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Excitation wavelength dependence of the anomalous circular photogalvanic effect in
undoped InGaAs/AlGaAs quantum wells
L. P. Zhu, Y. Liu, C. Y. Jiang, X. D. Qin, Y. Li, H. S. Gao, and Y. H. Chen
Citation: Journal of Applied Physics 115, 083509 (2014); doi: 10.1063/1.4867039
View online: http://dx.doi.org/10.1063/1.4867039
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JOURNAL OF APPLIED PHYSICS 115, 083509 (2014)
Excitation wavelength dependence of the anomalous circular photogalvanic
effect in undoped InGaAs/AlGaAs quantum wells
L. P. Zhu, Y. Liu, C. Y. Jiang, X. D. Qin, Y. Li, H. S. Gao, and Y. H. Chena)
Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors,
Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, People’s Republic of China
(Received 7 December 2013; accepted 15 February 2014; published online 26 February 2014)
The excitation wavelength dependence of the anomalous circular photogalvanic effect (ACPGE)
current arising from the reciprocal spin Hall effect (RSHE) in undoped InGaAs/AlGaAs quantum wells
is measured under normal incidence of circularly polarized light at room temperature. We found that
the spot location with the maximum ACPGE current is wavelength independent. And the normalized
ACPGE current decreases at smaller wavelengths, which can be attributed to the sharp decrease of the
spin relaxation time (ss ) and the hot electron relaxation time (s1 ) at smaller wavelengths. The study of
the excitation wavelength dependence of ACPGE current is a good supplement to the in-depth
C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4867039]
investigation of RSHE. V
I. INTRODUCTION
Much attention has been given to semiconductor spintronics
for the promising applications in information technology.1,2
However, techniques for efficient generation and manipulation
of spin currents are still the major issues. The spin Hall effect
(SHE) which has been studied extensively opens avenues to convert a charge current into a spin current due to the spin-orbit
interaction (SOI).2,3 As a reverse process, the SOI can also convert a spin current into a transverse charge current, which is
known as the reciprocal spin Hall effect (RSHE).4–9 RSHE has
so far been observed in bulk GaAs,4 Pt wire,5 AlGaN/GaN heterostructures,6 GaAs/AlGaAs heterostructures,7 InN films,8 and
MgZnO/ZnO heterostructures.9
The ordinary circular photogalvanic effect (CPGE) has
been applied widely to measure the Rashba and Dresselhaus
spin-orbit coupling coefficient in semiconductors.10–12
According to CPGE, the oblique incidence of circularly polarized light induces a spin polarized charge current whose direction and magnitude depend on the polarization degree of the
light.10 Different from the ordinary CPGE, a charge current
based on RSHE is excited exactly under normal incidence,
while the current induced by CPGE is zero on this occasion;
thus, this effect can be named as anomalous circular photogalvanic effect (ACPGE).6,10 The radiation sources applied in the
former studies for ACPGE were all single wavelength lasers.
But in this letter, we focus on the wavelength dependence of
the ACPGE in undoped InGaAs/AlGaAs quantum wells
(QWs), which might reveal more information about RSHE.
Usually the SOI is weak in GaAs system and consequently
RSHE is too weak to be detected at room temperature; however, the undoped InGaAs/AlGaAs QWs studied here had
demonstrated a strong Rashba spin-obit coupling.13
II. SAMPLE AND EXPERIMENT
The sample studied here is an undoped In0.15Ga0.85As/
Al0.3Ga0.7As QWs grown by molecular beam epitaxy. A
a)
[email protected]
0021-8979/2014/115(8)/083509/5/$30.00
200 nm buffer layer is initially deposited on (001) SI-GaAs
˚ -In0.15Ga0.85As/
substrate, followed by ten periods of 100 A
˚
˚
100 A-Al0.3Ga0.7As QWs. Then, a 500 A Al0.3Ga0.7As layer
˚ GaAs cap layer are deposited. The sample is
and 100 A
cleaved into a narrow strip along the GaAs ½1
10 direction
with a width of 4 mm and a length of 12 mm, respectively.
