$TiF has a large negative value. In conclusion, we found that N is the most appropriate dopant among B, C, N, O, and F.