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

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78 Chapter 4: Direction Dependence of Spin Relaxation and Diffusive-Ballistic Crossover can also support the method proposed in Ref.[SKK + 08] -to determine the relative strength of Rashba and Dresselhaus SOC from WL/WAL measurements without fitting parameterswith inclusion of cubic Dresselhaus term for wire directions different from [100] and [010] in an analytical manner. In the (110) system the situation is different: In the 2D case it was shown by Pikus et al., Ref.[HPB + 97], that in the absence of the Rashba terms the negative magnetoconductivity cannot be observed. In the case of a wire geometry we can conclude from Eqs.(4.41-4.46) that we have no width dependence if Rashba SOC vanishes. A change of the quantum correction to the static conductivity therefore cannot be achieved in this wire geometry by changing the wire width. The reason is the vector potential in the boundary condition, Eq.(4.40), which only depends on the Rashba SOC. 4.5 Diffusive-Ballistic Crossover In the following we assume a (001) 2D system with both, Rashba and linear and cubic Dresselhaus SO coupling. Experiments measuring WL in diffusive quantum wires with SOC[LSK + 07, SGB + 09] are in great agreement with theoretical calculations by S. Kettemann, Ref.[Ket07]. But considering e.g. the works Ref.[KKN09, KHG + 10], one realizes that the scope of application of the theory has to be extended to describe also the crossover to the ballistic regime, l e > W. In Fig.4.3 we show an example of an experiment done by Kunihashi et al.[KKN09]. The lines show a fit using Eq.(10) in the paper by S. Kettemann[Ket07] which is equal to the results presented in Sec.4.2.2 if the width dependence of the term due to cubic Dresselhaus SOC is neglected. To get the solid lines the term due to cubic Dresselhaus SOC was neglected, the dashed include it. When checking Fig.4.3 (a) the condition l e < W is not fulfilled at all wire width. It follows that this additional term is suppressed if the condition of a diffusive system does not hold anymore. We have shown in Sec.4.2.2 that the presence of cubic Dresselhaus SOC in the sample leads to a finite spin relaxation even for wire widths Q SO W ≪ 1, regardless of the boundary direction in a (001) system. To account for the ballistic case we have to modify the derivation of the Cooperon Hamiltonian, Eq.(4.5). In the case of a wire where the mean
Chapter 4: Direction Dependence of Spin Relaxation and Diffusive-Ballistic Crossover 79 (a) (b) Figure 4.3: Example of an experiment done by Kunihashi et al.[KKN09]. The width dependence of the spin relaxation length l 1D SO of different carrier density. Solid lines and dashed lines in (b) show the l 1D SO calculated from the theory presented in this work, with neglecting cubic Dresselhaus term and taking into account full SOIs, respectively.
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Itinerant Spin Dynamics in Structur
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Itinerant Spin Dynamics in Structur
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Contents v 3.2.2 Weak Localization
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Citations to Previously Published W
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Dedicated to Linda, my parents and
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Chapter 1 Introduction Structure of
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Chapter 1: Introduction 3 the coupl
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Chapter 1: Introduction 5 Throughou
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Chapter 2: Spin Dynamics: Overview
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Chapter 3 WL/WAL Crossover and Spin
Page 37 and 38: Chapter 3: WL/WAL Crossover and Spi
Page 77 and 78: Chapter 4 Direction Dependence of S
Page 79 and 80: Chapter 4: Direction Dependence of
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Page 93 and 94: Chapter 5 Spin Hall Effect 5.1 Intr
Page 95 and 96: Chapter 5: Spin Hall Effect 85 curr
Page 97 and 98: Chapter 5: Spin Hall Effect 87 with
Page 99 and 100: Chapter 5: Spin Hall Effect 89 1.0
Page 101 and 102: Chapter 5: Spin Hall Effect 91 as s
Page 103 and 104: Chapter 5: Spin Hall Effect 93 V⩵
Page 105 and 106: Chapter 5: Spin Hall Effect 95 0.4
Page 107 and 108: Chapter 5: Spin Hall Effect 97 oper
Page 109 and 110: Chapter 5: Spin Hall Effect 99 the
Page 111 and 112: Chapter 5: Spin Hall Effect 101 str
Page 113 and 114: Chapter 5: Spin Hall Effect 103 Com
Page 115 and 116: Chapter 5: Spin Hall Effect 105 Fin
Page 117 and 118: Chapter 6: Critical Discussion and
Page 119 and 120: Chapter 6: Critical Discussion and
Page 121 and 122: List of Figures 111 3.3 Exemplifica
Page 123 and 124: List of Figures 113 4.2 The spin de
Page 125 and 126: List of Tables 3.1 Singlet and trip
Page 127 and 128: Bibliography 117 [BB04] [BBF + 88]
Page 129 and 130: Bibliography 119 [DP71b] [DP71c] [D
Page 131 and 132: Bibliography 121 [HSM + 06] [HSM +
Page 133 and 134: Bibliography 123 [MACR06] T. Mickli
Page 135 and 136: Bibliography 125 [PMT88] [PP95] [PT
Page 137 and 138: 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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