The geometry has been shown in Fig. 2(b), where two ohmic
electrodes with a distance of 3 mm were made along y direction by indium deposition and annealed at about 420 C in
nitrogen atmosphere.
The experimental setup is sketched in Fig. 1. A modelocked Ti:sapphire laser with a repetition rate of 80 MHz
serves as the radiation source. As the full width at half maximum (FWHM) of the laser pulse is about 7 nm, the steplength of the spectral scanning should not be too small. In
this experiment, the excitation wavelength is tuned from
865 nm to 1000 nm with a step-length of 5 nm, which covers
both 1hh-1e (the first valence subband of heavy hole to the
first conduction) transition and 1lh-1e (the first valence subband of light hole to the first conduction) transition.14 The
incident light goes through a polarizer and a photoelastic
modulator (PEM), of which the peak retardation is set to be
k/4, to yield a modulated circularly polarized light with a
fixed modulating frequency at 50 KHz. A chopper with a frequency at 220 Hz is applied to produce a polarization independent light, which is used to measure the common
photoinduced current (JPC). The Gaussian profile light beam
irradiates vertically on the sample with a diameter of
about 2 mm at the central line x between two electrodes (see
Fig. 2(b)). The photogalvanic current is collected by two
lock-in amplifiers through the two circle electrodes.
III. THEORY BACKGROUND
For the undoped In0.15Ga0.85As/Al0.3Ga0.7As QWs with
C2v symmetry, the CPGE current can be expressed as
jy ¼ cyx e^x E20 Pcirc ;
(1)
where cyx is a second-rank pseudotensor proportional to the
spin-orbit coupling parameter; x, y are two orthogonal
115, 083509-1
C 2014 AIP Publishing LLC
V
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Zhu et al.
J. Appl. Phys. 115, 083509 (2014)
momentum of electron’s orbit motion. This transformation
means a coupling of two axial vectors and should not be limited to the gyrotropic materials. The intensity of the light
spot has a Gauss profile; thus an inhomogeneous spin density
will be excited on the sample plane, as shown in Fig. 2(b).
Under normal incidence, the gradient of the spin density will
induce a diffused spin polarization current (SPC)
FIG. 1. The schematic diagram of the experimental setup.
directions in the plane of the QWs; E0 ; Pcirc ; e^ are the electric field amplitude of the light, the degree of circular polarization, and the unit vector pointing in the direction of light
propagation, respectively.10 For normal incidence, e^ is parallel to [001] crystallographic orientation and hence the current
vanishes as e^x ¼ 0.10 However, under normal incidence, a
sizeable charge current induced by circularly polarized light
is observed with the light spot moving away from the original point of the x direction. This current corresponds to the
typical characteristics of CPGE which can be described by
formula
jc ¼ j0 sin 2u;
(2)
where j0 is the amplitude of current and u is the angle
between the polarization directions of incident light and the
optical axis of the quarter-wave plate (the PEM equals to a
quarter-wave plate), so it can be named as ACPGE current.
It has been believed that this current is derived from a swirly
current depending on the spin orientation of photo-induced
carriers.6
The swirling charge current can be regarded as a transformation of the photon angular momentum into the angular
qzr ¼ Drr nz ðrÞsin 2u;
(3)
where D is the electron diffusion coefficient, nz(r) is the spin
density along the z direction, and r is the radial direction in
the x–y plane. Since the radius of light spot is about 2 mm
which is much bigger than the spin diffusion length, the contribution of the SPC outside the light spot can be neglected.
Thus, nz(r) is decided by the distribution of the light intensity, namely, nz ðrÞ ¼ N0z GðrÞ, where N0z is the average electron spin density with the maximal circular polarization
degree and G(r) is the Gaussian distribution of the light spot.
