Theory of spintronics in nanostructure

THEORY OF SPINTRONICS IN NANOSTRUCTURES Nyuk Leong Chung B.Eng.(First Class Hons.), University of Swansea, Wales A Thesis Submitted for the Degree of Doctor of Philosophy Department of Electrical and Computer Engineering National University of Singapore 2012 Acknowledgments I would like to express my gratitude to all those who gave me the possibility to complete this thesis. I am deeply indebted to my supervisor Assoc. Prof. Mansoor Jalil for his guidance and encouragement throughout my scholarship. I feel extremely fortunate to have worked under such a passionate and understanding research leader. I am also grateful to Dr Tan Seng Ghee for his support, patience and invaluable advice during our countless discussions. Thanks must also go to my fellow colleagues including Takashi, Minjie, Bala, Gabriel, Zhuobin, Guojie, Mingjun and others, who have given me a lot of moral support through their warm friendships. Last, but not least, I am grateful to my family back in Miri, from whom I have received endless and unconditional love. i Contents Acknowledgments i Summary v List of Figures vii Publications, Conferences xii List of Abbreviations and Symbols xiv Introduction 0.1 The Importance of Spintronics . . . . . . . . . . . . . . . . . 0.2 Fundamentals of Spintronics . . . . . . . . . . . . . . . . . . . 0.3 Giant Magnetoresistance(GMR) and Spin Valve . . . . . . . . 0.4 General Theory of Spin Injection . . . . . . . . . . . . . . . . 0.5 Spin Transfer Torque and Magnetic Random Access Memory 0.6 Semiconductor Spintronics . . . . . . . . . . . . . . . . . . . . 0.7 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . 0.9 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interfacial Resistance and Spin Flip Effects in a Spin Valve 1.1 Interfacial Spin Flip in Spin Valve . . . . . . . . . . . . . . . . . . . . . 1.2 Theory and Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 The Effects of Interfacial Spin Flip Resistance on Interfacial Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 The Effects of Interfacial Spin Flip Resistance on Spin Asymmetry of Interfacial Scattering . . . . . . . . . . . . . . . . . . . . . . . 1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 10 12 17 18 19 21 24 24 25 28 29 31 33 ii CONTENTS Spin Current Injection through a Ferromagnetic-Insulator-Semiconductor Junction 35 2.1 Spintronics and Semiconductors(SCs) . . . . . . . . . . . . . . . . . . . 35 2.2 Introduction to Tight-Binding Non-Equilibrium Green’s Function . . . . 37 2.2.1 Why Non-Equilibrium Green’s Function(NEGF) . . . . . . . . . 37 2.2.2 NEGF Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.2.1 Matrix Representation for Tight-Binding NEGF . . . . 39 2.2.2.2 Truncating the matrix . . . . . . . . . . . . . . . . . . . 43 2.3 Theory and Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4.1 Schottky Barrier and Current Density . . . . . . . . . . . . . . . 52 2.4.2 Schottky Barrier and Spin Current Polarization . . . . . . . . . . 56 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Spin Transfer Torque Study through Noncollinear Spin Drift Diffusion Model 3.1 The Necessity of Noncollinear Model . . . . . . . . . . . . . . . . . . . . 3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Effects of Spin Relaxation on Spin Transfer Switching . . . . . . 3.3.2 Layer Thickness and Angular Dependence of Spin Transfer Torque in Ferromagnetic Trilayers . . . . . . . . . . . . . . . . . . . . . . 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effects of Capping Layer on the Spin Accumulation and Spin Torque in Magnetic Multilayers 4.1 Could Capping Layer Affect Spin Transfer Torque(STT)? . . . . . . . . 4.2 Theory and Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The Effects of Capping Layer Thickness . . . . . . . . . . . . . . 4.3.2 The Effects of Capping Layer SDL . . . . . . . . . . . . . . . . . 