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Title

Spin‑splitting analysis of a two‑dimensional
electron gas in almost strain‑freeIn̲<0.89>Ga̲<0.11>Sb/In̲<0.88>Al̲<0.12>Sb bymagnetoresistance measurements

Author(s)Akabori, M.; Guzenko, V. A.; Sato, T.; Schapers,Th.; Suzuki, T.; Yamada, S.

Citation

Physical Review B, 77(20): 205320

Issue Date

2008‑05‑15

Type

Journal Article

Text version

publisher

URL

http://hdl.handle.net/10119/4882

RightsM. Akabori, V. A. Guzenko, T. Sato, Th. Schapers,
T. Suzuki and S. Yamada, Physical Review B,
77(20), 2008, 205320‑. Copyright 2008 by theAmerican Physical Society.
http://dx.doi.org/10.1103/PhysRevB.77.205320

Description

Japan Advanced Institute of Science and Technology

PHYSICAL REVIEW B 77, 205320 共2008兲

Spin-splitting analysis of a two-dimensional electron gas in almost strain-free
In0.89Ga0.11SbÕ In0.88Al0.12Sb by magnetoresistance measurements
M. Akabori,1,2,* V. A. Guzenko,2 T. Sato,1,† Th. Schäpers,2 T. Suzuki,1 and S. Yamada1
1Center for Nano Materials and Technology (CNMT), Japan Advanced Institute of Science and Technology (JAIST), 1-1 Asahidai, Nomi,
Ishikawa 923-1292, Japan
2Institute of Bio- and Nanosystems (IBN-1) and Centre of Nanoelectronic Systems for Information Technology (CNI),
Research Centre Jülich, 52425 Jülich, Germany
共Received 24 October 2007; revised manuscript received 25 February 2008; published 20 May 2008兲
We investigated the spin-splitting in an almost strain-free In0.89Ga0.11Sb/In0.88Al0.12Sb two-dimensional electron gas 共2DEG兲 by magnetoresistance measurements at 1.5 K. A large effective gyromagnetic factor
共g factor兲 兩gⴱ兩 = 33– 34 was obtained by means of the coincidence method, which assumes an effective massmⴱ = 0.021m0 at the Fermi energy. In spite of the large g factor and the high mobility 共␮ = 9.8⫻ 104 cm2 / V s兲, a vanishing spin-splitting was also found around B ⬃ 0.8 T by analyzing the second derivative of the magnetoresistance. This effect originates from the interplay between the Rashba and Dresselhaus
spin-orbit interactions, and we theoretically confirmed the fact that the Dresselhaus spin-splitting energy⌬E0D = 3.5 meV was more than twice as large as the Rashba spin-splitting energy ⌬E0R = 1.5 meV. Moreover,
we demonstrated that the theoretical curves of the normalized spin splitting, including the g factor and thespin-orbit interactions, were well fitted to the experimental points with the Dresselhaus spin-orbit interaction.
Therefore, we concluded that the Dresselhaus spin-orbit interaction is dominant in our 2DEG in spite of its
narrow band gap.
DOI: 10.1103/PhysRevB.77.205320

