Magnetic anisotropy ofR2Fe14B(R=Nd, Gd, Y): …

The magnetocrystalline anisotropy energy (MAE) of rare-earth transition-metal intermetallics ${R}_{2}{\text{Fe}}_{14}\text{B}$ ($R=\text{Nd}$, Gd, Y) was calculated by using the linear combination of pseudo-atomic-orbital method. Electronic structures were calculated by using relativistic density functional theory with Hubbard-type on-site Coulomb potential $U$ for $f$ electrons in the $R$ sites. The calculated magnetic moments of ${\text{Y}}_{2}{\text{Fe}}_{14}\text{B}$ and ${\text{Gd}}_{2}{\text{Fe}}_{14}\text{B}$ are in agreement with the experimentally measured saturation moments of these compounds. The calculated MAEs of ${\text{Y}}_{2}{\text{Fe}}_{14}\text{B}$ and ${\text{Gd}}_{2}{\text{Fe}}_{14}\text{B}$ are also in agreement with the value measured at low temperature. Moreover, it was found that the shape of the charge density at the Nd sites is aspherical, which causes larger MAE of ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$ than that of ${\text{Gd}}_{2}{\text{Fe}}_{14}\text{B}$. However, the orbital moment of the $4f$ electrons at the Nd sites and the MAE of ${\text{Nd}}_{2}{\text{Fe}}_{14}\text{B}$ were underestimated within the scope of a relativistic local-density approximation plus $U$ with spherical average potential.