磁性為物質的基本屬性之一，對於不同材料的磁性研究，多年來廣泛的被研究以及應用。隨著近年來製程越作越小，奈米尺度下的一些基本物理現象越來越受重視。在微觀上，鐵磁性物質為了有效降低整體的系統總能量，樣品內部會切分成若干個磁區(magnetic domain) ，然而，從G. Leaf 等人的文章[34]我們看到在條狀的鈷樣品(Co bar) 中，在經歷外加場後的磁區組態其形成機制並非由總能量主導，而是與高外加場中的自旋波駐波頻率有關聯。為了進一步探討這個有趣的現象，我們利用電腦模擬的方式，對不同大小厚度具有垂直磁易向性的鈷圓盤(Co disk) 作一系列的模擬計算。從本研究中，我們將提出磁區翻轉的過程以及機制，同時也對能量與磁區間的關係作說明。

Magnetism is one of material essential attributes, the different material’s magnetic has been studied for many years as well as the application.The processing is smaller with recent years, and the submicro physical phenomenon adapt to more and more important. Microscopically, ferromagnetic material tend to reduce the total energy of the system, and the sample interior will response to devide several magnetic domains, however, from the article by G. Leaf et al[34], we saw the final domain structure at remanence of cobalt bar, which is not the configuration with lowest energy, is predicted from a high-field analysis of the frequencies of the standing spin waves. To further discuss this interesting phenomenon, we use the computer simulation method, and make a series of computation of cobalt disc with the various sizes and thickness. From this research, we will propose that the magnetic domain reverse process and mechanism, and also give showing relations to between the energy and the magnetic
domain.

1 前言1
2 磁學理論7
2.1 鐵磁性與交換能. . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 磁區. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Landau-Lifshitz equation . . . . . . . . . . . . . . . . . . . . 9
2.4 自旋波. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 模擬方法15
3.1 模擬原理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 結果與討論19
4.1 實驗參數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 磁滯曲線與磁化過程中磁區的改變. . . . . . . . . . . . . 21
4.3 週期. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 能量. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.5 對稱. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 總結 45
6 附錄 47
7 參考文獻 51

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