PACS number共s兲: 71.70.Ej, 73.61.Ey, 73.63.Hs, 73.43.Qt

I. INTRODUCTION

Recently, investigations of spin-related phenomena insemiconductors have been paid much attention because they
are essential to developing semiconductor spintronic devices,e.g., spin field effect transistors 共spin-FETs兲.1 The channel ofspin-FETs requires having a large spin-orbit interaction inorder to control the spin-precession motion of channel electrons at high temperatures. Narrow gap semiconductor twodimensional electron gases 共2DEGs兲 are promising materials
for such spintronic device applications because they essentially have a large gyromagnetic factor 共g factor兲, as well asa strong spin-orbit interaction. These quantities have been
mainly characterized by means of magnetoresistancemeasurements.2–6 The Zeeman spin-splitting energy, as wellas the effective g factor, can be estimated from the peak
splitting of the magnetoresistance. The strength of the spinorbit interaction has been estimated from the beating patternin the magnetoresistance and has been quantified by the spinorbit coupling parameter and/or the zero-field spin-splittingenergy. In particular, III-V narrow gap semiconductor
2DEGs with InAs or an InAs alloy channel were widely
investigated and have revealed the dominance of the Rashba
spin-orbit interaction,2–6 which originates from structure inversion asymmetry7 and can be controlled by external electric fields, i.e., gate electrodes. Furthermore, the other contribution, i.e., Dresselhaus spin-orbit interaction,8 which
originates from bulk inversion asymmetry has also been
discussed9,10 because it plays an important role in spin-FETs
as well.11
In this paper, we discuss an InGaSb/InAlSb 2DEG grown
on a semi-insulating GaAs 共001兲 substrate. The InGaSb conductive channel has a narrower band gap and a smaller effective electron mass than InAs-based 2DEGs. Therefore, it
1098-0121/2008/77共20兲/205320共6兲

is expected to show strong spin-related phenomena such as alarge Rashba spin-orbit interaction. In similar InSb/InAlSb
2DEGs, high mobility12 and high frequency operation13 werealready demonstrated. Moreover, evidence of the Rashba
spin-orbit interaction,14 as well as its theoretical support,15
was reported. However, these heterostructures had a strained
InSb channel with respect to the InAlSb barrier layers; thus,
it cannot be excluded that the strain introduces a spin-orbit
interaction similar to the Rashba one.4,16,17 A main feature ofour 2DEG is an almost strain-free InGaSb channel to the
InAlSb barrier layers; thus, it is more suitable to analyze
spin-related physical properties in the strain-free channels.
II. EXPERIMENT

Figure 1 shows a schematic layer structure of our InGaSb/
InAlSb 2DEG. We grew the 2DEG on a semi-insulating
GaAs 共001兲 substrate by using conventional molecular beam
epitaxy 共MBE兲 with a Sb cracker cell. The indium contents
for the InGaSb and the InAlSb were fixed to 0.89 and 0.88,
respectively, being lattice matched to each other. First, a
6-␮m-thick In0.88Al0.12Sb buffer layer was directly grown on
a GaAs surface. The strain due to the lattice mismatch between InAlSb and GaAs was almost relaxed during thebuffer layer growth; thus, the InGaSb/InAlSb layer systembecame metamorphic. After the buffer layer growth, a 30nm-thick In0.89Ga0.11Sb channel layer and a 50-nm-thick
In0.88Al0.12Sb spacer layer were continuously grown. Next, Sidelta doping was carried out, and then a 100-nm-thick
In0.88Al0.12Sb barrier layer growth was followed by a 10-nmthick InSb cap layer growth. In metamorphic systems, thethreading dislocations occur due to the strain relaxation.
Such threading dislocations can be simply reduced by growing a thick buffer layer because of the pair-annihilation

205320-1©2008 The American Physical Society

PHYSICAL REVIEW B 77, 205320 共2008兲

AKABORI et al.

     δ !"             

T = 1.5K


 

 µ





 

 



cosθ
1.00

1500

0.87
0.71
0.57

1000

 

 

2000

Magneto-resistance ρxx(Ω)

 

0.44
0.35

500
0

offset 250 Ω0

0.20

0.2 0.4 0.6 0.8 1 1.2 1.4
Inverse magnetic field 1/Bp (T-1)

FIG. 2. Magnetoresistance curves as a function of the inverse
perpendicular magnetic field 1 / B P for various tilted angles. The
curves are offset by 250 ⍀. The dashed curves are a guide to theeyes to indicate the Zeeman spin-splitting enhancement.