4.3.3 The Effects of Capping Layer Resistivity and Interfacial Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 The Effects of the Imaginary Mixing Conductance of Capping Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 61 63 68 68 72 73 76 76 78 86 87 89 91 94 97 Non-equilibrium Spatial Distribution of Rashba Spin Torque in Ferromagnetic Metal Layer 99 5.1 Spin Transfer Torque and Spin Orbit Coupling . . . . . . . . . . . . . . 99 5.2 Theory and Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.3.1 The Effects of RSOC, αR , and Exchange Interaction Strength, ∆ 106 5.3.2 The Spatial Distribution of the Spin Currents . . . . . . . . . . . 109 5.3.3 The Spin Density Distribution and Exchange Interaction Strengh, ∆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 iii CONTENTS Conclusions and Recommendations 115 6.1 Conlusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . 117 References 122 The Derivation of Non-equilibrium Green’s Function in Spin Space 132 The Relationship of Spin Transfer Torque and Spin Density 136 iv Summary Spintronics offers promise in employing intrinsic spin in nanoscale devices for next generation information technologies. In this Thesis, we theoretically study several critical aspects of spintronics, with a focus on the spin injection through interfaces with different properties, and the spin transfer torque (STT) phenomenon in single/multi-layer(s) ferromagnetic (FM) thin-film system. The studies focus on spin-dependent transport characteristics in nanoscale structures under the influence of various physical parameters of the system and the interactions with electric and magnetic fields. Firstly, a semi-classical spin drift-diffusion (SDD) model is constructed. This model later becomes the backbone for the study of the spin dynamics in magnetic multilayers system. The first spin-dependent study focuses on the effects of various characteristics of the interfaces on the magnetoresistance (MR) of pseudo-spin-valves (PSV). The physical parameters studied include the bulk polarization, interface polarization, and interface spin flipping of the PSV system. We examine conditions leading to high MR ratio in PSV. Following this, a brief introduction to the tight-binding non-equilibrium Green’s function (NEGF) is given, and subsequently a NEGF model is set up to study spin injection through a Schottky barrier at the ferromagnetic-insulator-semiconductor (FMI-SC) junction. The effects of the Schottky barrier on the spin injection are studied using this NEGF model. Based on the calculation results, several approaches have been v SUMMARY suggested to enhance the spin polarization from FM to SC through the implementation of a Schottky barrier. In-depth studies of STT follow the spin injection studies. Based on the SDD model, we study the optimized conditions to maximize the STT during the current induced magnetization switching (CIMS) process in PSV. CIMS is the result of coupling between spin-polarized conduction electrons and the magnetic moments in ferromagnetic layers on the magnetization. This study is essential as CIMS can offer a novel class of currentcontrolled magnetic memory devices, which does not rely on magnetic field switching. We investigate the optimization of the STT effect by tuning the relative magnetization angle, layer thickness, and material parameters. Later a SDD model is constructed with an additional capping layer, with the objective of studying the influences of capping layer on CIMS in PSV. A detailed analysis is done on the key physical parameters of the capping layer, and guidelines are laid down as to how to engineer the capping layer in order to maximize the spin transfer torque in CIMS. Finally, applying the NEGF approach again, a study is done on another form of spin torque, which is induced by the interaction of spin splitting and the Rashba spin-orbit coupling (SOC) effect in a single FM layer. The study focuses on parameters that affect the current induced effective field (Hef f ) in a single FM layer and the