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

26 Chapter 3: WL/WAL Crossover and Spin Relaxation in Confined Systems
precession axis and the amplitude of the total precession field is changing, since
| B+B SO (−p) |=| B−B SO (p) |≠| B+B SO (p) |,
resulting in spin dephasing and relaxation, as the sign of the momentum changes randomly.
3.1.2 Wires with W > λ F
In this Chapter, we show, however, that the condition for a coherent spin precession
is not only the 1d wire, 1/τ s is already strongly reduced in much wider wires:
as soon as the wire width W is smaller than bulk spin precession length L SO , which is
the length on which the electron spin precesses a full cycle. This explains the reduction
of the spin relaxation rate in quantum wires for widths exceeding both the elastic
mean-free path l e and λ F , as observed with optical[HSM + 06] as well as with WL
measurements[DLS + 05, LSK + 07, SGP + 06, WGZ + 06, KKN09]. As an example we show
two experiments in Fig.3.1, where the significant dimensional reduction has been observed.
Since L SO can be several µm and is not changed significantly as the wire width W is reduced,
such a reduction of spin relaxation can be very useful for applications: the spin
of conduction electrons precesses coherently as it moves along the wire on length scale
L SO . It becomes randomized and relaxes on the longer length scale L s (W) = √ D e τ s only
[D e = v F l e /2 (v F , Fermi velocity) is the 2D diffusion constant].
To understand the connection between the conductivity measurements and spin relaxation
we recall that quantum interference of electrons in low-dimensional, disordered conductors
is known to result in corrections to the electrical conductivity ∆σ. This quantum correction,
the WL effect, is a very sensitive tool to study dephasing and symmetry-breaking
mechanisms in conductors.[AAKL82, Ber84, CS86] The entanglement of spin and charge by
SO interaction reverses the effect of WL and thereby enhances the conductivity. This WAL
effect was predicted by Hikami et al.[HLN80] for conductors with impurities of heavy elements.
As conduction electrons scatter from such impurities, the SO interaction randomizes
their spin. The resulting spin relaxation suppresses interference in spin triplet configurations.
Sincethetime-reversal operation changes not only thesign of momentum but also the
sign of the spin, the interference in singlet configuration remains unaffected. Since singlet
interference reduces the electron’s return probability, it enhances the conductivity, which is
named the WAL effect. In weak magnetic fields, the singlet contributions are suppressed.
Thereby, the conductivity is reduced and the magnetoconductivity becomes negative. The