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

Chapter 1: Introduction 3
the coupling of spin degree of freedom and orbital motion of the electron. In this model
the electrons are moving ballistically in a quasi one-dimensional channel, due to a second
confinement. The result for weak SOC in first order perturbation theory is a modulation
of the spin current with a phase-shift
∆θ = 2αm e
2 L, (1.1)
with α the strength of SOC and m e the effective electron mass. This phase-shift ∆θ can be
manipulated by the confining field E z via the gate which in turn changes the probability
to find the spin in the ”down” state at the drain. The gate-control makes the spin-FET so
promising for spintronic applications. In Sec.2.3.3 we will review this transport in ballistic
wires.
Applying this model in an experiment one is, however, confronted with several problems.
Spintronic devices which rely on coherent spin precession of conduction electrons[DD90,
ZFD04] require a small spin relaxation rate 1/τ s . But as the electron momentum is randomized
due to disorder, the coupling between spin and orbital degree of freedom, the
spin-orbit (SO) interaction, is expected to result not only in a spin precession but in randomization
of the electron spin. This coupling can lead to counter intuitive effects as the
following, described by D’yakonov and Perel’[DP72]: Analyzing the spin transport in e.g.
n-type semiconductors at low temperature (T 5K), one finds that the more the electron
is scattered the longer is the life time of the initial spin state. Such experiments are
often performed in devises where the wire width W is several nanometers wide, so that
boundary effects can play an important role: Looking at the extreme situation where W
is of the order of Fermi wavelength λ F , the D’yakonov-Perel’ spin relaxation is expected
to vanish,[KK00, MFA02] since the back scattering from impurities can in one-dimensional
wires only reverse the SO field and thereby the spin precession. Immediately the following
question arises: How many channels can be added without enlarging the spin relaxation rate
significantly? In Ref.[Ket07], which is the starting point for the analysis presented in the
first part of the present work, S. Kettemann could show, that 1/τ s is already strongly reduced
in much wider wires: as soon as the wirewidth W is smaller than bulkspin precession
length L SO , which is the length on which the electron spin precesses a full cycle. Since L SO
can be several µm and is not changed significantly as the wire width W is reduced, the
reduction of spin relaxation can be very useful for applications.
Thestudyof thereduction of the spinrelaxation rate in quantum wires for widths exceeding