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Second-order Perturbation Formula for Magnetocrystalline Anisotropy using Orbital Angular Momentum Matrix

J. Phys. Soc. Jpn.

2014年3月17日(月)

J. Phys. Soc. Jpn. ( DOI: http://dx.doi.org/10.7566/JPSJ.83.044707 )
Taichi Kosugi ( AIST and RIKEN )
Takashi Miyake ( AIST )
Shoji Ishibashi ( AIST )

Abstract

We derive succinctly a second-order perturbation formula for the correction to the energy eigenvalue of an electronic system subject to spin-orbit interactions (SOI).
The energy correction is demonstrated to originate in the spin-conserving and the spin-flip transitions.
The former contributions are represented by the orbital angular momentum (OAM) acquired by the valence electrons via the SOI.
The latter contributions is found to come from the quantum fluctuation effect.
In the limit of strong exchange interaction with completely filled majority spin bands, the formula derived is reduced to the well known Bruno’s formula [Phys. Rev. B 39 (1989) 865].
By using our formula, we examine the relativistic electronic structures of two examples, a d orbital chain and L10 alloys.
The tight-binding calculations are performed for the d orbital chain.
The appearance of OAM in the chain is clearly understood by using a parabolic-bands model and the exact expressions of the single-particle states.
The total energy are found to be rather accurately reproduced by the formula, though the formula does not take into account the variation in the Fermi level.
The self-consistent fully relativistic (FR) first-principles calculations based on the density functional theory (DFT) are performed for five L10 alloys, FePt,CoPt, FePd, MnAl, and MnGa.
It is found that the formula reproduces qualitatively the behavior of their exact magnetocrystalline anisotropy (MCA) energies.
While the MCA of FePt, CoPt, and FePd is found to originate in the spin-conserving transitions, that in MnAl and MnGa is found to originate in the spin-flip contributions.
For FePt, CoPt, and FePd, the tendency of the MCA energy with the variation in the lattice constant is found to obey basically that of the spin-flip contributions.
These results indicate that not only the anisotropy of OAM itself, but also that of spin-flip contributions must be taken into account for the understanding of the MCA of the L10 alloys.
The formula derived in the present study is tractable and useful for self-consistent FR DFT calculations.

その他特記事項

本研究は、科研費新学術領域「コンピューティクスによる物質デザイン」、科研費基盤C、次世代スパコン戦略プログラム、CMSIの支援を受けた。


研究活動

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東工大元素戦略拠点 (東京工業大学)
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構造材料元素戦略研究拠点 (京都大学)
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高効率モーター用 磁性材料技術研究組合