distribution profile of spin densities and STT over the system. vi List of Figures Areal density trend since 1950. Fast increase can be observed after 1990, which is after the discovery of giant magnetoresistance. Reprinted figure: R. Freitas, J. Slember, W. Sawdon and L. Chiu, GPFS Scans 10 Billion c Files in 43 Minutes. ⃝Copyright IBM Corporation 2011. . . . . . . . . Schematic of electron tunneling in ferromagnet/insulator/ferromagnet (F/I/F) for Julli`ere’s model in (a) parallel configuration (b) antiparallel configuration of magnetizations. The lower scheme shows the corresponding spin resolved density of the d states in ferromagnetic regions. The reduction of density of states for spin up electrons gives rise to the high resistance in antiparallel configuration. . . . . . . . . . . . . . . . . . . . . . . . . . An illustration of different transport length scales and its corresponding electron transport characteristic. L refers to the device dimensions, and lF , lM P F , lϕ , and lsf , refer to Fermi-wavelength, mean free path, phase relaxation length and spin diffusion length, respectively. Ballistic transport occurs when L< lM F P , where electrons experience elastic collision without losing their momentum. Diffusive transport occurs when L≫ lM P F , where the electron momentum is not conserved. lsf characterizes how long an electron can travel in a diffusive conductor before its initial spin orientation is randomized. To maintain the spin coherence, the device dimensions must be kept smaller than lsf . Generally in metals, lM P F ≪ lsf . Spin valve effect. (a) Schematic representation of the spin valve in parallel configuration. (b) Schematic representation of spin valve in antiparallel configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic representation of (a) the current perpendicular to plane (CPP) (b) the current in plane (CIP) geometry. . . . . . . . . . . . . . . . . . . vii LIST OF FIGURES 1.1 1.2 1.3 An illustration of spatial variation of the electrochemical potential at the ferromagnetic/non-magnetic(FM/NM) junction. The interface is marked at x = 0. The spin resolved electrochemical potential (µ↑ , µ↓ , solid line) and the average electrochemical potential (dash line) are discontinuous at the interface. The spin accumulation, ∆µ = µ↑ − µ↓ , decays away from the interface and into the bulk region, and is characterized by the spin diffusion length in the FM(NM) region, labeled with superscript F(N), F (N ) lsf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current-induced magnetization switching (CIMS). (a) A current of electrons is injected through the thick ferromagnet, FM1, which acts as a spin plarizer, and acquire an average spin moment along the magnetization of FM1. When the electrons enter the thin ferromagnet, FM2, which is the free layer, the resulting s-d interaction aligns the average spin moment along the magnetization of FM2. Due to the conservation of momentum, the transverse spin angular momentum lost by the electrons will be absorbed by the magnetization of FM2, which thus experiences a torque tending to align FM2 towards the orientation of FM1. (b) By reversing the current flowing through the spin valve geometry, one can induce either parallel or antiparallel configuration of the two FMs, and thus store information in a single memory cell. . . . . . . . . . . . . . . . . . . . . Working principle of MRAM. In the basic cross-point architecture, the two basic configurations of a CPP spin valve geometry, namely parallel (P) and antiparallel (AP) configurations, represent the binary information ‘0’ and ‘1’. During the writing process, current pulses are passed through one line of each array, and only the current at the crossing points is high enough to switch the magnetization of the free layer. During the reading process, the resistance between the two lines of the addressed cell is measured. