臺灣博碩士論文加值系統

異常霍爾效應可說是不需要外加磁場的霍爾效應，一般被認為只出現在鐵磁性的導體，而且其強度正比於材料的磁化強度。近年來理論物理學家透過貝里相的概念以及第一原理計算，發現在非平行的反鐵磁系統也可能有不小的異常霍爾效應，起源於系統磁性結構的對稱破缺以及自旋軌道耦合的影響，而有非零的貝里曲率。由於自旋電子學研究的興起，反鐵磁系統有望被應用於自旋電子元件而引起不少注意。此論文透過第一原理密度泛函理論計算，研究非平行的反鐵磁系統Mn3X (X=Ga, Ge, Sn, Ir, Rh, Pt)的電子及磁性結構，在對稱破缺的方向，其異常霍爾電導率約在100到300 (S/cm)間，與常見的鐵磁Fe有相同的數量級。我們也透過軌道磁化強度的現代理論研究這些反>鐵磁系統的軌道磁化強度。對於Mn3Rh、Mn3Ir及Mn3Pt，其軌道磁化強度大小相當於自旋磁化強度。而對Mn3Ga、Mn3Ge及Mn3Sn而言，軌道磁化強度更大於自旋磁化強度，這個結果能解釋在實驗中觀察到的微弱鐵磁現象，可能是來自軌道的貢獻，有別於一般的磁性系統其自旋的貢獻才是主導整個系統的磁化強度。

The anomalous Hall effect (AHE) can be considered as a kind of Hall effect without external magnetic field. It has been thought to be present only in ferromagnetic conductors, with its size being proportional to the net magnetization. Using the Berry phase concept and first principle calculations, physicists recently demonstrated that large AHE may appear in noncollinear antiferromagnets, which is driven by the non-vanishing Berry curvature because of the symmetry breaking of their magnetic configuration and spin-orbit coupling. While the spintronics are becoming promising, the understanding of the antiferromagnets are of interest for its development. In this thesis, we study the electronic and magnetic structure of the noncollinear antiferromagnets Mn3X (X=Ga, Ge, Sn, Ir, Rh, Pt) by first principles density functional theory calculations. At broken-symmetry direction, the anomalous Hall conductivity is about 100 to 300 (S/cm), which has the same order as the normal ferromagnetic iron. We also study their orbital magnetization by modern theory of orbital magnetization. The magnitude of orbital magnetization in Mn3Rh, Mn3Ir and Mn3Pt is equivalent to spin magnetization. As for Mn3Ga, Mn3Ge and Mn3Sn, their orbital magnetization is even larger than spin magnetization. The results could explain that the weak ferromagnetism observed in experiments, is caused by the orbital contribution, instead of the spin contribution that dominates the magnetization in most of the magnetic system.

口試委員會審定書i
誌謝ii
摘要iii
Abstract iv
1 Introduction 1
2 Theoretical background 5
2.1 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Thomas-Fermi model . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 The Hohenberg-Kohn theorems . . . . . . . . . . . . . . . . . . 7
2.1.3 Kohn-Sham ansatz . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.4 Exchange and correlation . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Norm-conserving pseudopotentials . . . . . . . . . . . . . . . . . . . . . 14
2.3 Maximally-localized Wannier function . . . . . . . . . . . . . . . . . . . 17
2.3.1 Wannier function . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Reciprocal representation . . . . . . . . . . . . . . . . . . . . . . 19
2.3.3 Wannier interpolation . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Anomalous Hall effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Berry phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 Anomalous Hall conductivity . . . . . . . . . . . . . . . . . . . 23
2.5 Modern theory of orbital magnetization . . . . . . . . . . . . . . . . . . 25
2.6 Example: bcc-Fe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Anomalous Hall effect and orbital magnetization in Mn3Ir, Mn3Rh, and Mn3Pt 31
3.1 Crystal structure and magnetic configuration . . . . . . . . . . . . . . . . 31
3.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Symmetry and the Berry curvature . . . . . . . . . . . . . . . . . . . . . 34
3.5 Electronic structure, anomalous Hall effect and orbital magnetization . . . 35
4 Anomalous Hall effect and orbital magnetization in Mn3Ga, Mn3Ge, and Mn3Sn 42
4.1 Crystal structure and magnetic configuration . . . . . . . . . . . . . . . . 42
4.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 Magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 Symmetry and the Berry curvature . . . . . . . . . . . . . . . . . . . . . 45
4.5 Electronic structure, anomalous Hall effect and orbital magnetization . . . 47
5 Summary 52
Bibliography 54

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