FIG. 1. Schematic layer structure of our InGaSb/InAlSb
2DEG.

mechanism.18,19 The threading dislocation density near thesurface of our 2DEG was estimated to be about 3byplane-viewtransmission
electron⫻ 108 cm−2
microscopy.20 Moreover, the threading dislocations in the
In0.89Ga0.11Sb channel seemed to act as donors; therefore,
they also provide channel electrons, whose concentration
was estimated to be 1 ⫻ 1016 cm−3.20 Additionally, the dislocations seemed to limit the mobility of the channel electrons
due to the ionized scattering.20
In order to investigate the transport properties of our
2DEG, we carried out magnetoresistance measurements on
Hall-bar structures. The Hall bars were defined by using conventional photolithography techniques. The conductive channel defined by using wet chemical etching was aligned alongthe 关010兴 direction. The Ohmic contacts were formed by using AuGeNi evaporation and annealing in an Ar/H2 atmosphere at 250 ° C. The channel width and the probe distancewere 50 and 200 ␮m, respectively. The temperature for themagnetoresistance measurements was 1.5 K in a liquid He
cryostat with a superconducting magnet. In order to rotate
the magnetic field with respect to the plane of the 2DEG, thesample holder was equipped with a tilting mechanism. We
used an ac lock-in setup with a typical current of 100 nA
for the magnetoresistance measurements. The sheet electron
concentration and mobility from the Hall measurement
were estimated to be NS = 2.9⫻ 1011 cm−2 and ␮ = 9.8⫻ 104 cm2 / V s, respectively.

共SdH兲 oscillations were clearly observed at all angles. With
increasing tilt angle ␪, each peak splitting of SdH oscillations
becomes larger due to the increase in the lateral component
in the magnetic field, which corresponds to an increase in the
Zeeman spin-splitting. The ratio between the Landau levelseparation and the Zeeman spin-splitting is an essential parameter in the coincidence method, and it is given byr=兩␯兩 = r cos ␪ .

共2兲

By means of the coincidence method, it is possible to experimentally know 兩␯兩. A double frequency of SdH oscillations
corresponds to an equidistant separation between the spinresolved Landau levels, i.e., r = 1 / 2, from Eq. 共1兲. The
double frequency was clearly observed at cos ␪ = 0.71
共␪ ⬇ 45°兲; thus, we obtained 兩␯兩 = 0.36. A further increase in
the tilt angle ␪ leads to a stronger Zeeman spin-splitting anda phase inverse of the SdH oscillation without the peak splitting corresponds to the coincidence of the spin-up and spindown levels originating from the neighboring Landau levels,
i.e., r = 1, from Eq. 共1兲. The phase inverse was observed atcos ␪ = 0.35 共␪ ⬇ 70°兲, which directly resulted in 兩␯兩 = 0.35.
Theoretically, the effective g factor is given by23
ⴱ
=2−
gbulk

In order to estimate the effective g factor, which determines the Zeeman spin splitting, we applied the coincidence
method in the magnetoresistance measurements.21 Figure 2
shows the magnetoresistance curves for various tilt angles asa function of the inverse magnetic field 1 / B P = 1 / 共B cos ␪兲,i.e., the perpendicular component.22 Shubnikov–de Haas

共1兲

where 兩gⴱ兩 is the absolute value of the effective g factor,
␻C = eB p / mⴱ is the cyclotron frequency, and ␮B = បe / 2m0 is
the Bohr magneton. If we define the parameter ␯= gⴱmⴱ / 2m0, which is proportional to the product of gⴱ andm*, we obtain the following relation:

III. RESULTS AND DISCUSSION
A. Effective g factor兩gⴱ兩␮BB,ប␻C

2
E P⌬SO,
3 EG共EG + ⌬SO兲

共3兲

where EG is the band gap energy, ⌬SO is the spin-orbit
splitting energy, and E P is the equivalent energy of theinterband momentum matrix element. With EG = 0.26 eV,⌬SO = 0.80 eV, and E P = 24 eV of In0.89Ga0.11Sb,24 the effective g factor is estimated to be −44. This is the value at theⴱconduction band bottom, i.e., the bulk one. With mbulk= 0.016m0, which is the effective mass at the conduction

205320-2

PHYSICAL REVIEW B 77, 205320 共2008兲

SPIN-SPLITTING ANALYSIS OF A TWO-DIMENSIONAL…

-d2Rxx/dB2 (arb. unit)