According to the RSHE, the SPC flowing in the plane of the
sample will suffer from a spin transverse force.6,15 As a
result, a transverse electric current (density) perpendicular to
both the direction of the SPC and the direction of the spin
polarization is produced, which can be expressed as
j ¼ ceqzr ^z ;
(4)
where e, c are the elementary charge, the spin-orbit interaction coefficient based on RSHE, respectively. Similar to the
SHE, RSHE has the extrinsic and intrinsic mechanisms. The
former originates from spin-dependent scattering of defects
and the latter is based on the spin band splitting. Since the
FIG. 2. (a) The ACPGE currents as a function of the spot location corresponding to 1hh-1e and 1lh-1e. The dashed lines are for ease of viewing. (b) Geometry
of the sample. And schemed mechanism of RSHE induced by Gauss-profile light spot. Illustration of the movement of spin polarized electrons under normal
incidence of rþ polarized light. The red dashed arrows denote the spin diffusional direction and the black dashed arrows denote the spin polarized direction.
The solid (black) arrows denote the SOC induced transverse electric current. The blue circles denote two electrodes, and the ACPGE current is collected by
the two electrodes. (c) The two-dimensional colored figure denotes the ACPGE currents at different spot locations and different wavelengths (near the transitions of 1hh-1e and 1lh-1e). The crosses (the triangles) mark the maximum (the minimum) positions at certain wavelengths.
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083509-3
Zhu et al.
J. Appl. Phys. 115, 083509 (2014)
undoped QWs studied here has a sizeable Rashba effect,13,14
the extrinsic and intrinsic mechanisms probably coexist. As
a result, a swirling electric current will be induced around
the light spot, which will further generate an observed
ACPGE current.
IV. RESULTS AND DISCUSSION
In the experiment, the ACPGE currents are measured as
a function of the spot location at different wavelengths (near
the transitions of 1hh-1e (905 nm) and 1lh-1e (955 nm)). It is
worth noting that the current corresponding to 1lh-1e is
actually contributed by not only the 1lh-1e transition but also
the 1hh-1e transition. As shown in Fig. 2(a), the ACPGE currents reverse the sign from the left to right side, just like a
sine curve. It suggests that there is not a directed current but
a current swirling over the center of the light spot. The
movement of the swirling current along x direction will
change the amplitude of the ACPGE current. The sine-like
curve can be understood as follows. When the light spot irradiates on the left side of the original point (see Fig. 2(b)), a
pure spin current along þx direction will flow through the
original point. Due to the RSHE, an electric current along
y direction is collected by the two circle electrodes. On the
contrary, when the light spot irradiates on the right side of
the original point, the pure spin current will flow along x
direction; therefore, the induced electric current is along þy
direction. When the light spot irradiates just on the original
point, the ACPGE current is zero because there is no pure
spin current flow through the original point. When the light
spot irradiates far away from the original point (more than
4.5 mm), the ACPGE current disappears for the smaller pure
spin current. According to Eq. (3), Eq. (4) and Fig. 2, the
ACPGE current can be expressed phenomenologically as
JACPGE ¼ ceDSN0z wðx; rÞrr GðrÞ;
(5)
where S is the cross sectional area of the current and wðx; rÞ
is a sine-like function depending on the location and the radius of the light spot.
As shown in Fig. 2(c), the extreme positions are focused
on the location of x ¼ 61.5 mm (the little bit of shift near
1lh-1e transition is probably due to the contribution from the
1hh-1e transition), which indicates that the extreme position
of ACPGE current is wavelength independent. Before giving
a theoretical explanation to this independence, we will
deduce the specific expression of the average electron spin
density N0z in Eq. (10). Under normal incidence, the circularly polarized light will induce spin polarized electrons. In
particular, the left-handed circular polarized light ðrþ Þ will
induce spin-up electrons, and a small part of spin-down electrons still exist due to the spin-flipping of spin-up electrons.
