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研究生： 陳含章
Han-Zhang Chen
論文名稱： 鐵磁共振量測的訊噪比技術提升研究
SNR Enhancement Technique for FMR
指導教授： 盧志權
Lo, Chi-Kuen
學位類別： 碩士
Master
系所名稱： 物理學系
Department of Physics
論文出版年： 2015
畢業學年度： 103
語文別： 中文
論文頁數： 88
中文關鍵詞： 鐵磁共振 、訊號 、訊噪比 、鎖相放大 、磁性參數 、擬合
英文關鍵詞： Ferromagnetic resonance, Signal, SNR, Lock-in amplifier, Magnetic parameters, Fitting
DOI URL： https://doi.org/10.6345/NTNU202205256
論文種類： 學術論文
相關次數： 點閱：232  下載：38 
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    • 中文摘要

    磁性材料的鐵磁共振量測是研究自旋動力特性的一大利器，其原理非簡單，可是商用的共振量測儀非常昂貴，數年前本實驗室成功開發出一臺以網路分折儀(Vector-Network Analyzer; VNA)為基礎的鐵磁共振儀(Ferromagnetic Resonance Spectrometer;FMR)，然而它的數據擷取速度與靈敏度都有許多改善空間。因此本論文主要用不同的量測方法與技術來探討鐵磁共振儀的訊噪比(signal-to-noise ratio;SNR)表現，期望找出最佳的儀器量測參數。
    VNA-FMR量測速度較慢的主因是VNA內部的數據平均處理慢，每點作十次平均約需0.5 秒，一千點的頻譜便要8分鐘左右，若樣品的訊號較弱則所需的時間更長，數個角度的FMR量測會使電磁鐵過熱而終止實驗。為了加快FMR的量測速度，我們跳過了VNA內部的訊號處理，這時VNA只作為一台提供X-band微波波源的機器，微波經由環路器注入共振腔，經樣品反射再由環路器的另一端進入微波偵測器，擷取偵測器的輸出訊號與外磁場的變化關係便得到FMR頻譜，這時增加了量測速度但犧牲了靈敏度，因此我們再加入調變磁場－鎖相放大技術來提升其靈敏度。由於渦电流(Eddy current)的影響，共振腔內磁場隨調變頻率(fm)增加而遞減，因此在fm =3 kHz時訊噪比表現最佳，這時調變磁場約為5.5高斯。在時間常數tc = 100 ms時，10nm Py的FMR訊噪比高於300，這高於使用VNA-FMR和沒有鎖相法直接測量的結果。若要再增強SNR，需要提高調變磁場到10-20高斯間，因此渦电流的問題需要解决才能達成。
    FMR現象可用Landau-Lifshitz-Gilbert (LLG)方程式來描述，從其解與實驗數據的分析可得到如磁異向性常數、耦合因子、阻尼常數等重要磁性特徵參數，本論文也編寫Matlab程式碼來找出坡莫合金(Permalloy)薄膜的磁性特徵參數。

    Abstract
    The measurement of Ferromagnetic resonance is a powerful tool to study the characteristics of spin dynamics. Though having developed a Ferromagnetic Resonance Spectrometer (FMR) based on the Vector-Network-Analyzer (VNA) in our laboratory, the sensitivity and acquisition rate of the spectrometer has more room for improvement. Thus, we studied the spectrometer with different methods and technique to improve the signal-to noise ratio (SNR), and found the best parameters for measurements.
    It is because the internal signal processing of VNA slower the acquisition rate. If the period of measurements is too long, it will overheat the electromagnet coil and suspend the experiment. In order to accelerate the acquisition rate, we skipped the internal signal processing of VNA and let the microwave detector to accomplish the measurements. Thus, VNA was just the source of X-band microwave which emits the wave into cavity via the circulator. The reflection of the wave by the sample in the cavity will be transmitted to the detector through another port of circulator, so we can combine the signal of reflection power with the measurements of applied field to get the FMR spectrum.
    Though enhancing the acquisition rate, it sacrifices the signal to noise ratio (SNR). In order to improve the SNR, we employed lock-in technique with a small modulation field which superimposes on the DC magnetic field. Due to the effect of the Eddy current on the metallic surface of the cavity, the modulation field decreases as modulation frequency increases, thus , the best performance of signal was about 3kHz with modulation field 5.5 gauss. In the situation that time constant of Lock-in amplifier was set to 100ms and thickness of Permalloy film is about 10nm, the SNR was higher than 300 which was better than the performance of VNA-FMR.To further enhance the SNR, it should improve the modulation field between 10 and 20 Gauss at high frequency, so the problem of the eddy current must be solved.
    The phenomenon of ferromagnetic resonance can be described by the Landau-Lifshitz-Gilbert equation(LLG eq.).With the solution of LLG eq. and the experiment data of FMR, we can obtain magnetic parameters such as anisotropy constant, exchange coupling factor, damping constant, etc. In the thesis, we use the Matlab program code to obtain the magnetic parameters of the Permalloy thin film.