T = 1.5 K

0.5

1

1.5

2

2.5

3

Inverse magnetic field 1/B (T-1)

FIG. 3. Second derivative of a magnetoresistance curve as afunction of the inverse magnetic field 1 / B. The arrow indicates thenarrowest peak corresponding to zero spin splitting.

band bottom, i.e., the bulk value of In0.89Ga0.11Sb,24 we obtain 兩␯兩 = 0.35, which agrees well with the experimental results.
An absolute value of the effective g factor can be determined from the measured 兩␯兩 value with an effective mass ofthe electrons at the Fermi energy. By taking nonparabolicity
into account, the energy dependence of the effective mass ina narrow gap semiconductor can be calculated from25冉ⴱmⴱ = mbulk
1+

冊

2E
.
EG

共4兲

Since the 2DEG density of states is also affected by mⴱ, theFermi energy of the 2DEG has to be described as follows:
EF =

冑

2
EG
␲ប2
EG
+ ⴱ N SE G −.
4 mbulk
2

共5兲

ⴱ
mbulk
= 0.016m0,
and
NS = 2.9
With
EG = 0.26 eV,
11−2⫻ 10 cm , we obtain EF = 38 meV. Applying this value
into Eq. 共4兲, we obtained mⴱ = 0.021m0 at EF, which is close
to the experimental value of mⴱ extracted from the cyclotron
resonance in our 2DEG.26 Taking 兩␯兩 ⬇ 0.35– 0.36 into account, we have determined the absolute value of the effective
g factor 兩gⴱ兩 ⬇ 33– 34.

B. Zero-field spin splitting

In order to investigate zero-field spin-splitting, we analyzed the magnetoresistance curves at low magnetic fields.
Figure 3 shows the second derivative of a magnetoresistancecurve. The tilt angle ␪ was 0°, i.e., with the magnetic field
B perpendicular to the 2DEG plane and with no lateralcomponent. Clear SdH oscillations with peak splitting wereobserved at high magnetic fields 1 / B ⬍ 1 T−1 共B ⬎ 1 T兲;
however, one can see that such splitting abruptly vanishes
around 1 / B ⬃ 1.25 T−1 共B ⬃ 0.8 T兲. At lower magnetic
fields 1 / B ⬎ 1.5 T−1 共B ⬍ 0.67 T兲, the peaks become broadwith shoulders and then a beatlike pattern can also be
seen. The peak splitting of SdH oscillations generally corresponds to spin-splitting, and the broadening and the beatlike pattern also imply that the spin-splitting appears again

FIG. 4. Schematics of Landau levels 共a兲 with the Rashba spinorbit interaction and 共b兲 with the Dresselhaus spin-orbit interaction.
The effective g factor is negative.

at lower magnetic fields. The vanishing of peak splittingmeans that the spin-splitting energy is close to zero; thus,
the spin-splitting effectively vanishes there22,27 despite thefact that the Landau level broadening of our 2DEG extracted from the cyclotron resonance26 was sufficiently narrow 共⌫ ⬃ 0.6 meV兲 to show spin splitting at this large gfactor. However, the Landau level broadening could not beproperly determined from the SdH oscillations because of
the background conduction, as well as the spin-splitting. Thisis completely different from other reports concluding the
Rashba spin-orbit interaction in narrow gap semiconductor
systems,3–7,14,15 wherein the spin-splitting energy is almost
constant around the Rashba spin-splitting energy until the
Zeeman spin-splitting is dominant. A vanishing behavior ofspin-splitting was predicted for the GaAs/AlGaAs systems.28
It originates from the Dresselhaus spin-orbit interaction,
which is usually dominant in wide band gap semiconductors. Figures 4共a兲 and 4共b兲 show schematics of the spinresolved Landau levels from n − 1 to n + 1 including the
Rashba or Dresselhaus spin-orbit interaction.4 Here, we neglect the k-cubic term of the Dresselhaus spin-orbit interaction. The spin-resolved Landau levels for the Landau index
n = 0 , 1 , 2 , ... are described as follows:2–5

