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研究生:蔡佳晉
研究生(外文):Chia-Chin Tsai
論文名稱:利用投影式向量磁鐵進行自旋軌道矩之角度分析
論文名稱(外文):Angular Analysis of Spin-Orbit Torques with a Projected Field Vector Magnet
指導教授:白奇峰
指導教授(外文):Chi-Feng Pai
口試委員:洪銘輝樊昕
口試委員(外文):Minghwei HongXin Fan
口試日期:2023-01-13
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:材料科學與工程學系
學門:工程學門
學類:材料工程學類
論文種類:學術論文
論文出版年:2023
畢業學年度:111
論文頁數:144
中文關鍵詞:自旋電子學自旋霍爾效應自旋軌道矩二次諧波霍爾電壓量測自旋軌道矩鐵磁共振向量磁鐵
外文關鍵詞:SpintronicsSpin Hall EffectSpin-Orbit TorqueSecond Harmonic Hall Voltage MeasurementSpin-Torque Ferromagnetic ResonanceVector Magnet
DOI:10.6342/NTU202300150
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近年來,自旋軌道矩因具有實現高速自旋電子學裝置的強大潛力與前景而受到廣泛關注,例如:自旋軌道矩磁性隨機存取記憶體(SOT-MRAM)、自旋振盪器和太赫茲發射器。為了研究新穎材料中的自旋軌道矩,已開發出多種量測技術,包括自旋軌道矩鐵磁共振、二次諧波霍爾電壓量測和磁滯曲線平移量測。然而這些測量通常需要對磁場進行複雜操作,若使用單一電磁鐵作為磁場來源進行量測會相當棘手,像是旋轉磁場的量測就會需要修正為旋轉試片,自然試片製備工序就會增加。而使用向量磁鐵作為磁場源問題就迎刃而解,因為它可以在原先的量測架構上直接輸出旋轉磁場,並大幅縮短量測時間。

在本論文中,利用實驗室中校準良好的向量磁鐵,建立了二次諧波霍爾電壓(HHV)測量和自旋軌道矩鐵磁共振(ST-FMR)測量的分析流程。通過對 鉑/鈷鐵硼/氧化鎂/鉭 和 鎢/鈷鐵硼/氧化鎂/鉭 標準試片對照組的一系列檢查,證明此分析技術的可靠度與有效性。由於二次諧波霍爾電壓需要對於不同外加場強度進行角度掃描,以向量磁鐵取代一般固定磁場搭配旋轉馬達系統可以最大化量測效率。此外,還將比較兩種不同的HHV測量設置的優缺點:一種使用交流電流,另一種使用相反方向的直流電之電壓差。儘管掃場量測圖譜足以進行ST-FMR分析,其角度掃描分析可以額外獲得異常自旋之資訊,包含異常自旋軌道矩的方向與強度。本論文利用向量磁鐵建構角度掃描的自旋軌道矩分析技術,這些流程可以幫助我們在未來對更多奇異系統進行研究。
Spin-orbit torques (SOTs) have gained significant attention in recent years due to their potential to enable high-speed spintronic devices, such as SOT-magnetic random ac- cess memory (SOT-MRAM), spin-Hall nano-oscillators, and terahertz emitters. To study SOTs in novel materials, several characterization methods have been developed, including harmonic Hall technique, spin-torque ferromagnetic resonance, and hysteresis loop shift measurement. However, these measurements often require complex manipulation of magnetic fields, which can be challenging using a compact electromagnet setup. A vector magnet can help overcome this challenge. With such a magnet, angle-dependent measurements can be achieved without the need for time-consuming wire-bonding processes, allowing for measurements to be taken directly using a rotating magnetic field.

