Itinerant Spin Dynamics in Structures of ... - Jacobs University
Itinerant Spin Dynamics in Structures of ... - Jacobs University Itinerant Spin Dynamics in Structures of ... - Jacobs University
62 Chapter 3: WL/WAL Crossover and Spin Relaxation in Confined Systems R[E]/DeQ 2 SO I[E]/DeQ 2 SO 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 2 1 0 1 2 K x 0.6 0.4 0.2 0.0 0.2 0.4 0.6 (a) 2 1 0 1 2 K x (b) ˜B 0 0.5 0.8 Figure 3.17: (a) Real and(b) imaginary parts of thespectrumof the Cooperonwith Zeeman term of the strength gµ B B/D e Q 2 SO = 0...0.8 in steps of 0.1 in a finite wire of the width Q SO W = 0.5. The B independent mode E t0 is not shown.
Chapter 3: WL/WAL Crossover and Spin Relaxation in Confined Systems 63 the correction to the static conductivity in the case of a magnetic field which we include by means of a Zeeman term together with an effective magnetic field appearing in the cutoff 1/τ B as described in Sec.3.2. The ˜g = g/8m e D e factor is used as a material-dependent parameter. In Fig. 3.18, we see that for large enough ˜g factor, the system changes from positive magnetoconductivity—in the case without Zeeman field and a small-enough wire width—to negative magnetoconductivity at a finite Zeeman field for the same wire. Hence, the ratio W c /W WL changes and one has to be careful not to confuse the crossover defined by a change of the sign of the quantum correction, WL→WAL, and the crossover in the magnetoconductivity. To give an idea how the crossover W c depends on ˜g and the strength of the Zeeman field we analyze two different systems as plotted in Fig.3.19: The first one, plot (a), shows the drop of W c in a system as just described where we have one magnetic field which we include with an orbital and a Zeeman part. For small ˜g we have Q SO W c (˜g) = Q SO W c (˜g = 0)−const˜g 2 , where const is about 1 in the considered parameter space. Inthe second system [Fig.3.19(b)], we assumethat we can change theorbital and the Zeeman field separately. The critical width is plotted against the Zeeman field. To calculate W c , we fix the Zeeman field to a certain value, horizontal axis in plot (b), while we vary the effective field and calculate if negative or positive magnetoconductivity is present. For differentZeemanfieldsB Z /H s wegetdifferentW c . WeseethatW c isshiftedtolargerwidths as the Zeeman field is increased, Q SO W c (B Z /H s ) = Q SO W c (B Z = 0) + const(B Z /H s ) 2 , whereconst is about1in the considered parameter space, while∆σ(1/τ B = 0) (not plotted) is lowered as long as we assume small Zeeman fields. If we notice that B Z mixes singlet and triplet states it is understood that there is no gapless singlet mode anymore and therefore ∆σ(1/τ B = 0) must decrease for low Zeeman fields. To estimate ˜g, we take typical values for a GaAs/AlGaAs system and assume the electron densitytoben s = 1.11×10 11 cm −2 , theeffective massm e /m e0 = 0.063, theLandéfactorg = 0.75 and an elastic mean-free path of l e = 10 nm in a wire with Q SO W = 1, corresponding to W = 1.2µm, if we assume a Rashba spin-orbit coupling strength of α 2 = 5 meVÅ. We thus get ˜g ≈ 0.1 and find that the Zeeman coupling due to the perpendicular magnetic field can have a measurable, albeit small effect on the magnetoconductance in GaAs/AlGaAs systems.
- Page 21 and 22: Chapter 2: Spin Dynamics: Overview
- Page 23 and 24: Chapter 2: Spin Dynamics: Overview
- Page 25 and 26: Chapter 2: Spin Dynamics: Overview
- Page 27 and 28: Chapter 2: Spin Dynamics: Overview
- Page 29 and 30: Chapter 2: Spin Dynamics: Overview
- Page 31 and 32: Chapter 2: Spin Dynamics: Overview
- Page 33 and 34: 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
- Page 39 and 40: Chapter 3: WL/WAL Crossover and Spi
- Page 41 and 42: Chapter 3: WL/WAL Crossover and Spi
- Page 43 and 44: Chapter 3: WL/WAL Crossover and Spi
- Page 45 and 46: Chapter 3: WL/WAL Crossover and Spi
- Page 47 and 48: Chapter 3: WL/WAL Crossover and Spi
- Page 49 and 50: Chapter 3: WL/WAL Crossover and Spi
- Page 51 and 52: Chapter 3: WL/WAL Crossover and Spi
- Page 53 and 54: Chapter 3: WL/WAL Crossover and Spi
- Page 55 and 56: Chapter 3: WL/WAL Crossover and Spi
- Page 57 and 58: Chapter 3: WL/WAL Crossover and Spi
- Page 59 and 60: Chapter 3: WL/WAL Crossover and Spi
- Page 61 and 62: Chapter 3: WL/WAL Crossover and Spi
- Page 63 and 64: Chapter 3: WL/WAL Crossover and Spi
- Page 65 and 66: Chapter 3: WL/WAL Crossover and Spi
- Page 67 and 68: Chapter 3: WL/WAL Crossover and Spi
- Page 69 and 70: Chapter 3: WL/WAL Crossover and Spi
- Page 71: Chapter 3: WL/WAL Crossover and Spi
- Page 75 and 76: 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
- Page 81 and 82: Chapter 4: Direction Dependence of
- Page 83 and 84: Chapter 4: Direction Dependence of
- Page 85 and 86: Chapter 4: Direction Dependence of
- Page 87 and 88: Chapter 4: Direction Dependence of
- Page 89 and 90: Chapter 4: Direction Dependence of
- Page 91 and 92: Chapter 4: Direction Dependence of
- 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
62 Chapter 3: WL/WAL Crossover and <strong>Sp<strong>in</strong></strong> Relaxation <strong>in</strong> Conf<strong>in</strong>ed Systems<br />
R[E]/DeQ 2 SO<br />
I[E]/DeQ 2 SO<br />
1.4<br />
1.2<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
2 1 0 1 2<br />
K x<br />
0.6<br />
0.4<br />
0.2<br />
0.0<br />
0.2<br />
0.4<br />
0.6<br />
(a)<br />
2 1 0 1 2<br />
K x<br />
(b)<br />
˜B<br />
0 0.5 0.8<br />
Figure 3.17: (a) Real and(b) imag<strong>in</strong>ary parts <strong>of</strong> thespectrum<strong>of</strong> the Cooperonwith Zeeman<br />
term <strong>of</strong> the strength gµ B B/D e Q 2 SO<br />
= 0...0.8 <strong>in</strong> steps <strong>of</strong> 0.1 <strong>in</strong> a f<strong>in</strong>ite wire <strong>of</strong> the width<br />
Q SO W = 0.5. The B <strong>in</strong>dependent mode E t0 is not shown.
Change language