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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28 Chapter 3: WL/WAL Crossover and <strong>Sp<strong>in</strong></strong> Relaxation <strong>in</strong> Conf<strong>in</strong>ed Systems<br />
(a)<br />
(b)<br />
Figure 3.1: Two different experimental approaches to extract the wire width dependence<br />
<strong>of</strong> sp<strong>in</strong> relaxation rate. (a) Measurement by Kerr rotation (extracted from [HSM + 06]) and<br />
(b) us<strong>in</strong>g magnetoconductivity experiments (extracted from [LSK + 07]).<br />
all classical paths α with their correspond<strong>in</strong>g actions S α<br />
P(r,r ′ ) ≈ ∑ α<br />
A α e iSα . (3.1)<br />
It is <strong>in</strong>tuitively clear that only this <strong>in</strong>terference processes will survive self-averag<strong>in</strong>g which<br />
are <strong>in</strong>dependent <strong>of</strong> the impurity position. Disadvantageous for conductivity is clearly, if an<br />
electron returns to the po<strong>in</strong>t he started from. This are paths where the relative phase is<br />
<strong>in</strong>dependent <strong>of</strong> the position <strong>of</strong> the impurities:<br />
|P(r,r)| 2 ≈ ∑ α,β<br />
A α A β e i(Sα−S β) . (3.2)<br />
There are two possibilities, which cancel the phase factor: The first one is pure classic,<br />
namely represent<strong>in</strong>g a scatter<strong>in</strong>g that causes the electron to traverse the way α backwards.<br />
The reason for the second one is with the time-reversal-symmetry <strong>of</strong> the system, which<br />
allows to be β the time-reversed path <strong>of</strong> α, more specific<br />
|P(r,r)| 2 ≈ ∑ α<br />
〈|A α| 2 +|A α| 2 〉+2R ∑ α<br />
〈A αA ∗<br />
α 〉 (3.3)<br />
= |P class (r,r)| 2 +|P WL (r,r)| 2 . (3.4)