Understanding Oscillatory Domain Wall Motion via Spin Waves Theory

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姓名

莊宇正(Yu-Cheng Chuang) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Understanding Oscillatory Domain Wall Motion via Spin Waves Theory)

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至系統瀏覽論文 (2025-7-1以後開放)

摘要(中)

自旋波是自旋動力學中調控磁矩方向的一種重要且嶄新的解決方案，與透過由自旋極化電流的引起的磁矩翻轉相比，具有生成更低的焦耳熱的優勢、更廣泛的材料適用性以及更有效的翻轉機制，適合應用在未來在磁阻式隨機存取記憶體（ MRAM）的產業上。在本論文中，我們基於 Landau-Lifshitz-Gilbert（ LLG）方程式的展開，從理論角度研究了自旋波引起的磁疇壁（ DW）運動。我們首先驗證了，在忽略退磁場的情況下，自旋波通過磁疇壁的傳播可達到完全穿透而不引起反射，並驗證自旋波確實能夠產生自旋波角動量轉移矩（ Magnonic-STT）。由於自旋波本身和其引起的有效場的相互作用，自旋波角動量轉移矩來自於二階展開項。我們的研究結果表明，自旋轉移矩的確驅使磁疇壁和朝向和自旋波傳播方向相反的方向運動並提供穩定的磁疇壁速度。我們進一步驗證了先前研究中提出的磁振子等效電流的數學形式。我們使用自旋動力學數值模擬軟體， OOMMF 驗證了我們的理論。此外，我們提出了一種等效的能量模型來解釋由於自旋波的傳輸和反射而引起的自旋波引起的磁疇壁振盪行為。在材料形狀產生的退磁效應下，我們求解並比較磁疇壁內外的色散關係，得到自旋波的波數為磁疇壁傾斜角的函數，並將其映射為有效能量和勢能。我們的模型成功地解釋了數值模擬中發現的傾斜角度旋轉所改變的自旋波傳輸行為，並展示了一種更有效的控制磁疇壁運動的方法。在論文的最後，我們給出了在穿透係數為常數的假設下獲得穩定振盪磁疇壁運動的臨界傳輸的解析解。

摘要(英)

Spin wave is a new solution in the magnetic moment switching process, featuring lower joule heating production, wide material applicability, and a more efficient mechanism for future application in the magnetoresistance access memory (MRAM) industry compared to the switching achieved by the spin-polarized current. In this thesis, we investigate the spin-waves-induced domain wall (DW) motion from a theoretical point of view based on the expansion of the Landau-Lifshitz-Gilbert (LLG) equation. We have first shown that in the absence of demagnetization, the spin waves propagating through the domain wall undergo complete transfer without reflection. The spin waves indeed generate a magnonic-spin-transfer torque (magnonic-STT), with the driving torque originating from the second order in the expansion due to the interaction of spin waves and spin-waves-induced effective field. Our results indicate that this effective torque supports a backward domain wall motion with constant domain wall
velocity. We further validate the mathematical form of the magnonic spin current proposed in the previous study. We verify our theory with OOMMF, a macrospin dynamics numerical simulation software. Additionally, we propose an effective energy model to explain the oscillatory behavior of spin-waves-induced DW motion due to the
transmission and reflection of spin waves. Under the demagnetizing effect generated from the shape of the material, we compare the dispersion relations solved inside and outside the domain wall. We find out the wave number of the spin wave and map it to the effective energy and potential as a function of the tilted angle of the domain
wall. Our model successfully explains the transmission behavior found in numerical simulation with the rotation of a tilted angle and shows a more efficient approach to control DW motion. At the end of the thesis, we give an analytical solution to obtain a critical transmission for a stable oscillatory DW motion under the constant transmission assumption.

關鍵字(中)

★ 自旋
★ 自旋波
★ 磁疇壁
★ 磁疇壁運動
★ 自旋轉移矩

關鍵字(英)

★ Spin
★ Spin waves
★ Domain wall
★ Domain wall motion
★ Spin transfer torque

論文目次

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2 Micromagnetic Interaction . . . . . . . . . . . . . . . . 6
2.1 The Continuum Approximation . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Exchange Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Zeeman Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Uniaxial Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Demagnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Landau-Lifshitz-Gibert equation . . . . . . . . . . . . . . . . . . . . . 13
2.7 Spin Transfer Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 3 Domain Wall Theory and Spin Waves . . . . . . . . . . . . 17
3.1 Walker’s profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Domain wall dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Spin waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Chapter 4 Methodology . . . . . . . . . . . . . . . . . . . . . . 24
4.1 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter 5 Results and Discussion . . . . . . . . . . . . . . . . . . 28
5.1 Spin wave induced backward domain wall motion . . . . . . . . . . . .
28
5.2 Spin wave transmission under demagnetizing field . . . . . . . . . . . .
35
5.2.1 Dispersion relation as a function of frequency . . . . . . . . . . 38
5.2.2 Dispersion relation as a function of tilted angle . . . . . . . . . 39
5.2.3 Transmission and dispersion relation . . . . . . . . . . . . . . . 40
5.3 Oscillatory Domain wall motion under constant transmission . . . . . .
44
Chapter 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . 46
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
A Exchange Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
B Domain Wall Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 48
C Effective Hamiltonian in LLG Equation . . . . . . . . . . . . . . . . . 50
C.1 Demagnetizing field in the LLG equation . . . . . . . . . . . . 51
D Mathematical identity . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

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指導教授

唐毓慧

審核日期

2023-7-24

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