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The organisation of the thesis and the related mathematical methods for spin dynamics simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic diagram of FM1-NM-FM2 pseudo-spin-valve trilayer structure, with current flow in the CPP direction. . . . . . . . . . . . . . . . . . . Logarithmic plot of MR ratio as a function of interfacial resistance, R0 , for different interfacial spin flip resistance RSF . . . . . . . . . . . . . . . (a) Logarithmic plot of MR ratio as a function of interfacial resistance R0 , for different values of spin asymmetry ratio, γ. The solid lines correspond to RSF = 104 mΩµm2 , while the dotted line with RSF = 10−1 mΩµm2 . (b) MR ratio as a function of R0 in the absence of any bulk or interfacial spin flipping, i.e. with RSF and lsf tending to infinity. . . . . . . . . . . 10 14 16 19 25 29 32 viii LIST OF FIGURES 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5 4.1 4.2 Schematic of a device divided into three regions, i.e. left and right contacts (blue) and the central region (yellow). The central region is descretized into lattice sites labeled from to N, with intersite distance ‘a’. The binding energy between two neighbouring sites is labeled as ‘t’. The coupling between the contacts and the central region is treated as selfconsistent potential, namely self-energy, ΣR p , where p can either be left (l) or right (r) contact. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)Illustration for retarded Green’s function, GR , and (b) advanced Green’s function, GA , on an infinite 1D wire. . . . . . . . . . . . . . . . . . . . . Energy band-diagram of a FM/I/SC system with a Schottky barrier in the SC region. The parameters depicted in the diagram are: ϕ1 = conduction band offset at the FM/I interface, ϕc = conduction band offset at the I/SC interface, ϕB = Schottky barrier height, ϕbi = built-in potential, ϕ2 = ϕB + ϕc , EF = Fermi level, VA = applied bias, and tF , tI and WD = thickness of the FM, I and depletion region, respectively. . . . . . . . Calculated current density J as a function of applied bias voltage, VA , when the following parameters are varied: (a) FM/I conduction band offset, ϕ1 , (b) Schottky barrier height, ϕB , (c) doping density in the SC layer, ND , and (d) built-in potential, ϕbi . . . . . . . . . . . . . . . . . . Calculated spin polarization as a function of applied bias voltage, VA , when the following parameters are varied: (a) FM/I conduction band offset, ϕ1 , (b) Schottky barrier height, ϕB , (c) doping density in the SC layer, ND , and (d) built-in potential, ϕbi . . . . . . . . . . . . . . . . . . Schematic diagram of a FM1-NM-FM2-Cap pseudo-spin-valve structure. (a) Spin transfer torque (STT) τ expressed in Oersteds (Oe), and (b) areal resistance, R(θ), as a function of magnetization angle, θ, with different (Cu) spacer spin diffusion lengths, lsf . . . . . . . . . . . . . . . . . . . . . . (a) Spin transfer torque (STT) τ expressed in Oersteds (Oe), and (b) areal resistance, R(θ), as a function of magnetization angle, θ, with different (Co2) transverse spin diffusion lengths, lsf ⊥ . . . . . . . . . . . . . . . . . . . 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Lett. 93, 127204 (2004). 131 The Derivation of Non-equilibrium Green’s Function in Spin Space The spin up and spin down eigenstates are expressed as:   1 | ↑⟩ =     0 | ↓⟩ =   The projector |↑⟩ ⟨↑| is expressed as:     ( ) 1 1 0 |↑⟩ ⟨↑| =   =   0 132 THE DERIVATION OF NON-EQUILIBRIUM GREEN’S FUNCTION IN SPIN SPACE Similarly,  0 |↓⟩ ⟨↓| =   0 |↑⟩ ⟨↓| =   0 |↓⟩ ⟨↑| =   0   1   0  The spin operator Sx and Sz can be expressed as:  0 Sx =   1 Sz =   1  = |↑⟩ ⟨↓| + |↓⟩ ⟨↑|  0  = |↑⟩ ⟨↑| − |↓⟩ ⟨↓| −1 Let n ˆ be the arbitrary magnetization direction: n ˆ = sin θ cos ϕi + sin θ sin ϕj + cos θk ϕ is in the model, the spin around the magnetisation is expressed as n ˆ · S: n ˆ · S = sin θ cos 0Sx + sin θ sin 0Sy + cos θSz = sin θ(|↑⟩ ⟨↓| + |↓⟩ ⟨↑|) + cos θ(|↑⟩ ⟨↑| − |↓⟩ ⟨↓|) The Hamiltonian is: H= ∑ σ,λ σ ϵσλ cσ† λ cλ + ∑ σ tσλµ cσ† λ cµ σ,λ,µ 133 THE DERIVATION OF NON-EQUILIBRIUM GREEN’S FUNCTION IN SPIN SPACE σ cσ† λ cλ is expanded as: ↑† ↑ ↑† ↓ ↓† ↑ ↓† ↓ σ cσ† λ cλ = cλ cλ + cλ cλ + cλ cλ + cλ cλ → |λ, ↑⟩ ⟨λ, ↑| + |λ, ↑⟩ ⟨λ, ↓| + |λ, ↓⟩ ⟨λ, ↑| + |λ, ↓⟩ ⟨λ, ↓| λ(µ) will be replaced by spatial denotation xn (xn±1 ). For the on site energy, it is expressed as: ′ ϵσσ nn = (2t + U ){|xn , ↑⟩ ⟨↑, xn | + |xn , ↓⟩ ⟨↓, xn |} + ∆ cos θ{|xn , ↑⟩ ⟨↑, xn | − |xn , ↓⟩ ⟨↓, xn |} + ∆ sin θ{|xn , ↑⟩ ⟨↓, xn | + |xn , ↓⟩ ⟨↑, xn |} Here, U is the potential energy and ∆ the exchange splitting constant. For tσλµ , it is considered t↑λµ = t↓λµ , and there is no spin flip from one site to adjacent sites, which means: t{|xn , ↑⟩ ⟨↓, xn−1(n+1) | + |xn , ↓⟩ ⟨↑, xn−1(n+1) |} = 0. Therefore, by considering the tight binding model, the Hamiltonian is expaneded as H = (2t + U ){|xn , ↑⟩ ⟨↑, xn | + |xn , ↓⟩ ⟨↓, xn |} + ∆ cos θ{|xn , ↑⟩ ⟨↑, xn | − |xn , ↓⟩ ⟨↓, xn |} + ∆ sin θ{|xn , ↑⟩ ⟨↓, xn | + |xn , ↓⟩ ⟨↑, xn |} − t{|xn , ↑⟩ ⟨↑, xn+1 | + |xn , ↓⟩ ⟨↓, xn+1 | + |xn , ↑⟩ ⟨↑, xn−1 | + |xn , ↓⟩ ⟨↓, xn−1 |} 134 THE DERIVATION OF NON-EQUILIBRIUM GREEN’S FUNCTION IN SPIN SPACE The matrix element of H is determined by: ⟨↑, xn | H |α⟩ = (2t + U + ∆ cos θ) ⟨↑, xn |xn , ↑⟩ ⟨↑, xn |α⟩ + ∆ sin θ ⟨↑, xn |xn , ↑⟩ ⟨↓, xn |α⟩ − t ⟨↑, xn |xn , ↑⟩ ⟨↑, xn+1 |α⟩ − t ⟨↑, xn |xn , ↑⟩ ⟨↑, xn−1 |α⟩ and ⟨↓, xn | H |α⟩ = (2t + U − ∆ cos θ) ⟨↓, xn |xn , ↓⟩ ⟨↓, xn |α⟩ + ∆ sin θ ⟨↓, xn |xn , ↓⟩ ⟨↑, xn |α⟩ − t ⟨↓, xn |xn , ↓⟩ ⟨↓, xn+1 |α⟩ − t ⟨↓, xn |xn , ↓⟩ ⟨↓, xn−1 |α⟩ Expressed in Green’s function: ∑ (E − H + iη)G↑↑ nn = n ∑ (E − H + iη)G↓↓ nn n ∑ ↑↓ ↑↑ ↑↑ (E + iη − U − 2t − ∆ cos θ)G↑↑ nn − ∆ sin θGnn + tGn+1,n + tGn−1,n = I n ∑ ↓↑ ↓↓ ↓↓ = (E + iη − U − 2t + ∆ cos θ)G↓↓ nn − ∆ sin θGnn + tGn+1,n + tGn−1,n = I n The matrix form of the Green’s function:  . . . . . . .  .     . . . t E + iη − U − 2t − ∆ cos θ −∆ sin θ t . . .    ×   −∆ sin θ E + iη − U − 2t + ∆ cos θ t . . . . . . t   . . . . . . . . . . . .   . . .   .   ↓↑  . . . G↑↑ G . . .   n−1,n n−1,n     ↑↓ ↓↓ . . . Gn−1,n Gn−1,n . . .     ↓↑ . . . G↑↑ Gn,n . . . n,n   =I    ↑↓ ↓↓ Gn,n . . . . . . Gn,n     ↓↑  . . . G↑↑ G . . . n+1,n n+1,n     ↓↓  . . . G↑↓ G . . .   n+1,n n+1,n   . . . . 135 The Relationship of Spin Transfer Torque and Spin Density We start the definition of Rashba torque, τˆ: ˆ × Hef f . τˆ = −γ M (2) ˆ which is the magnetization, is along z-direction, i.e. Mz , Hef f , In the model, the M, the effective field, along y, so we got τx . Another definition of torque, τˆ: ˆ τˆ = − m ˆ × M, =− ∆µB ˆ s׈ z. (3) In Eq.3, we also take τx . m ˆ is the magnetic moment, which is expressed as µBˆ s, where µB is the Bohr magneton. We can obtain ˆ s, which is the spin density, from ˆ is the unit vector, i.e. ˆ Green’s function, and M z, while ∆ is the spin splitting energy. 136 THE RELATIONSHIP OF SPIN TRANSFER TORQUE AND SPIN DENSITY From Eq. 2, the unit of τx : rad J × × T, Ts T m3 rad · J = . T sm3 γ × Mz × Hef f = (4) From Eq. 3, the unit of τx : ∆ × µB × Here, we take 1eV = 1J, and V × eV rad = eV × × × , V T eV s m3 rad · J = . T sm3 (5) is the spin density per volumn. Comparing Eq. and Eq. 3, we have τx , Mz τx = , Ms V Hef f = (6) where Hef f is in Tesla. 137 [...]... manipulation of spins in devices In view of these challenges, a thorough understanding of fundamental spin dynamics in solids as well as the effects of dimensionality, defects, and band structure in modulating the spin dynamics is necessary to implement efficient and effective control over the spin degree of freedom in spintronic devices 3 Introduction 0.2 Fundamentals of Spintronics The physics behind spintronics. .. ultimate goal of spintronics study is to manipulate spin currents in spintronic devices with accuracy and precision, allowing faster operations, and lower energy consumptions However, major challenges of spintronics remain, including the optimization of spin polarization and spin lifetimes of injected electrons, the detection of spins in