Development of DFT-Based Spin-Orbit Torque Calculations in Magnetic Heterostructures

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姓名

黃寶輝(Bao-Huei Huang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Development of DFT-Based Spin-Orbit Torque Calculations in Magnetic Heterostructures)

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至系統瀏覽論文 (2026-6-30以後開放)

摘要(中)

在磁阻式隨機存取記憶體（magnetoresistive random-access memory，MRAM）的產業中，基於自旋轉移力矩（spin-transfer torque，STT）的STT-MRAM被提議為下一代記憶體裝置，因其具備高速的寫入和讀取性能以及低能耗。然而，直接通過元件的穿隧電流，可能因焦耳熱效應而降低其壽命。在另一方面，新提出的基於自旋軌道力矩（spin-orbit torque，SOT）的SOT-MRAM可能可以克服這一問題。與穿隧電流不同的是，通過重金屬的平面寫入電流在界面產生SOT效應，從而翻轉了自由層的磁化方向。

從理論的角度來看，我們旨在了解自旋力矩的機制，同時考慮材料的性質、磁性、自旋軌道耦合（spin-orbit coupling，SOC）和電控制。我們為此開發了「JunPy」程式，利用非平衡格林函數（nonequilibrium Green′s function，NEGF）方法，與基於第一原理的自洽哈密頓量，來計算零電壓狀態和電流誘導的STT和SOT效應。

在這篇論文中，我們研究四個系統來演示自旋力矩的計算：（1）單分子磁性異質接面（single-molecule magnetic junctions，SMMJs）；（2）Fe/MgO/Fe磁性穿隧異質接面（magnetic tunnel junction，MTJ）；（3）鐵薄膜；（4）新穎凡德瓦二維鐵磁異質接面，Cr3Te4/PtTe2。研究SMMJs和MTJs中的零電壓和電流產生的STT，使我們能夠研究exchange bias效應和電流驅動的磁翻轉。除了利用常見的能量計算法，零電壓的SOT有助於我們探索平面或垂直磁各向異性。最後，我們研究了Cr3Te4/PtTe2中的電流誘導的SOT和介面產生的Rashba效應，演示了使用二維鐵磁材料來設計室溫SOT-MRAM的潛力。這些研究為自旋力矩的機制和操控提供了重要的見解，推動下一代記憶體裝置的發展，並進一步突顯了二維鐵磁材料在實現高效且可靠的MRAM技術中的潛力。

摘要(英)

In the magnetoresistive random-access memory (MRAM) industry, spin-transfer torque (STT) based STT-MRAM has been proposed as a next-generation memory device because of its high-speed writing and reading processes and low energy consumption. However, the direct tunneling current passing through the device can reduce its lifetime due to Joule heating. On the other hand, the newly proposed spin-orbit torque (SOT) based SOT-MRAM may overcome this issue. Instead of a tunneling current, an in-plane writing current flowing through a heavy metal generates a SOT effect at the interface, rotating the magnetization direction of the magnetic free layer.

From a theoretical perspective, we aim to understand the mechanism of spin torques, considering material properties, magnetism, spin-orbit coupling (SOC), and electrical control. For this purpose, we developed the "JunPy" package to calculate STT and SOT using first-principles calculated self-consistent Hamiltonians with the nonequilibrium Green′s function (NEGF) method. This allows us to study both equilibrium and current-induced STT and SOT.

In this dissertation, we examine four systems to demonstrate spin torque calculations: (1) single-molecule magnetic junctions (SMMJs), (2) a conventional Fe/MgO/Fe magnetic tunnel junction (MTJ), (3) iron thin films, and (4) a novel van der Waals two-dimensional ferromagnetic (2DFM) heterojunction, Cr3Te4/PtTe2. Studying the equilibrium and current-induced STT in SMMJs and MTJs allows us to investigate the exchange bias effect and current-driven magnetization switching. The equilibrium SOT helps us exploring in-plane or perpendicular magnetic anisotropy beyond the energy method. Finally, we investigate the current-induced SOT and interfacial Rashba effect in Cr3Te4/PtTe2, demonstrating the potential for designing a room-temperature SOT-MRAM using 2DFM materials. These studies provide valuable insights into the mechanisms and control of spin torques, advancing the development of next-generation MRAM technology. Furthermore, our works highlight the potential of 2DFM materials in achieving efficient and reliable MRAM technology.

