Itinerant Spin Dynamics in Structures of ... - Jacobs University
Itinerant Spin Dynamics in Structures of ... - Jacobs University
Itinerant Spin Dynamics in Structures of ... - Jacobs University
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12 Chapter 2: <strong>Sp<strong>in</strong></strong> <strong>Dynamics</strong>: Overview and Analysis <strong>of</strong> 2D Systems<br />
precess around the x-axis as it moves along. For narrow quantum wells, where 〈kz 2〉 ∼<br />
1/a 2 z ≥ kF 2 the l<strong>in</strong>ear term exceeds the cubic Dresselhaus terms. For a typical value <strong>of</strong><br />
〈kz 2〉 = 0.036/nm2 , one gets accord<strong>in</strong>gly[W<strong>in</strong>04b], α 1 =0.99 meVnm (GaAs), 0.98 meVnm<br />
(InAs), 27.4 meVnm (InSb). A special situation arises for quantum wells grown <strong>in</strong> the [110]-<br />
direction, where it turns out that the sp<strong>in</strong>-orbit field is po<strong>in</strong>t<strong>in</strong>g normal to the quantum<br />
well, as shown <strong>in</strong> Fig.2.2, so that an electron whose sp<strong>in</strong> is <strong>in</strong>itially polarized along the<br />
normal <strong>of</strong> the plane, rema<strong>in</strong>s polarized as it moves <strong>in</strong> the quantum well.<br />
0 SIA<br />
0<br />
BIA111<br />
0<br />
0<br />
010<br />
0<br />
BIA001<br />
110 0<br />
BIA110<br />
0 001<br />
0<br />
1 10<br />
0<br />
100<br />
Figure 2.2: The sp<strong>in</strong>-orbit vector fields for l<strong>in</strong>ear structure <strong>in</strong>version asymmetry (Rashba)<br />
coupl<strong>in</strong>g, and for l<strong>in</strong>ear bulk <strong>in</strong>version asymmetry (BIA) sp<strong>in</strong>-orbit coupl<strong>in</strong>g for quantum<br />
wells grown <strong>in</strong> [111], [001] and [110] direction, respectively.<br />
In quantum wells with asymmetric electrical conf<strong>in</strong>ement the <strong>in</strong>version symmetry is broken<br />
as well. The result<strong>in</strong>g sp<strong>in</strong>-orbit coupl<strong>in</strong>g, the structural <strong>in</strong>version asymmetry coupl<strong>in</strong>g