Presentation Information
[O14-5]First-Principles Calculation of Magnetocrystalline Anisotropy in Rare-Earth-Containing RE2Fe14B Alloys
*Haruki Okumura1, Tetsuya Fukushima1, Taro Fukazawa1, Takashi Miyake1, Hisazumi Akai2, Masako Ogura3 (1. AIST (Japan), 2. Osaka Univ. (Japan), 3. LMU Munich (Germany))
Keywords:
First-principles calculation,magnetocrystalline anisotropy,full-potential KKR method,rare-earth,2-14-1 permanent magnet
The calculation of magnetocrystalline anisotropy constants at finite temperature and spin reorientation temperatures has become one of the key challenges in material design. The temperature dependence of the magnetocrystalline anisotropy constant is crucial for improving the performance and predicting the properties of new magnetic materials, thus a comprehensive theoretical approach is strongly required. A material with unique temperature-dependent magnetocrystalline anisotropy is the Nd2Fe14B-based magnet, which is widely used as a permanent magnet material. It is known that at low temperatures, the magnetization easy axis of Nd2Fe14B is oriented approximately 30 degrees from the [001] direction towards the [110] direction, exhibiting a distinct magnetic anisotropy. Similarly, Ho2Fe14B also shows a similar anisotropy. As the temperature increases, both Nd2Fe14B and Ho2Fe14B undergo spin reorientation and exhibit an out-of-plane anisotropy. Furthermore, for RE2Fe14B systems with rare earth elements (RE) such as Pr, Nd, Pm, and Sm, it is reported that the magnetic anisotropy transitions from out-of-plane to in-plane as the temperature increases. These magnetic anisotropies are primarily determined by the magnetic interactions between the RE elements and iron.
To calculate these magnetic anisotropies using first-principles methods, it is essential to accurately account for the localization of the 4f orbitals of the RE elements. However, conventional density functional theory struggles to accurately express this localization, necessitating the introduction of open-core and self-interaction corrections (SIC) for the 4f orbitals. In addition, full-potential calculations are crucial for calculating magnetic anisotropies. The objective of this study is to establish a new computational method based on density functional theory to accurately calculate the magnetic anisotropy of RE2Fe14B magnets with RE elements (RE = Pr, Nd, Pm, Sm, Dy, Ho, Er), and to validate the effectiveness of the method. As a preliminary step toward extending the method to finite temperatures, we present the results of the calculation of the magnetic anisotropy constant at 0 K based on the full-potential Korringa-Kohn-Rostoker (FPKKR) method.
For Nd2Fe14B, when the 4f orbitals were treated as spherical, the experimental easy axis could not be reproduced. In contrast, the open-core + SIC method successfully reproduced the easy axis tilted 30 degrees from the [001] direction toward the [110] direction. The figure illustrates the calculated total energy as a function of angular distribution (θ, φ) for Nd2Fe14B and Ho2Fe14B. For Nd2Fe14B, the minimum total energy is observed at θ = 30 degrees and φ = 45 degrees. Other minima arise due to the tetragonal symmetry of the crystal structure. Similarly, for Ho2Fe14B, the minimum energy is observed at θ = 35 degrees and φ = 45 degrees, suggesting that the easy axis is oriented in this direction. Experimentally, the easy axis for Ho2Fe14B is observed at θ = 22 degrees, but the first-principles calculations qualitatively reproduce the direction of the easy axis.
Next, calculations were performed by varying the type of RE element. As a result, it was found that the magnetic anisotropy of RE2Fe14B transitions from out-of-plane to in-plane, with varying among Pr, Nd, Pm, and Sm. Similar trends were observed for heavy RE elements (Dy, Ho, and Er). This difference in magnetic anisotropy is likely due to the shape of the RE 4f charge distribution. Within the framework of crystal field theory, focusing on the Stevens factor reveals that its sign differs between Pr and Sm (or Dy and Er). This distinction offers an intuitive explanation for the differences in magnetic anisotropy between Pr-based and Sm-based systems. However, the discussion presented here alone cannot explain the peculiar easy axis observed in Nd2Fe14B and Ho2Fe14B. The origin of these anisotropies is currently under investigation.
To calculate these magnetic anisotropies using first-principles methods, it is essential to accurately account for the localization of the 4f orbitals of the RE elements. However, conventional density functional theory struggles to accurately express this localization, necessitating the introduction of open-core and self-interaction corrections (SIC) for the 4f orbitals. In addition, full-potential calculations are crucial for calculating magnetic anisotropies. The objective of this study is to establish a new computational method based on density functional theory to accurately calculate the magnetic anisotropy of RE2Fe14B magnets with RE elements (RE = Pr, Nd, Pm, Sm, Dy, Ho, Er), and to validate the effectiveness of the method. As a preliminary step toward extending the method to finite temperatures, we present the results of the calculation of the magnetic anisotropy constant at 0 K based on the full-potential Korringa-Kohn-Rostoker (FPKKR) method.
For Nd2Fe14B, when the 4f orbitals were treated as spherical, the experimental easy axis could not be reproduced. In contrast, the open-core + SIC method successfully reproduced the easy axis tilted 30 degrees from the [001] direction toward the [110] direction. The figure illustrates the calculated total energy as a function of angular distribution (θ, φ) for Nd2Fe14B and Ho2Fe14B. For Nd2Fe14B, the minimum total energy is observed at θ = 30 degrees and φ = 45 degrees. Other minima arise due to the tetragonal symmetry of the crystal structure. Similarly, for Ho2Fe14B, the minimum energy is observed at θ = 35 degrees and φ = 45 degrees, suggesting that the easy axis is oriented in this direction. Experimentally, the easy axis for Ho2Fe14B is observed at θ = 22 degrees, but the first-principles calculations qualitatively reproduce the direction of the easy axis.
Next, calculations were performed by varying the type of RE element. As a result, it was found that the magnetic anisotropy of RE2Fe14B transitions from out-of-plane to in-plane, with varying among Pr, Nd, Pm, and Sm. Similar trends were observed for heavy RE elements (Dy, Ho, and Er). This difference in magnetic anisotropy is likely due to the shape of the RE 4f charge distribution. Within the framework of crystal field theory, focusing on the Stevens factor reveals that its sign differs between Pr and Sm (or Dy and Er). This distinction offers an intuitive explanation for the differences in magnetic anisotropy between Pr-based and Sm-based systems. However, the discussion presented here alone cannot explain the peculiar easy axis observed in Nd2Fe14B and Ho2Fe14B. The origin of these anisotropies is currently under investigation.
