Kondo effect in a semiconductor quantum dot coupled to ferromagnetic electrodes

Abstract

Using a laterally-fabricated quantum-dot (QD) spin-valve device, we experimentally study the Kondo effect in the electron transport through a semiconductor QD with an odd number of electrons (N). In a parallel magnetic configuration of the ferromagnetic electrodes, the Kondo resonance at N = 3 splits clearly without external magnetic fields. With applying magnetic fields (B), the splitting is gradually reduced, and then the Kondo effect is almost restored at B = 1.2 T. This means that, in the Kondo regime, an inverse effective magnetic field of B ~ 1.2 T can be applied to the QD in the parallel magnetic configuration of the ferromagnetic electrodes. Comment: 4 pages, 3 figures

Full text

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arXiv:0711.2124v2 [cond-mat.mes-hall] 16 Dec 2007
Kondo effect in a semiconductor quantum dot
coupled to ferromagnetic electrodes
K. Hamaya,∗†M. Kitabatake, K. Shibata, M. Jung, M. Kawamura, K. Hirakawa,†‡and T. Machida†‡§
Institute of Industrial Science, University of Tokyo,
4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
T. Taniyama¶
Materials and Structures Laboratory, Tokyo Institute of Technology,
4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan
S. Ishida and Y. Arakawa†
Research Center for Advanced Science and Technology and Institute of Industrial Science,
University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
(Dated: February 5, 2008)
Using a laterally-fabricated quantum-dot (QD) spin-valve device, we experimentally study the
Kondo effect in the electron transport through a semiconductor QD with an odd number of electrons
(N). In a parallel magnetic configuration of the ferromagnetic electrodes, the Kondo resonance at
N = 3 splits clearly without external magnetic fields. With applying magnetic fields (B), the
splitting is gradually reduced, and then the Kondo effect is almost restored at B = 1.2 T. This
means that, in the Kondo regime, an inverse effective magnetic field of B ∼ 1.2 T can be applied to
the QD in the parallel magnetic configuration of the ferromagnetic electrodes.
PACS numbers:
Using fabrication techniques of nano-gap electrodes
consisting of Ti/Au, Jung et al.
transport measurements of electrons through a single
self-assembled InAs quantum dot (QD),[1] and observed
shell-dependent charging energies due to an artificial
atomic nature.[2] Recently, Shibata et al. and Igarashi
et al.
got a device with strong coupling between the
InAs QD and Ti/Au electrodes and succeeded in the ob-
servation of the Kondo effect in a single self-assembled
InAs QD.[3, 4] The Kondo effect, which is due to the
screening of a localized spin in the QD from conduc-
tion electrons in the electrodes, is one of the many-body
phenomena.[5, 6, 7] Below the Kondo temperature, the
zero-bias conductance is enhanced through spin-flip pro-
cesses, i.e., Kondo resonance. In external magnetic fields,
the Kondo effect in QDs with an odd number of electrons
is suppressed due to the spin splitting of the unparied lo-
calized electron state, resulting in splitting of the Kondo
resonance.[5, 6, 7]
established lateral
On the other hand, using similar fabrication tech-
niques, we have fabricated lateral QD spin-valve (SV)
devices which consist of a single self-assembled InAs QD
with ferromagnetic electrodes. To date, clear spin trans-
port via the tunneling magnetoresistance (TMR) effect
was observed in Co/InAs QD/Co and Ni/InAs QD/Ni
∗hamaya@iis.u-tokyo.ac.jp
†Also at: Institute for Nano Quantum Information Electronics,
University of Tokyo.
‡Also at: Japan Science and Technology Agency, CREST.
§tmachida@iis.u-tokyo.ac.jp
¶Also at: Japan Science and Technology Agency, PRESTO.
QDSVs.[8, 9] Since we can achieve an electric-field con-
trol of the TMR,[8, 9] these QDSVs are expected to
be a novel spintronic application such as a gate-tunable
spin memory.[10, 11] Recently, the Kondo effect in the
presence of ferromagnetism was studied in Ni/C60/Ni
SVs,[12] and the splitting of the Kondo resonance (sup-
pression of the Kondo effect) was demonstrated even in
the absence of external magnetic fields. However, the
Kondo effect and its related phenomena for semiconduc-
tor QDSVs have never been reported.
In this Letter, we experimentally study the Kondo ef-
fect in the electron transport through a semiconductor
QD with an odd number of electrons (N) using a Ni/InAs
QD/Ni QDSV device. Not only suppression of the Kondo
effect but also its restoration by applying external mag-
netic fields (B) is demonstrated. In a parallel magnetic
configuration of the Ni electrodes, the zero-bias anomaly
at N = 3 splits clearly without an external magnetic
field. With applying magnetic fields, the splitting grad-
ually disappears, and then the Kondo effect is almost re-
stored at B = 1.2 T. This fact indicates that an inverse
effective magnetic field of B ∼ 1.2 T can be applied to
the QD in the parallel magnetic configuration of the fer-
romagnetic electrodes.
We grew self-assembled InAs QDs on a substrate
consisting of 170-nm-thick GaAs buffer layer/90-nm-
thick AlGaAs insulating layer/n+-GaAs(001). The n+-
GaAs(001) was used as a backgate electrode. The wire-
shaped Ni electrodes with a ∼ 30-nm gap were fabricated
by using a conventional electron-beam lithography and a
lift-off method. Before the evaporation of Ni thin films,
we etched InAs surface with buffered HF solution for 6 s.
The detailed fabrication procedures have been described