205320-3

⫿ 21

再

共

冑

n + 21 ⫾ 21

兲共1 − ␯兲2 +2
共n + 21 ⫾ 21 兲⌬E0R

E Fប ␻ C

冎

0.3

,

共6兲

which represents the spin-resolved Landau levels with only
the Rashba term, and再En⫾ = ប␻C 共

n + 21 ⫿ 21

兲

⫾ 21

冑

4

0.4

共1 + ␯兲2 +2
共n + 21 ⫿ 21 兲⌬E0D

E Fប ␻ C冎3

m* = 0.018 m0

0.2

2

0.1

1

0

0

-0.1

Ez = 37 meV -1<E> = 1.4×106 V/m

,

-0.2
150

共7兲

which represents the spin-resolved Landau levels with only
the Dresselhaus term, where ⌬E0R and ⌬E0D are the Rashba
and Dresselhaus spin-splitting energies, respectively. The
Rashba spin-orbit interaction shifts spin-down sublevels En−
upward and spin-up sublevels En+ downward, whereas theDresselhaus spin-orbit interaction has an opposite effect.
When the g factor has a negative value at a large magnetic
field, the spin-splitting is enhanced by the Rashba spin-orbit
interaction and is suppressed by the Dresselhaus one, as
shown in the right sides of Figs. 4共a兲 and 4共b兲. As the magnetic field becomes smaller, the influence of the Rashba or
Dresselhaus spin-orbit interaction becomes larger comparedto that of the Landau separation, as well as the Zeeman spinsplitting, which are both proportional to the magnetic field.
In case of the Rashba spin-orbit interaction, the enhancementof spin splitting leads to equidistance between the spinresolved Landau levels corresponding to a node of the beating of the SdH oscillations. Upon a further decrease in themagnetic field, the enhancement leads to an overlap ofneighboring levels with different Landau indices corresponding to an antinode of beating and then, almost periodically,
the beating is repeated. In the case of the Dresselhaus spinorbit interaction, the suppression results in a vanishing spin
splitting at a finite magnetic field, as shown by an arrow in
Fig. 3, which also corresponds to an antinode of beating.
Upon a further decrease in the magnetic field, the spin splitting reappears; however, it has the opposite sign to the Zeeman splitting with the negative g factor, and nodes and antinodes of the SdH oscillation beating appear similar to the
Rashba case with a decreasing magnetic field. It indicatesthat an observation of the SdH beating is not unambiguous
evidence of the Rashba spin-orbit interaction.
In order to confirm the dominance of the Dresselhaus
spin-orbit interaction, we theoretically estimated the Rashba
and the Dresselhaus spin-splitting energies from the calculated conduction band profile. Figure 5 shows the conduction
band profile, as well as the distribution of electrons near thechannel. The calculation was performed by using a onedimensional Poisson–Schrödinger solver assuming a surface
barrier of 115 meV and a flat band condition at the substrateside. The activated donors are located in the delta doping andthe channel regions with the densities of NDD = 1.5⫻ 1012 cm−2 and NCD = 1 ⫻ 1016 cm−3, respectively. For thiscalculation, we did not use the effective mass at the Fermi
energy but rather the average effective mass mⴱ = 0.018m0.
This value was chosen to satisfy the relation

NS = 2.9×1011 cm-2

160

170 180 190
Depth (nm)-2200Electron concentration (1017 cm-3)

En⫾ = ប␻C

PHYSICAL REVIEW B 77, 205320 共2008兲

Energy (eV)AKABORI et al.

FIG. 5. Calculated conduction band profile 共solid curve兲, as wellas the distribution of electron concentration 共dashed curve兲 near thechannel.