In order to explain the experimental result, an LOP (longitudinal optical phonons)-assisted, spin-preserving relaxation
time of the hot electrons which jump from the excited states
to the bottom states of conduction band (inelastic process) is
introduced.16–18 In the relaxation time approximation, one
can get
dn"
n" n" n" n# n#
¼ g þ þ ;
dt
s0 s1 ss s1 ss
(6)
dn#
n# n# n# n" n"
¼ þ þ ;
dt
s0 s1 ss s1 ss
(7)
where n" ; n# , g are the density of spin-up electrons, the density of spin-down electrons, and the generation rate of spinup electrons, respectively; s0 is the lifetime of photoinduced
electrons, s1 the LOP-assisted, spin-preserving relaxation
time of the hot electrons, and ss is the spin relaxation time.
The reason why there is the spin relaxation time in the above
two expressions rather than the momentum relaxation time
will be discussed later. Under the condition of steady state,
one can get further expressions as
n" þ n# ¼ gs0 ;
1
1
2
2
:
¼
þ þ
n" n# ¼ gs ;
s
s0 s1 ss
(8)
(9)
In Eq. (8), n" þ n# is the total electron spin density, which is
proportional to the PC current. And in Eq. (9), s is an effective relaxation time. We regard n" n# as the average electron spin density, namely, N0z ¼ gs . Then, the ACPGE
current can be further expressed as
JACPGE ¼ gs ceDSwðx; rÞrr GðrÞ:
(10)
When the wavelength is tuned from 905 nm to 965 nm, the
changes of the size of the light spot can be neglected. In fact,
the vary of wavelength only changes the generation rate g
and the effective relaxation time s . Therefore, according to
Eq. (10), the vary of wavelength only affects the amplitude
of the ACPGE current but does not change the extreme
position.
Fig. 3(a) shows the ACPGE current as a function of
wavelength when the light spot is fixed on the position of
x ¼ þ1.5 mm. If the ACPGE current origins from RSHE, one
FIG. 3. The light spot is fixed on the position of x ¼ þ1.5 mm. (a) The red
empty circles denote the ACPGE current as a function of excitation wavelength. (b) The black empty circles denote the common photoinduced current as a function of excitation wavelength. The external electric field
applied on the two circle electrodes is 100 V/cm. (c) The blue (yellow)
empty circles denote the ACPGE (ALPGE) current normalized by the common photoinduced current. All of the solid lines are for ease of viewing.
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Zhu et al.
J. Appl. Phys. 115, 083509 (2014)
should observe that the ACPGE current reverses the direction when the optical interband transition changes between
1lh-1e and 1hh-1e, as a result of sign change of electron spin
involved. However, we did not observe obvious opposite in
the sign, which is probably due to the fact that the signal corresponding to 1lh-1e is contributed from not only the 1lh-1e
transition but also the 1hh-1e transition. In other words, signal corresponding to 1lh-1e is small and the current corresponding to the so-called 1lh-1e marked in Figs. 2 and 3 is
actually the combined action of 1lh-1e and 1hh-1e. As a
comparison, the common photoinduced current is also measured under the same conditions, as shown in Fig. 3(b).
According to Eq. (8) and Ohm’s law, the common photoinduced current can be expressed as
JPC ¼ gs0 elES;
(11)
where l is the mobility of electrons, E is the electric field
applied on the two circle electrodes (in Fig. 3(b),
E ¼ 100 V/cm), and S is the cross sectional area of the current. One can surprisingly find that the two curve shapes in
Figs. 3(a) and 3(b) are quite different. To eliminate the difference of the nonequilibrium electron’s density at different
wavelengths, we normalize the ACPGE current with the
common photoinduced current, because the common photoinduced current is proportional to the density of photoinduced nonequilibrium electrons. And the normalized
ACPGE current is shown in Fig. 3(c). What is more, the normalized anomalous linear photogalvanic effect (ALPGE)
current is also illustrated in Fig. 3(c), which is measured by
the lock-in amplifier with the reference frequency at
100 KHz. (The peak retardation of PEM still remains to be
k/4.) For further details of ALPGE, please see Ref. 19. It is
clear from Fig. 3(c) that the two curves are different in not
only the shape but also the size of value. Since the ALPGE
is derived from the momentum relaxation, the ACPGE will
not come from the momentum relaxation, and we believe
that the spin relaxation is dominant to the ACPGE. Thus,
there is the spin relaxation time rather than momentum relaxation time in Eqs. (6) and (7). According to Eq. (10), Eq.
