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

18 Chapter 2: Spin Dynamics: Overview and Analysis of 2D Systems
S
1
1 2
0.89
Sz
0
1 2
0.77
0 L so 2 L so
x
Figure 2.5: The spin density for linear Rashba coupling which is a solution of the spin
diffusion equation with the relaxation rate 1/τ s = 7/16τ s0 . Note that, compared to the
ballistic spin density, Fig.2.3, the period is slightly enhanced by a factor 4/ √ 15. Also, the
amplitude of the spin density changes with the position x, in contrast to the ballistic case.
The color is changing in proportion to the spin density amplitude.
get the continuity equation
∂s i
∂t = −∇j S i
+τ〈∇v F (B SO (k)×S) i
〉− 1
(ˆτ s ) ij
s j . (2.27)
It is important to note that in contrast to the continuity equation for the density, there are
two additional terms, due to the spin-orbit interaction. The last one is the spin relaxation
tensor which will be considered in detail in the next section. The other term arises due
to the fact that Eq.(2.23) contains a factor 2 in front of the spin-orbit precession term,
while the spin diffusion current Eq.(2.26) does not contain that factor. This has important
physical consequences, resulting in the suppression of the spin relaxation rate in quantum
wires and quantum dots as soon as their lateral extension is smaller than the spin precession
length L SO , as we will see in Chapter3.
2.4 Spin Relaxation Mechanisms
The intrinsic spin-orbit interaction itself causes the spin of the electrons to precess
coherently, as the electrons move through a conductor, defining the spin precession length