EF =

␲ប2
NS ,
mⴱ

共8兲

with NS = 2.9⫻ 1011 cm−2 and EF = 38 meV. Furthermore,
we obtained the quantum confinement energy Ez = 37 meVfor the ground state level from the conduction band bottom
and the average electric field in the channel 具E典 = 1.4⫻ 106 V/m. Since our channel is rather broad 共30 nm兲, we
neglected the contributions of the interface and barrier layers
to the average electric field 具E典. The Rashba and the Dresselhaus spin-splitting energies can be estimated with these parameters and the weight factors a46 and a42.4 The Rashba andthe Dresselhaus spin-orbit coupling parameters are given bya = a46具E典,

共9兲␤ = a42具kz2典,

共10兲

where kz is z component of wave vector estimated from Ez.4
The corresponding zero-field spin-splitting energies are
given by
⌬E0R = 2akF ,共11兲
⌬E0D = 2␤kF ,共12兲

where kF is the Fermi wave vector estimated from EF.4 kz
and kF have almost the same value at present and are estimated to be 1.3⫻ 108 m−1. We note that the k-cubic term of
the Dresselhaus spin-orbit interaction is neglected at present.
With a46 = 400 eÅ2 and a42 = 770 eV Å3 of InSb,28 ␣ and ␤
are calculated to be 5.6⫻ 10−12 eVm and 1.3⫻ 10−11 eVm,
while ⌬E0R and ⌬E0D are estimated to be 1.5 and 3.5 meV,
respectively. Thus, the Dresselhaus spin-splitting energy ismore than twice as large as the Rashba spin-splitting energy.
As we will show below, the dominance of the Dresselhaus
spin-orbit interaction is qualitatively consistent with the experimental result despite the fact that our 2DEG has a narrow
band gap channel. The large Dresselhaus contribution in our
InSb-based heterostructure mainly results from the large
weight factor a42 compared to the other material systems.
Additionally, the sheet electron concentration of our 2DEG
was relatively low; thus, the average electric field was notefficiently large to enhance the Rashba spin-orbit interaction.

205320-4

PHYSICAL REVIEW B 77, 205320 共2008兲

SPIN-SPLITTING ANALYSIS OF A TWO-DIMENSIONAL…

FIG. 6. Magnetic field dependence of the normalized spin splitting with the experimental and the calculated results assuming 共a兲
the Rashba term and 共b兲 the Dresselhaus term. The closed and open
circles indicate the experimental and the calculated points, respectively. The error bars of the experimental points correspond to theLandau level broadening of 0.6 meV.
C. Magnetic field dependence of spin-splitting

In order to investigate the spin-splitting behavior in moredetail, we compared the experimental result to the theoretical
calculations of the magnetic field dependence of normalized
spin splitting. We solved Eqs. 共6兲 and 共7兲 for the harmonicenergy ប␻C with the condition of En⫾ = EF, then we definednormalized spin-splitting ␦ / ប␻C as follows:

冉 冊

1
␦
En⫾
,
=
− n+
2
ប␻C ប␻C

crossing of curves can be confirmed. The crossing point
shifts to a higher magnetic field when ⌬E0D becomes larger.
The crossing corresponds to a vanishing spin-splitting because the Zeeman and Dresselhaus effects cancel each other关cf. Fig. 4共b兲兴; thus, spin-up and spin-down states are locatedat the same level. The experimental points around the crossing seem to fit well to ⌬E0D ⬃ 4 meV, which is close to⌬E0D = 3.5 meV estimated from the calculated conduction
band profile. Additionally, one can see that the spin-up states
at a high magnetic field connect to the spin-down states at alow magnetic field and vice versa. It means that the spinsplitting energy at a high magnetic field has the opposite signof the zero-field spin-splitting energy, as mentioned before.
That is completely different from the analysis for the InSb/
InAlSb systems of Pfeffer and Zawadzki,15 which was exclusively based on the Rashba spin-orbit interaction but similar
to the prediction for the GaAs/AlGaAs systems of Lommer
et al.,28 which was based on the Dresselhaus spin-orbit interaction. Due to the fact that InSb-based materials have an
essentially large Dresselhaus spin-orbit interaction and our
2DEG is almost strain-free, i.e., strain-induced effects are
negligible, we were able to successfully observe a vanishingspin-splitting and inversion of a sign of the Zeemanlike
spin-splitting.
A close inspection of Fig. 6共b兲 reveals a difference between the experimental points and the calculated curves at ahigher magnetic field. This might originate from the exchange interaction among spin-up and spin-down electrons,29
i.e., due to the difference between spin-up and spin-down
electron densities. Since the difference is almost one-half thevalue of the Landau degeneracy eB / 2h and is proportional toB, the exchange interaction gives a constant shift of the normalized spin-splitting at high magnetic fields.
In addition, we have also investigated weak antilocalization in our 2DEG.30 Weak antilocalization measurements arealso an important method to analyze spin-orbit interactions.31
In our weak antilocalization results, we obtained a zero-fieldspin-splitting of about 1 meV by fitting the experimental data
to a theoretical model of Golub.32 This value is not consistent
with the results obtained by analyzing the SdH oscillations.
In order to consistently understand the whole behavior, it isnecessary to investigate the magnetoresistance in a wide
range of electron concentrations by using a gate electrode,especially from the vanishing field to the zero field, as wellas to improve the applicable theoretical models.