In this thesis, taking advantage of the well-calibrated vector magnet available in the lab, the measurement protocols of in-plane second harmonic Hall voltage (HHV) measurements and spin-torque ferromagnetic resonance (ST-FMR) measurements are established. The validity of these protocols will be demonstrated through a series of examinations on control series Pt(d)/CoFeB(3)/MgO(1)/Ta(1) and W(d)/CoFeB(3)/MgO(1)/Ta(1). HHV measurements are significantly accelerated by the vector magnet, as they typically require time-consuming field-dependent angle-scan measurements using a compact electromagnet and motor. In addition, the pros and cons of two different setups for HHV measurements will be compared: one using an alternating applied current to measure the transverse response and the other using opposite direct current directions to probe the voltage difference. Although field-scan procedures are sufficient for ST-FMR analysis, the power of angle-dependent ST-FMR measurements in extracting anomalous spin efficiencies will be demonstrated as well. This thesis utilizes the vector magnet to facilitate angle-dependent SOT characterization techniques. After these protocols are mature and reliable, more exotic systems can be well-studied.
Verification Letter from the Oral Examination Committee i
Acknowledgements iii
摘要 v
Abstract vii
Contents ix
List of Figures xiii
List of Tables xxiii
Denotation xxv

Chapter 1 Introduction 1
1.1 Anisotropic Magnetoresistance 1
1.2 Hall Effect 2
1.2.1 Ordinary Hall Effect 3
1.2.2 Planar Hall Effect 4
1.2.3 Anomalous Hall Effect 4
1.2.4 Spin Hall Effect 7
1.3 Nernst Effect 9
1.3.1 Ordinary Nernst Effect 9
1.3.2 Anomalous Nernst Effect 10
1.3.3 Planar Nernst Effect 10
1.4 Magnetization Dynamics 12
1.4.1 Landau-Lifshitz-Gilbert Equation 12
1.4.2 Ferromagnetic Resonance 13
1.4.3 Spin-Transfer Torque 15
1.4.4 Spin-Orbit Torque 17
1.5 Motivation of This Work 19

Chapter 2 Sample Preparation 21
2.1 Fabrication Techniques 21
2.1.1 Magnetron Sputtering 21
2.1.2 Photolithography 23
2.1.3 Ion Beam Etching 26
2.2 Preparation Flows 28

Chapter 3 Measurement 31
3.1 Projected Vector Field Magnet Setup 31
3.2 Harmonic Hall Voltage (HHV) Measurement 33
3.2.1 PHE Curve Shift Measurement Setup (DC Setup) 37
3.2.2 Harmonic Hall Measurement Setup (AC Setup) 40
3.3 Spin-Torque Ferromagnetic Resonance (ST-FMR) Measurement 44
3.3.1 Microwave Circuit Setup 52
3.3.2 Summary of the Experiments 58

Chapter 4 Spin-Orbit Torque Characterizations via Harmonic Hall 61
4.1 Measurement Setup 61
4.2 Analysis Protocols 63
4.3 Current Dependence 67
4.4 W/CoFeB and Pt/CoFeB Control Samples 72
4.5 Comparison between DC and AC Measurements 82
4.6 Short Summary 86

Chapter 5 Spin-Orbit Torque Characterizations via ST-FMR 89
5.1 Measurement Setup and Analysis Protocol 90
5.2 Frequency-Dependent Analysis 91
5.3 Thickness-Dependent Analysis 93
5.4 Angle-Dependent Analysis 97
5.5 Observation of Unconventional Spins 102

Chapter 6 Summary 107

References 111

Appendix A — Mathematical derivations of ST-FMR 125
A.1 Definitions of coordinate axes 125
A.2 Spin rectification effect 126
A.3 Solve for the oscillatory components 128
A.3.1 The damping term αmˆ × mˆ 128
A.3.2 The equilibrium torques 129
A.3.3 The non-equilibrium torques 130
A.3.4 Solving the LLGS equation 131
A.3.5 The in-phase component 133
A.3.6 Expansion about the resonance field 134
A.4 Standard measurement 136

Appendix B — Code 139
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