利用單能階緊密鍵結模型計算磁性穿隧接合的自旋傳輸特性

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朱法杰(Fa-Chieh Chu) 查詢紙本館藏

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物理學系

論文名稱

利用單能階緊密鍵結模型計算磁性穿隧接合的自旋傳輸特性
(Spin Transport Properties in Magnetic Tunneling Junction with Single-Band Tight-Binding Model)

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摘要(中)

在氧化鎂基底之磁性傳輸接合(magnetic tunneling junction)中的穿隧磁阻(tunneling magnetoresistance)和自旋傳輸矩(spin-transfer torque)效應目前為止已經吸引了磁性記憶體和磁性感應器相關應用領域中大量的研究。這樣的現象來自於鐵磁性材料和氧化鎂晶體左右邊接合面上的高度自旋極化的電子態密度(density of state)。而在氧化鎂基底的磁性穿隧接合上成功的研究提供了尋找替代接合中之中間層材料一個非常重要的線索。
理論計算上的研究成果對於自旋電子學(spintronics)的應用有著極為重要的貢獻，而緊密連結模型(Tight-binding model)這種將原子和電子結構簡化的計算方法能夠相對輕易地處理複雜的自旋傳輸特性，如需要在磁性材料的磁性方向為非同一直線(non-collinear)的排列情況才會出現的自旋矩效應。因此，對於一些較難處理的計算，緊密連結模型就適合用來先行預測結果。儘管單軌道緊密連結模型(single-band tight binding model)加上格林函數(Green’s function)的計算是非常簡化的，但還是成功地算出於氧化鎂基底的自旋穿隧接合下與實驗測量結果相吻合的自旋傳輸矩。
由於在處理non-collinear系統下計算上的困難，尋找另外一種方法去計算自旋矩相較於直接使用第一原理計算是有益處的。自旋矩的通用表示式(general expression)就提供了這樣的功用，它能夠建立non-collinear系統下才能得到的平行(T_∥)和垂直(T_⊥)磁性方向所構成平面的自旋矩和collinear系統下得到的自旋極化電流(對於 T_∥)和電子自旋能階耦合(對於 T_⊥)的關聯性。如此一來，利用通用表示式將可以從第一原理計算出的自旋極化電流和電子自旋能階耦合的結果得到T_∥與T_⊥對電壓的響應。我們認為對於預測材料接合中的自旋矩效應，這是一個非常實用的方法。
在這篇研究中，我們用單軌道緊密連結模型首先計算傳統的三層-鐵磁性/絕緣/鐵磁性材料的磁性穿隧接合，驗證了自旋矩的通用表示式在如此的三層材料中的適用性，並且用Brinkman’s model概略地分析結果對於電壓的表現。接著，我們計算了更加有趣的五層-鐵磁性/絕緣/自旋過濾/絕緣/鐵磁性材料的磁性穿隧接合下兩個方向的自旋矩，結構等同於在傳統的三層結構的中間多加上一層有自旋過濾特性的材料。在這樣的五層結構中，我們發現了中間的自旋過濾層大幅的增加了T_⊥的值，並且藉由公式推導去了解其原因。我們同樣的也驗證了通用表示式在這樣的結構中的適用性。此篇成果確認了通用表示式在三層及五層的接合中是適用的，也因為發現了巨大的T_⊥而希望能提供於磁性記憶體的應用具有發展性的新型態讀跟寫的程序。

摘要(英)

The giant tunnel magnetoresistance (TMR) and the spin transfer torque (STT) effect in MgO-based magnetic tunnel junctions (MTJs) have attracted intensive studies for applications in nonvolatile magnetic random access memories and magnetic sensors, resulting from the highly spin-polarized density of states on both left and right FM/MgO interfaces, where FM denotes ferromagnetic materials. The success of MgO-based MTJs points out an important clue for finding alternative central materials in MTJs.
The theoretical research has significant contributions to the spintronics applications. The tight-binding (TB) model is a calculation method, which simplifies the calculation details of the materials and can easily deal with the complicated spin transport properties such as spin torque effect calculated in the non-collinear magnetization configuration. Therefore, the TB model is suitable to predict the trend of the results to the difficult calculations. Despite its simplification, the single-band tight-binding model with the Keldysh Green’s function method have been successfully employed to calculate the spin-transfer torque (T_∥) in the conventional MgO-based magnetic tunneling junctions, which Δ_1 band dominate the transportation.
Due to the difficulty of the calculation to the non-collinear system, compare to direct calculation by the first principle method, it is beneficial to look for another way to obtain the spin torque. The general expressions of spin torque, which connect the relations between non-collinear STT (FLST) and the collinear spin-polarized current (interlayer exchange coupling), provide the function. This allows us to predict the highly asymmetric bias behavior of non-collinear STT or FLST directly by the interplay between the first principles calculated spin current densities or interlayer exchange couplings in collinear magnetic configurations. We believe that it is a practical way to connect the tight-binding model with the first principles calculation in predicting the spin torque effect.
In this study, we use the single-band tight-binding model to build the conventional FM/I/FM MTJ and to verify the general expression of the STT and field-like spin torque (FLST or T_⊥) in this 3-layers case. Next, we calculate the T_∥ and T_⊥ in the 5-layers FM/I/SF/I/FM, which is added one spin-filter layer at the center compare to the 3-layers case, and discovers the contribution of the spin-filter to the FLST, which largely enhance the value of T_⊥. We as well test the usability of the general expressions for the two spin torque in 5-layers case. This work proof the formular derived general expression is capable in FM/I/FM and FM/I/SF/I/FM cases, and provide a promising dual control for both reading and writing process for the nonvolatile magnetic random access memories (MRAM) applications according to the giant effect of the FLST.

關鍵字(中)

★ 緊密鍵結
★ 雌性穿隧接合
★ 格林函數
★ 自旋傳輸
★ 自旋過濾

關鍵字(英)

★ Tight-Binding
★ Magnetic Tunneling Junction
★ Green′s Function
★ Spin Transport
★ Spin filter

論文目次

Chapter 1. Introduction 1
Chapter 2. Theory 4
2.1 Green’s Function [28] 4
2.1.1 Brief Introduction 4
2.1.2 Retarded and Advanced Green’s Function 5
2.1.3 Tight Binding Model 9
2.1.4 Self Energy 13
2.2 Non-Equilibrium Green’s Function [29] 16
2.2.1 Brief introduction 16
2.2.2 Correlation and Scattering Functions 17
2.2.3 Kinetic Equation 19
2.2.4 Current Flow 22
2.3 Spin Torque Effect [30,31] 25
Chapter 3. Computational Details 32
3.1 Parameter Setup 32
3.2 Hamiltonian Matrix 35
3.3 Self Energy 37
3.4 Green’s Function 41
3.5 Model Setup 42
3.5.1 3-Layers Model 42
3.5.2 5-Layers Model 44
Chapter 4. Result and Discussion 47
4.1 3-Layers MTJ Structure 47
4.1.1 TMR 47
4.1.2 Spin Transfer Torque 52
4.1.3 Field-like Spin Torque 56
4.2 FM / I / SF / I / FM (5-Layers case) 61
4.2.1 Spin Transfer Torque 61
4.2.2 Field-Like Spin Torque 63
Chapter 5. Summary 68
References 69

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指導教授

唐毓慧(Yu-Hui Tang)

審核日期

2017-8-23

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