nanoscale solid-state systems, the transport of spin-polarized... effects of interfacial spin flip in practical devices and achieve high MR ratio In Chapter 2, we introduce the theory of tight-binding NEGF and explain the features of this formalism We then present a theoretical description of the spin transport through another type of interface, i.e., the Ferromagnetic-Insulator-Semiconductor (FM/I/SC) interface based on a tight-binding NEGF model The advantage of applying... since, for spintronics, one would prefer an all-electrical means of generating spin current The various spin injection means include using (a) a diffusive Ohmic contact; (b) 100% polarized injectors, such as half-metals; (c) tunnel injectors and (d) a magnetic semiconductor structure as 17 Introduction spin-injector According to Schmidt et al., spin injection into SC from FM metals with partially spin-polarized... conduction band is dominated by the unsplit 4s band Due to the unbalanced density of spin-states in 3d band at EF , strong spin-dependent scattering results In between two spin-flip scattering events, 4 Introduction an electron can undergo many scattering events but maintain the same spin direction Within this limit where no spin-flip scattering happens, electrons conduct in parallel through two spin channels... seamless integration between logic and storage devices However, before SC spintronics can be commercialized, a number of challenges have to be overcome One of them is to induce spin density in a SC This process is called ‘spin-injection’ and it involves creating spin currents which comprise unequal numbers of spin-up and spin-down carriers A second problem is to devise a means of controlling the spin transport,... General Theory of Spin Injection The theory of spin injection at FM/NM junctions will be described in this section based on the framework of the spin drift diffusion equation Spin injection in FM/NM junctions was initially studied in detail by Johnson and Silsbee [32], van Son et al [26], Valet and Fert [6], and others Here we consider electrons flow along the x direction in a geometry consisting of a metallic... spin currents are of sufficient density, the resulting transfer of spin momentum can cause magnetization switching or induce stable precession of the magnetization in thin magnetic layers The flow of the spin currents is determined by the spin dependent transport properties, such as conductivity, interface resistance and spin-flip scattering in a particular system Due to the exchange interactions with... application of spintronics has been in the area of magnetic recording, which has been taken to a new height in the past two decades This is measured by the evolution of the areal density in magnetic hard disks, which has 2 Introduction increased tremendously since the introduction of spintronics (see Fig 1) In order to push the areal density to new boundaries, it is necessary to study the magnetic and spin... study of spintronics is to understand the spin dynamics in solid-state systems and to make useful devices based on the acquired knowledge Fundamental studies of spintronics often include the effects of physical parameters of solid-state systems on electron spins, the spin transports at nanoscale dimensions and the spin transport behaviors under the in uence of electric and magnetic fields As a matter of . Derivation of Non-equilibrium Green’s Function in Spin Space 132 The Relationship of Spin Transfer Torque and Spin Density 136 iv Summary Spintronics offers promise in employing intrinsic spin in nanoscale. of spintronics remain, including the optimization of spin polarization and spin lifetimes of injected electrons, the detection of spins in nanoscale solid-state systems, the transport of spin-polarized. function of R 0 in the absence of any bulk or interfacial spin flipping, i.e. with R SF and l sf tending to in nity. . . . . . . . . . . 32 viii LIST OF FIGURES 2.1 Schematic of a device divided into