Physics Letters A 365 (2007) 501–504
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Spin relaxation time, spin dephasing time and ensemble spin dephasing time
in n-type GaAs quantum wells
C. Lü
a,b
, J.L. Cheng
b
,M.W.Wu
a,b,∗
, I.C. da Cunha Lima
a
a
Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
b
Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
Received 18 October 2006; received in revised form 3 February 2007; accepted 5 February 2007
Available online 13 February 2007
Communicated by R. Wu
Abstract
We investigate the spin relaxation and spin dephasing of n-type GaAs quantum wells. We obtain the spin relaxation time T
1
, the spin dephasing
time T
2
and the ensemble spin dephasing time T
∗
2
by solving the full microscopic kinetic spin Bloch equations, and we show that, analogous to the
common sense in an isotropic system for conduction electrons, T
1
, T
2
and T
∗
2
are identical due to the short correlation time. The inhomogeneous
broadening induced by the D’yakonov–Perel term is suppressed by the scattering, especially the Coulomb scattering, in this system.
©
2007 Elsevier B.V. All rights reserved.
PACS : 72.25.Rb; 71.10.-w
Much attention has been devoted to the spin degree of free-
dom of carriers in zinc-blende semiconductors, both in bulk
systems and in reduced dimensionality structures, like quan-
tum wells and quantum dots. Understanding spin dephasing and
spin relaxation of carriers in these systems is a key factor for the
realization of high quality spintronic devices [1–4]. Of special
interest is the calculation of quantities known as spin relaxation
time, T
1
, and spin dephasing time, T
2
. T
1
is defined as the time it
takes for the spins along the longitudinal field to reach equilib-
rium. Therefore, it is related with the relaxation of the average
spin polarization. On the other hand, T
2
is defined as the time
it takes for the transverse spins, initially precessing in phase
about the longitudinal field, to lose their phase [4]. In general
T
2
2T
1
, and T
1
= T
2
is believed to be true when the system
is isotropic and the correlation time for the interaction is very
short compared with the Larmor period [5,6].
A qualitative reason for T
1
= T
2
is that if the correlation time
is short compared with the Larmor period the interaction with
the magnetic fields is not affected by a transformation into a
coordinate system rotating at the Larmor frequency. The sur-
*
Corresponding author.
E-mail address: mwwu@ustc.edu.cn (M.W. Wu).
rounding seems isotropic and the rate of decay will be the same
for all directions. Therefore, longitudinal and transverse relax-
ation times will be the same. Hence the decay of the spin signal
will be the same in all directions and T
1
equals T
2
, as argued
in Ref. [5]. For several years T
1
and T
2
where considered as
the only important factors describing the spin dynamics under
external fields.
In recent years, however, many experiments have been per-
formed reflecting the dephasing process of the ensemble of
electrons, instead of the dynamics of a single one [7]. In fact,
electrons with different momentum states have different pre-
cession frequencies due to the momentum dependence of the
effective magnetic field acting on the electron spin, and this in-
homogeneity of precession frequencies can cause a reversible
phase lose. A parameter name, T
∗
2
, was coined to describe the
dephasing process associated to this inhomogeneous broaden-
ing of the precessing frequencies.
Wu et al. have already shown that in the presence of this
inhomogeneous broadening, any scattering, including the spin-
conserving scattering, can cause irreversible spin dephasing
[8–10]. This fact leads to the belief that, in general, T
∗
2
T
2
.
However, for conduction electrons T
∗
2
= T
2
is known to be a
very good approximation because the inhomogeneous broaden-
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doi:10.1016/j.physleta.2007.02.030