(11), and Einstein’s relation (Dl ¼ kBeT ), the normalized
JACPGE (see Fig. 3(c)) can be expressed by
JACPGE
s kB Tcwðx; rÞrr GðrÞ
:
¼
JPC
s0 eE
(12)
c, T, E are invariable at different excitation wavelengths.
The little difference of wðx; rÞ or G(r) at different wavelengths can be ignored. Therefore, Eq. (12) is simplified as
JACPGE s
/ :
JPC
s0
(13)
The normalized ACPGE current that decreases at smaller
wavelengths can be understood as follows. The current corresponding to the transition of 1lh-1e is so small that it can
be ignored. And the current mainly comes from the transition
of 1hh-1e. As the mixing of 1hh band and 1lh band, the current coming from the transition of 1hh-1e extends to a broad
spectrum (see Fig. 3(a)). The splitting of the conduction
band can be described as the result of action on the electron
spin of an effective magnetic field. Spin precession around
this field in the intervals between collisions gives rise to spin
relaxation. Previously, Tackeuchi et al.20 have shown that
the spin relaxation at room temperature in GaAs/AlGaAs
quantum well is mainly governed by “Dyakonov-Perel” (DP)
interaction. Since InGaAs has many physical similarities
with GaAs, DP interaction seems to be the most plausible
spin relaxation mechanism.21 Taking the spin splitting of the
conduction band into consideration, the spin relaxation rate
of nondegenerate carriers can be simplified by neglecting the
energy dependence of sp as21,22
1
2kB TðaE1e =hÞ2 sp
;
¼
exp Eg
ss
kB T
(14)
where a, E1e, are the dimensionless numerical coefficient
governing the spin splitting of the conduction band, the
quantum confined energy denoting the bottom energy of the
first conduction subband, and the kinetic energy of electrons
in the first conduction subband, respectively. ss in Eq. (14),
different from that in Ref. 21 where it is an average relaxation time, is a local variable. If we just consider the transitions near the bottom of conduction subband, especially for
< kB T; ss will decrease rapidly with the increase of .
Since is decided by the energy of exciting light, ss will
decrease rapidly with the decrease of wavelength. What is
more, with the decrease of excitation wavelength, the relaxation time s1 of hot electrons jumping from the excited states
to the bottom states of conduction band decreases sharply for
the scattering of longitudinal optical phonon.16,18,23,24 The
lifetime s0 of photoinduced electrons is a constant at room
temperature. To sum up, the effective relaxation time s in
Eq. (13) will decrease, and then the normalized JACPGE
(shown in Fig. 3(c)) will decrease rapidly at smaller excitation wavelengths.
V. CONCLUSIONS
In conclusion, the excitation wavelength dependence of
the ACPGE current arising from RSHE in undoped InGaAs/
AlGaAs quantum wells is measured under normal incidence of
circularly polarized light at room temperature. We found that
the spot location with the maximum ACPGE current is wavelength independent. And the normalized ACPGE current
decreases at smaller wavelengths, which can be attributed to
the sharp decrease of spin relaxation time (ss ) and hot electron
relaxation time (s1 ) at smaller wavelengths. The study of the
excitation wavelength dependence of ACPGE current is a
good supplement to the in-depth investigation of RSHE. This
work shows promising applications of undoped InGaAs/
AlGaAs QWs in spintronics based on RSHE.
ACKNOWLEDGMENTS
The work was supported by the 973 program
(2012CB921304, 2012CB619306) and the National Natural
Science Foundation of China (No. 60990313).
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´ , J. Fabian, and S. D. Sarma, Rev. Mod. Phys. 76, 323 (2004).
I. Zutic
Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science
306, 1910 (2004).