    目錄 第1章 緒論 ........................................................................................................................... 12 前言 ..................................................................................................................................... 12 研究動機 ............................................................................................................................. 13 第2章 文獻回顧 ................................................................................................................... 14 第1節 鐵磁共振儀的基本架構 ....................................................................................... 14 第2節 磁能與磁異向性 ................................................................................................... 15 2-2.1 賽曼能(Zeeman energy) ................................................................................... 15 2-2.2 交互作用能(exchange energy)[4] ................................................................. 15 2-2.3 去磁場能(demagnetizing field energy) ..................................................... 16 2-2.4 磁晶異向性能(magneto crystalline anisotropy energy)[10] ............... 19 第3節 磁區結構 ............................................................................................................... 22 2-3.1 磁區(magnetic domain) ................................................................................... 22 2-3.2 磁區壁(domain wall)[12] ............................................................................... 23 第4節 鐵磁共振原理 ....................................................................................................... 26 2-4.1 動力學觀點[14] ................................................................................................. 26 2-4.2 能量觀點[17] ..................................................................................................... 31 第5節 鐵磁共振的量測方法[18-20] ............................................................................. 34 2-5.1 掃頻式鐵磁共振儀 ............................................................................................. 34 2-5.2 掃場式鐵磁共振儀 ............................................................................................. 37 第6節 鎖相放大技術[25] ............................................................................................... 40 第3章 實驗儀器 ................................................................................................................... 42 第1節 脈衝雷射沉積儀(Pulsed Laser Deposition;PLD) ......................................... 42 第2節 鐵磁共振儀(Ferromagnetic Resonance Spectrometer) ............................... 43 3-2.1 VNA-FMR spectrometer[12] ............................................................................. 44 3-2.2 VNA-Detector-FMR spectrometer ................................................................... 47 6 3-2.3 VNA-FMR spectrometer with Lock-in Technique [25] ............................. 49 第4章 實驗步驟 ................................................................................................................... 54 第1節 基板清洗 ............................................................................................................... 55 第2節 脈衝雷射沉積系統實驗流程 ............................................................................... 55 第3節 VNA-FMR量測 ........................................................................................................ 56 第4節 VNA-Detector-FMR量測 ...................................................................................... 56 第5節 VNA-FMR with Lock-in Technique量測 .......................................................... 57 第5章 實驗結果與討論 ....................................................................................................... 59 第1節 VNA-FMR訊號的磁性分析 .................................................................................... 59 5-1.1 分析方法 ............................................................................................................. 59 5-1.2 分析結果 ............................................................................................................. 61 第2節 VNA-FMR、VNA-Detector-FMR和VNA-FMR with Lock-in technique三種測量方法的訊號比較 ................................................................................................................. 63 第3節 VNA-FMR with Lock-in Technique的數據分析與討論 .................................. 66 5-3.1 調頻振幅對訊號的影響 ..................................................................................... 66 5-3.2 調頻頻率對訊號的影響 ..................................................................................... 68 5-3.3 Time Constant對訊號的影響 .......................................................................... 72 5-3.4 薄膜厚度對訊號的影響 ..................................................................................... 74 第6章 總結 ........................................................................................................................... 77 第7章 未來研究工作與方向 ............................................................................................... 78 第8章 參考文獻 ................................................................................................................... 79 附錄一 計算fitting的Matlab Code .............................................................................. 81 附錄二 計算SNR的Matlab Code ...................................................................................... 86

    第8章 參考文獻
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