臺灣博碩士論文加值系統

本論文探討具有垂直異向性之Ta/CoFeB/MgO結構，在通入in-plane電流下，自旋霍爾效應(Spin Hall effect,SHE)產生之等效場驅動磁矩翻轉的現象。
我們透過Landau–Lifshitz–Gilbert(LLG)方程式模擬磁矩隨時間演進的運動過程，並將計算結果與實驗數據進行比較，主題可分為以下幾類：(1)固定外加磁場下的電流掃瞄模擬：模擬各外加磁場下的電流翻轉曲線，經由計算結果可得知不同電流方向與外加磁場方向所產生之SHE等效場差異，並透過解析方法計算翻轉電流密度(Jc)，且經由改變外加磁場角度與易磁化軸傾斜角度研究Jc之變化。(2)固定電流下的磁場掃瞄模擬：模擬各電流下的磁滯曲線，以解析方法計算矯頑場(Hc)，並經由易磁化軸傾斜下Hc之變化，發現多次磁翻轉的磁滯曲線，了解SHE等效場與外加磁場間的交互關係。
(3)實驗數據與模擬結果的比較：透過實驗(以Ta(5)/Co4Fe4B2(1.1)/MgO(1)/Ta(5) (單位:nm)薄膜樣品做為參考)與模擬的比較，發現電流翻轉曲線之圖形、磁滯曲線於正負電流下的變化皆與實驗結果趨勢相同，並在易磁化軸傾斜的假設下，兩者Jc、Hc所繪製之相圖十分一致。(4)無外加磁場下有無電流翻轉之探討：藉由自旋霍爾效應等效場公式的模擬，解釋無外加磁場下電流無法使磁矩翻轉之原因，並透過易磁化軸傾斜的假設，可實現無外加磁場下使電流驅動磁矩翻轉，進一步分析傾斜之單軸異向性與零場翻轉的關係，以及以雙軸異向性之假設無法達到零場翻轉之原因。

In this thesis, we study magnetization switching by spin Hall effect (SHE), which is induced by in-plane injected currents in the Ta/CoFeB/MgO system with perpendicularly anisotropic. We use the Landau–Lifshitz–Gilbert(LLG) equation to simulate the time evolution of magnetization and compare the result with experimental observations. The simulated results are divided into 4 parts:
1. Simulations of the magnetic switching by varying injected currents with a fixed in-plane magnetic field and predictions for current-induced magnetic switching with the LLG equation. The critical current density of magnetic switching (Jc) is calculated by analytic methods with the condition of variance of Jc with respect to various angles of the applied magnetic field.
2. Simulations of varying applied magnetic field with a fixed injected current
We simulate the dependence of hysteresis loops upon positive (negative) current density with different values. We obtain the coercivity (Hc) by analytic methods and its dependence on the angle of applied magnetic field.
3. A comparison between simulations and experimental data in Ta(5)/Co4Fe4B2(1.1)/MgO(1)/Ta(5) structure (unit: nm).
The comparison has led us to obtain the effective field induced by SHE and phase diagrams of Jc and Hc. These results were also used to analyze the behaviors of changing the angle of applied magnetic field.
4. Possibility of current induced magnetic switching without applied external magnetic field
By introducing a tilted uniaxial perpendicular magnetic anisotropy, we are able to simulate of the magnetic switching without external field. From these results we learned physics behind the breaking of the intrinsic symmetry in the SHE induced magnetic switching in perpendicular magnetized thin film structures.

致謝 1
摘要 2
Abstract 4
第一章 序論 12
第二章 理論背景 14
2.1 Stoner–Wohlfarth model 14
2.2 Landau–Lifshitz–Gilbert equation 16
2.3 異常霍爾效應(Anomalous Hall effect,AHE or Extraordinary Hall Effect,EHE) 18
2.4 自旋霍爾效應 (Spin Hall Effect,SHE) 20
2.5 相關文獻回顧 22
第三章 計算方法與實驗簡介 24
3.1 計算原理 24
3.2 電性量測簡介 26
第四章 模擬結果與討論 28
4.1 單層結構模擬結果 28
4.1.1 單層結構電流翻轉曲線模擬 28
4.1.2 單層結構電流翻轉曲線解析解分析 28
4.1.3 翻轉電流密度計算 29
4.1.4 翻轉電流密度模擬相圖 33
4.1.5 外加場角度變化對翻轉電流之影響 34
4.1.6 易磁化軸傾斜對翻轉電流密度之影響 36
4.1.7 水平外加場磁滯曲線模擬 38
4.1.8 矯頑場模擬相圖 40
4.1.9 外加場角度變化對矯頑場之影響 42
4.1.10 易磁化軸傾斜對矯頑場之影響 43
4.2 模擬結果與實驗數據的比較 46
4.2.1 Ta(5)/Co4Fe4B2(1.1)/MgO(1)/Ta(5) 下結構EHE量測結果 46
4.2.2 Ta(5)/Co4Fe4B2(1.1)/MgO(1)/Ta(5) 磁滯曲線之矯頑場相圖 50
4.2.3 Ta(5)/Co4Fe4B2(1.1)/MgO(1)/Ta(5) 下結構電流翻轉結果 54
4.2.4 Ta(5)/Co4Fe4B2(1.1)/MgO(1)/Ta(5) 翻轉電流密度相圖 55
4.3 單層結構無外加磁場下有無電流翻轉之探討 56
4.3.1 有無外加磁場下電流驅動磁矩之運動路徑分析 56
4.3.2 無外加磁場下之解析解與實驗數據比較 58
4.3.3 無外加磁場下電流可驅動磁翻轉之分析 60
第五章 結論 64
參考文獻 66

[1] L’ubom´ır Baˇnas” Numerical Methods for the Landau-Lifshitz-Gilbert Equation”
[2] Kang L. Wang” Magnetization switching through spin-Hall-effect-induced chiral domain wall propagation”
[3] N. Perez, E. Martinez, L. Torres, S.-H. Woo, S. Emori, and G. S. D. Beach” Chiral magnetization textures stabilized by the Dzyaloshinskii-Moriya interaction duringspin-orbit torque switching”
[4] Long You, OukJae Lee, Debanjan Bhowmik, Dominic Labanowski, Jeongmin Hong, Jeffrey Bokor, Sayeef Salahuddin”
Switching of Perpendicularly Polarized Nanomagnets with Spin Orbit Torque without an External Magnetic Field by Engineering a Tilted Anisotropy”