Itinerant Spin Dynamics in Structures of ... - Jacobs University

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2 Chapter 1: Introduction of this work will mainly focus on the second point, manipulation of the spin and understanding the limitations of spin propagation. The main objective is to shed light on some interesting effects in the field of spin-dependent electronic transport. Looking in the literature one realizes that many proposals for two-dimensional (2D) spintronic devices are based on the presence of spin-orbit coupling (SOC) in a 2D electron system (2DES) semiconductor heterostructure. This idea goes back to the spin field-effect transistor proposed by Datta and Das[DD90] which is schematically plotted in Fig.1.1. The (a) (b) Figure 1.1: (a) a) Schematic of Datta-Das spin modulator device in a cross-section. The 2D electron gas (2DEG) has a distance of L from the emitter (↑) to the collector (↓). Normal to thiscross-section thereisanadditional confinement. b)Theconductionbandwhichconfines the electrons to a 2D system and the electron distribution (dotted) are shown. Taken from Ref.[NATE97]. (b) Manipulation of spin precession due to SOC by gate voltage. electrons are injected from metallic leads into the 2DES with the spin parallel to the transport direction. In the nonmagnetic region the spin is changed along the distance L due to
Chapter 1: Introduction 3 the coupling of spin degree of freedom and orbital motion of the electron. In this model the electrons are moving ballistically in a quasi one-dimensional channel, due to a second confinement. The result for weak SOC in first order perturbation theory is a modulation of the spin current with a phase-shift ∆θ = 2αm e 2 L, (1.1) with α the strength of SOC and m e the effective electron mass. This phase-shift ∆θ can be manipulated by the confining field E z via the gate which in turn changes the probability to find the spin in the ”down” state at the drain. The gate-control makes the spin-FET so promising for spintronic applications. In Sec.2.3.3 we will review this transport in ballistic wires. Applying this model in an experiment one is, however, confronted with several problems. Spintronic devices which rely on coherent spin precession of conduction electrons[DD90, ZFD04] require a small spin relaxation rate 1/τ s . But as the electron momentum is randomized due to disorder, the coupling between spin and orbital degree of freedom, the spin-orbit (SO) interaction, is expected to result not only in a spin precession but in randomization of the electron spin. This coupling can lead to counter intuitive effects as the following, described by D’yakonov and Perel’[DP72]: Analyzing the spin transport in e.g. n-type semiconductors at low temperature (T 5K), one finds that the more the electron is scattered the longer is the life time of the initial spin state. Such experiments are often performed in devises where the wire width W is several nanometers wide, so that boundary effects can play an important role: Looking at the extreme situation where W is of the order of Fermi wavelength λ F , the D’yakonov-Perel’ spin relaxation is expected to vanish,[KK00, MFA02] since the back scattering from impurities can in one-dimensional wires only reverse the SO field and thereby the spin precession. Immediately the following question arises: How many channels can be added without enlarging the spin relaxation rate significantly? In Ref.[Ket07], which is the starting point for the analysis presented in the first part of the present work, S. Kettemann could show, that 1/τ s is already strongly reduced in much wider wires: as soon as the wirewidth W is smaller than bulkspin precession length L SO , which is the length on which the electron spin precesses a full cycle. Since L SO can be several µm and is not changed significantly as the wire width W is reduced, the reduction of spin relaxation can be very useful for applications. Thestudyof thereduction of the spinrelaxation rate in quantum wires for widths exceeding
Page 1 and 2: Itinerant Spin Dynamics in Structur
Page 3 and 4: Itinerant Spin Dynamics in Structur
Page 5 and 6: Contents v 3.2.2 Weak Localization
Page 7 and 8: Citations to Previously Published W
Page 9 and 10: Dedicated to Linda, my parents and
Page 11: Chapter 1 Introduction Structure of
Page 15 and 16: Chapter 1: Introduction 5 Throughou
Page 17 and 18: Chapter 2: Spin Dynamics: Overview
Page 35 and 36: Chapter 3 WL/WAL Crossover and Spin
Page 37 and 38: Chapter 3: WL/WAL Crossover and Spi
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Chapter 3: WL/WAL Crossover and Spi
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Chapter 4 Direction Dependence of S
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Chapter 4: Direction Dependence of
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Chapter 5 Spin Hall Effect 5.1 Intr
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Chapter 5: Spin Hall Effect 85 curr
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Chapter 5: Spin Hall Effect 87 with
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Chapter 5: Spin Hall Effect 89 1.0
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Chapter 5: Spin Hall Effect 91 as s
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Chapter 5: Spin Hall Effect 93 V⩵
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Chapter 5: Spin Hall Effect 95 0.4
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Chapter 5: Spin Hall Effect 97 oper
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Chapter 5: Spin Hall Effect 99 the
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Chapter 5: Spin Hall Effect 101 str
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Chapter 5: Spin Hall Effect 103 Com
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Chapter 5: Spin Hall Effect 105 Fin
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Chapter 6: Critical Discussion and
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Chapter 6: Critical Discussion and
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List of Figures 111 3.3 Exemplifica
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List of Figures 113 4.2 The spin de
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List of Tables 3.1 Singlet and trip
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Bibliography 117 [BB04] [BBF + 88]
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Bibliography 119 [DP71b] [DP71c] [D
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Bibliography 121 [HSM + 06] [HSM +
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Bibliography 123 [MACR06] T. Mickli
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Bibliography 125 [PMT88] [PP95] [PT
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Bibliography 127 [Tor56] H. C. Torr
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Appendix A SOC Strength in the Expe
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Appendix A: SOC Strength in the Exp
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Appendix B: Linear Response 133 in
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Appendix B: Linear Response 135 Pro
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Appendix C Cooperon and Spin Relaxa
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Appendix C: Cooperon and Spin Relax
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Appendix D: Hamiltonian in [110] gr
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Appendix E: Summation over the Ferm
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Appendix F: KPM 151 integer running
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