關鍵字(中)

★ 自旋軌道力矩
★ 第一原理計算
★ 磁性異質結構
★ 凡德瓦材料
★ 非平衡格林函數
★ JunPy

關鍵字(英)

★ Spin-orbit torque
★ First-principles calculation
★ Magnetic heterostructures
★ Van der Waals materials
★ NEGF
★ JunPy

論文目次

摘要 i
Abstract iii
誌謝 v
Contents vii
List of Figures xi
List of Tables xix
1 Introduction 1
1.1 Current-Driven Magnetic Recording 1
1.1.1 MRAM and Magnetoresistance Effect 1
1.1.2 STT-MRAM and SOT-MRAM 2
1.2 Physics of Spin Current and Spin Torque 3
1.2.1 Spin-Transfer Effect 3
1.2.2 Spin Hall Effect 4
1.2.3 Rashba-Edelstein Effect 5
1.3 Physics of Magnetization Dynamics 7
1.4 Outline of Dissertation 8
2 First-Principles Calculation 11
2.1 Many-Electron Problems 11
2.2 Hartree-Fock Method 12
2.3 Density Functional Theory (DFT) 15
2.3.1 Hohenberg-Kohn Theorems 15
2.3.2 Kohn-Sham Equations 18
2.3.3 Exchange-Correlation Energy Functionals 20
2.4 Pseudopotentials 23
3 Nonequilibrium Green′s Function Formalism (NEGF) 27
3.1 Problems in Quantum Transport 27
3.2 Green′s Function Formalism 29
3.2.1 Time Evolution of Wavefunction 30
3.2.2 Green′s Function Representation 30
3.3 One-Electron Systems 32
3.3.1 Local Density of States 32
3.3.2 Expectation Value and Density Matrix 34
3.3.3 Matrix Representation 35
3.4 Many-Electron Systems 38
3.4.1 Self-Energy and Dyson Equation for Equilibrium Systems 38
3.4.2 Keldysh Equation for Nonequilibrium Systems 40
3.4.3 Expectation Value and Density Matrix 42
3.4.4 Matrix Representation 43
3.5 Two-Probe Systems 44
3.5.1 Hamiltonians and Green′sFunctions. 44
3.5.2 CurrentandTransmission 48
3.5.3 NEGF-DFT in Nanodcal 50
4 Theory of Spin Dynamics and Spin Torques 51
4.1 Theoretical Formalism 51
4.1.1 System Hamiltonian Operator 51
4.1.2 Spin Continuity Equation 52
4.1.3 Dynamics of Local Magnetic Moments 54
4.1.4 Role of Spin Torque in Magnetic Dynamics 55
4.2 First-Principles Implementation 57
4.2.1 Localized Orbital Representation 57
4.2.2 NEGF Formalism 61
5 JunPy Examples 63
5.1 Combining Nanodcal Package (factory.nanodcal) 63
5.1.1 Carbon Chain (Part1) 63
5.1.2 Carbon Chain (Part2) 66
5.1.3 Graphene 71
5.2 Combining Tight-Binding Model (factory.stack) 73
5.2.1 Simple Metallic Chain 73
5.2.2 FM/I/FM Magnetic Tunnel Junction 77
6 Amine-Ended Single-Molecule Magnetic Junctions 81
6.1 Introduction 81
6.2 Computational Details 83
6.3 Results and Discussion 85
6.3.1 EB Effect with Equilibrium FLST Field: DFT+JunPy+LLG 85
6.3.2 Role of Linker and Strain in Equilibrium FLST Field: TB+JunPy 88
6.3.3 Current-Driven Magnetization Switching: DFT+JunPy+LLG 91
6.4 Summary 94
7 Fe/MgO/Fe Magnetic Tunnel Junction 97
7.1 Introduction 97
7.2 Computational Details 99
7.3 Results and Discussion 101
7.3.1 Current-Driven STT without SOC 101
7.3.2 Interfacial SOT and PMA at Equilibrium 104
7.3.3 Layer-Resolved Spin Torque 105
7.4 Summary 107
8 Spin-Orbit Torque and Interfacial Magnetic Anisotropy 109
8.1 Introduction 110
8.2 Computational Details 111
8.3 Results and Discussion 114
8.3.1 Comparison between MAE and SOT 114
8.3.2 Layer-Resolved SOT 115
8.4 Summary 117
9 Cr3Te4-Based van der Waals Heterojunctions 119
9.1 Introduction 119
9.2 Computational Details 122
9.3 Results and Discussion 123
9.3.1 Surface Magnetic Anisotropy 124
9.3.2 Band Structure and Spin Texture 124
9.3.3 Current-Induced Spin-Orbit Torque 127
9.3.4 LLG Simulation 132
9.4 Summary 135
10 Conclusions 137
A Miscellaneous 139
A.1 Exchange Spin Torque in the Form of Cross Product 139
A.2 Extracting Hamiltonian Components 140
A.3 Energy Integration of Equilibrium Part 141
A.3.1 Spin Torque 142
A.3.2 Spin Accumulation 143
Bibliography 145

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指導教授

唐毓慧(Yu-Hui Tang)

審核日期

2024-8-20

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