共13兲
IV. CONCLUSION

where ␦ implies the additional energy induced by the
spin-splitting relative to the spin-degenerated Landau levelប␻C共n + 1 / 2兲. In Figs. 6共a兲 and 6共b兲, the small open circles
with lines as guide to the eyes represent the calculated datafrom Eqs. 共6兲 and 共7兲. The experimental points taken from
Fig. 3 are shown as the large closed circles, assuming EF= 38 meV, mⴱ = 0.018m0, and ␯ = −0.35. In Fig. 6共a兲, it can beseen that by assuming the Rashba spin-orbit interaction, thespin-splitting monotonously increases with increasing B−1,
which is not consistent with the experimental situation. In
contrast to Fig. 6共b兲, i.e., with the Dresselhaus term, theIn conclusion, we investigated the magnetoresistanceproperties of an almost strain-free In0.89Ga0.11Sb/
In0.88Al0.12Sb 2DEG grown on GaAs 共001兲 by MBE. Bymeans of the coincidence method, we extracted a large effective g factor 兩gⴱ兩 ⬇ 33– 34 and demonstrated consistency
with the theoretically expected value. By analyzing the second derivative of the magnetoresistance, we found that the
spin-splitting vanishes around B ⬃ 0.8 T, in spite of the large
g factor and the high mobility. We argued that the vanishingspin-splitting originates from the Dresselhaus spin-orbit interaction. In fact, we could theoretically confirm that the205320-5

AKABORI et al.

PHYSICAL REVIEW B 77, 205320 共2008兲

Dresselhaus spin-splitting energy ⌬E0D = 3.5 meV is larger
than the Rashba spin-splitting energy ⌬E0R = 1.5 meV by
calculation based on the conduction band profile of ourheterostructure. Moreover, we compared magnetic field dependence of the normalized spin-splitting between the experimental and the theoretical data, and we found good
agreement between them at ⌬E0D ⬃ 4 meV. Therefore, we
concluded that the Dresselhaus spin-orbit interaction isdominant in our 2DEG in spite of the narrow band gap channel.

ACKNOWLEDGMENTS

The authors thank T. Naito, T. Kakegawa, T. Sunouchi,
and T. Harita for their help in the sample fabrication and in
the measurements. This work was partially supported by aGrant-in-Aid for Scientific Research in Priority Areas “Semiconductor Nanospintronics” 共Contract No. 14076213兲 of the
Ministry of Education, Culture, Sports, Science and Technology, Japan, and also by Mitsubishi and SCAT Foundationsfor Science and Technology.

*akabori@jaist.ac.jp; m.akabori@fz-juelich.de

16 S. A. Crooker and D. L. Smith, Phys. Rev. Lett.

†

Present address: Advantest Laboratories Ltd. 48-2 Matsubara, Kamiayasi, Aoba, Sendai, Miyagi 989-3124, Japan.
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41, 7685 共1990兲.
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