3
M. I. Dyakonov and A. V. Khaetskii, Spin Physics in Semiconductors
(Springer, 2008), pp. 211.
4
H. Zhao, E. J. Loren, H. M. Van Driel, and A. L. Smirl, Phys. Rev. Lett.
96, 246601 (2006).
5
T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa, Phys. Rev.
Lett. 98, 156601 (2007).
6
X. W. He, B. Shen, Y. H. Chen, Q. Zhang, K. Han, C. M. Yin, N. Tang, F.
J. Xu, C. G. Tang, and Z. J. Yang, Phys. Rev. Lett. 101, 147402 (2008).
7
C. G. Tang, Y. H. Chen, Y. Liu, and Z. G. Wang, J. Phys.: Condens.
Matter 21, 375802 (2009).
8
F. H. Mei, N. Tang, X. Q. Wang, J. X. Duan, S. Zhang, Y. H. Chen, W. K.
Ge, and B. Shen, Appl. Phys. Lett. 101, 132404 (2012).
9
J. X. Duan, N. Tang, J. D. Ye, F. H. Mei, K. L. Teo, Y. H. Chen, W. K.
Ge, and B. Shen, Appl. Phys. Lett. 102, 192405 (2013).
10
S. D. Ganichev and W. Prettl, J. Phys.: Condens. Matter 15, R935 (2003).
11
C. Y. Jiang, Y. H. Chen, H. Ma, J. L. Yu, and Y. Liu, Appl. Phys. Lett. 98,
232116 (2011).
12
J. L. Yu, Y. H. Chen, Y. Liu, C. Y. Jiang, H. Ma, and L. P. Zhu, Appl.
Phys. Lett. 100, 152110 (2012).
13
J. L. Yu, Y. H. Chen, C. Y. Jiang, Y. Liu, and H. Ma, J. Appl. Phys. 109,
053519 (2011).
1
2
J. Appl. Phys. 115, 083509 (2014)
14
J. L. Yu, Y. H. Chen, C. Y. Jiang, Y. Liu, H. Ma, and L. P. Zhu, Appl.
Phys. Lett. 100, 142109 (2012).
15
S. Q. Shen, Phys. Rev. Lett. 95, 187203 (2005).
16
D. Von der Linde and R. Lambrich, Phys. Rev. Lett. 42, 1090
(1979).
17
W. M. Chen, I. A. Buyanova, G. Y. Rudko, A. G. Mal-Shukov, K. A.
Chao, A. A. Toropov, Ya. Terentev, S. V. Sorokin, A. V. Lebedev, S. V.
Ivanov et al., Phys. Rev. B 67, 125313 (2003).
18
J. F. Ryan, R. A. Taylor, A. J. Turberfield, A. Maciel, J. M.
Worlock, A. C. Gossard, and W. Wiegmann, Phys. Rev. Lett. 53,
1841 (1984).
19
X. Y. Peng, Q. Zhang, B. Shen, J. R. Shi, C. M. Yin, X. W. He, F. J. Xu,
X. Q. Wang, N. Tang, C. Y. Jiang, Y. H. Chen, and K. Chang, Phys. Rev.
B 84, 075341 (2011).
20
A. Tackeuchi, Y. Nishikawa, and O. Wada, Appl. Phys. Lett. 68, 797
(1996).
21
A. Tackeuchi, O. Wada, and Y. Nishikawa, Appl. Phys. Lett. 70, 1131
(1997).
22
M. I. Dyakonov and V. Yu. Kachorovski, Sov. Phys. Semicond. 20, 110
(1986).
23
C. V. Shank, R. L. Fork, R. Yen, J. Shah, B. I. Greene, A. C. Gossard, and
C. Weisbuch, Solid State Commun. 47, 981 (1983).
24
Z. Y. Xu, Y. Z. Li, J. Y. Xu, J. Z. Xu, B. Z. Zheng, W. H. Zhuang, and W.
K. Ge, Acta Phys. Sin. 36, 1330 (1987).
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159.226.228.14 On: Tue, 17 Mar 2015 01:23:55