巨磁阻系統的廣泛應用和發展對訊息技術領域帶來了巨大的影響，特別是在硬 碟 (HDD) 等儲存設備的性能提升方面。這項技術自 1988 年首次被引入以來，已經在 硬碟的讀取傳感器中得到了廣泛應用，推動了儲存密度的提高，使得硬碟變得更加 小型化且容量更大。
本論文專注於探討巨磁阻系統中的雙二次層間交互作用項 (J2)，這是影響磁性結 構排列和性能的一個關鍵因素。文章開頭回顧巨磁阻效應的歷史，過往的重心主要 在了解雙線性層間交互作用項 (J1)，釐清層間交互作用對巨磁阻系統中的影響。
進一步，我們討論巨磁阻系統中鐵磁層磁矩排列的非傳統性，即雙二次系統 (biquadratic system)。這一現象的根本原因為兩個鐵磁性材料之間引發的 J2。藉由探討非傳統巨磁阻系統的物理模型，尤其是金屬間隔層中未成對自旋的局部電子態， 提供了對這種排列機制的深入解釋。
我們選擇三層的巨磁阻系統進行模擬，金屬層和鐵磁層的結構形成一個量子井， 將電子約束在特定區域內，影響著電子的運動行為，藉由量子井的概念與計算方法， 我們可以快速的預測巨磁阻系統的定性。
文中對於 J1 和 J2 的探討，得到 J1 是系統總能量中的主導項，對系統的磁矩穩 定性起著至關重要的作用。相比之下，J2 的作用較小，主要影響磁矩的非共線排列。 然而，J2 的微小影響仍然可以改變系統的磁矩和穩定性，並牽扯到電子自旋在系統 中的狀態。
本文旨在釐清雙二次系統出現的條件，研究中討論了改變金屬層厚度對 J1 和 J2 的影響。特別是在 J1 為零的情況下，系統更傾向磁矩的垂直排列，並提出 J1 和 J2 相位差的機制，以實現控制二次系統的出現。
整體而言，本文通過深入研究巨磁阻系統，揭示 J2 在系統中的重要性。這種理 解有望促進巨磁阻技術的進一步發展，尤其是在自旋電子學、磁感測器和磁性記憶 體等領域的應用中。

The widespread application and development of giant-magnetoresistance (GMR) systems have had a profound impact on the field of information technology, particularly in enhancing the performance of storage devices such as hard disk drives (HDDs). Since its introduction in 1988, this technology has found extensive use in the read sensors of HDDs, driving an increase in storage density and allowing for smaller, more capacious hard drives.
This thesis focuses on exploring the interlayer coupling term known as the biquadratic interlayer exchange coupling (J2) within GMR systems. We begin by reviewing the history of GMR effects, emphasizing the historical focus on understanding the bilinear interlayer ex- change coupling (J1) and clarifying its importance in GMR systems.
Furthermore, we focus on the unconventional magnetic arrangement in ferromagnetic layers within GMR systems, known as the biquadratic system. The fundamental cause of this phenomenon is attributed to the J2 coupling between two ferromagnetic bodies, resulting in a unconventional arrangement. By delving into the physical model of J2, particularly the local electronic states of unpaired spins in non-magnetic metal spacer layers, we provide a comprehensive explanation of this arrangement mechanism.
To better comprehend the system’s behavior, a three-layer GMR system is selected for simulation. This choice considers the formation of a quantum well, constraining electrons to specific regions and affecting their motion behavior. Utilizing the concept of the quantum well and computational methods, we can quickly predict the qualitative behavior of GMR systems.
In discussing the influence of J1 and J2, we find that J1 is the dominant term in the total energy of the system, contributing significantly to the overall energy of metal multilayer systems. J1 plays a crucial role in the magnetic domain structure and stability of the system. In contrast, the role of J2 is relatively minor, primarily affecting the non-collinear arrangement of magnetic moments and introducing anisotropy. However, the slight impact of J2 can still modify the magnetic domain structure and stability, influencing the dynamics of spin.
To gain a clear understanding of the conditions under which the biquadratic system appears, we discuss the impact of changing the thickness of the metal layers on J1 and J2. Especially in the case where J1 is zero, the system is more likely to achieve a vertical arrangement of magnetic moments. We propose understanding the mechanism of the phase difference be- tween J1 and J2 to maximize the occurrence of the biquadratic system.
In conclusion, this thesis, through in-depth research into the biquadratic coupling term (J2) within GMR systems, reveals its importance in system performance. This understanding is expected to promote further development of GMR technology, especially in applications such as spintronics, magnetic sensors, and magnetic memory.

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