自旋1/2海森堡鏈與磁性多層薄膜的自旋波特性

Spin Waves in Spin-1/2 Heisenberg Chain and Magnetic Multilayers

林勝隆(Sheng-Long Lin)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.10679

摘要

本論文主要目的在探討鐵磁性物質的自旋波特性。首先介紹磁性的來源與分類，隨後使用交換能與塞曼能來分析不同結構，並探討能帶結構的物理特性。對於一維自旋1/2海森堡鏈，我們計算隊列態、單偏離態與雙偏離態的能量分布，對於磁性多層薄膜，我們分析自旋波振幅的運動方程式。透過數值分析結果顯示，對這兩種結構，當外部磁場變化為線性時，系統的能量也會線性變化，因此可以非常容易地控制其允許帶位置。另外對磁性多層薄膜，相鄰兩層之間的交換耦合與允許帶寬度成正比，而特定的平面參數值會使允許帶簡併。另外針對反鐵磁性自旋1/2海森堡鏈，使用密度矩陣重整化群法，探討外部磁場線性變化下的基態能量分布，透過數值分析結果顯示，基態能量變化也呈線性，並且我們發現此方法有相當好的準確性。

關鍵字

自旋波 ； 交換能 ； 塞曼能 ； 磁性多層薄膜 ； 自旋1/2海森堡鏈 ； 密度矩陣重整化群 ； 能帶結構

並列摘要

The main purpose of this thesis is to investigate the spin wave properties of ferromagnetic materials. At first, the concept of magnetism is introduced. Then the exchange energy and Zeeman energy are considered to analyze physical properties by the band structures of the different structures. For one-dimensional spin-1/2 Heisenberg chain, we calculate the energy distribution of aligned state, single deviation state and two deviation state. For magnetic multilayers, we investigate the equation of motion for the spin wave amplitude. For these structures, the system energy will be linear if the change in external magnetic field is linear. Thus the allowed band can be adjusted easily. In addition, for magnetic multilayers, the exchange coupling between adjacent layers is proportional to the allowed band width, and the allowed band degeneracy results from specific values of plane parameter. For the antiferromagnetic spin-1/2 Heisenberg chain, we use DMRG method to analyze the ground state energy when the change in external magnetic field is linearly. By numerical calculation, it shows that the change in ground state energy is also linearly. Thus we could find that this method have a good accuracy.

並列關鍵字

spin wave ； exchange energy ； Zeeman energy ； magnetic multilayers ； spin-1/2 Heisenberg chain ； DMRG ； band structure

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