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VSD(mV)
VG(V)
2
3
-2 -1 0 1 2
1.2
1.0
0.8
VSD
Ni
Ni
InAs
200 nm
(a)
(b)
0.6
0.4
0.2
N = 0
1
4
FIG. 1: (Color online) (a) A scanning electron micrograph
of our Ni/InAs/Ni QDSV device. (b) A color scale plot of
differential conductance, dI/dVSD, as a function of VSD and
VG without an external magnetic field. Light regions show
the finite dI/dVSD regime and the number of electrons is in-
dicated.
in our previous works.[8, 9] An enlarged scanning elec-
tron micrograph of the QDSV used here is shown in Fig.
1(a). We can see a single InAs QD (120 ∼ 140 nm) in
contact with two Ni electrodes which have a thickness of
40 nm. The overlapped regions of the InAs QD reach
more than ∼ 30 nm. Before cooling down of the device,
we have checked the two-terminal contact resistance of
∼ 70 kΩ at room temperature. We emphasize that Ti
seed layer is not used, which is unlike the case of previ-
ous works.[3, 4] Transport measurements were performed
by a dc method at 30 mK. External magnetic fields (B)
were applied parallel to the long axis of the wire-shaped
Ni electrodes.
First of all, we applied a magnetic field of B = 1 T to
the wire-shaped Ni electrodes and made a parallel mag-
netic domain configuration. After the saturation of the
magnetization, when the magnetic field is reduced down
to B = 0 T, the magnetic configuration remains par-
allel because of the strong shape anisotropy of the Ni
electrodes.[8, 9] In this condition, we measure the differ-
ential conductance dI/dVSD as a function of VSD and
VG.Figure 1(b) displays a representative data; The
light regions exhibit higher conductance regimes and the
number of electrons (N) is indicated. We can see the
enhancement in the conductance in the vicinity of zero
-2-1012
VSD (mV)
dI /
SD (a.u.)
dV
0.3 T
0 T
0.6 T
0.9 T
1.2 T
1.5 T
1.8 T
2.1 T
2.4 T
N = 3
∆ε
VSD(mV)
VG(V)
N = 2
3
-2 -1 0 1 2
1.4
1.2
1.0
0.8
FIG. 2: (Color online) The dI/dVSD as a function of VSD
for various external magnetic fields at VG = 1.25 V (N = 3).
The inset shows the corresponding Coulomb diamonds near
N = 2 and 3.
bias (VSD∼ 0 V) at N =1 and 3 Coulomb valleys. The
enhanced conductance at N =1 and 3 implies the S =
1/2 Kondo effect, as previously reported by Shibata et
al. and Igarashi et al.[3, 4] Surprisingly, we observe an
evident splitting of the zero-bias anomaly at N = 3,[13]
i.e., suppression of the Kondo effect at VSD= 0 V, with-
out an external magnetic field (B = 0 T). The dI/dVSD
vs VSD measured at N = 3 is shown in the red curve
in Fig. 2.[14] The peak spacing (∆ǫ) of the splitting is
∼ 0.74 mV. The splitting feature shows an asymmetry
about the polarity of VSD. This feature may result from
the asymmetric tunnel coupling between ferromagnetic
electrodes and the QD,[15] which is not controllable for
these systems,[1, 2, 3, 4, 8, 9] or the difference in the spin
polarization at the Ni/InAs interfaces.[15]
With increasing external magnetic fields parallel to the
long axes of the wire-shaped electrodes, the splitting of
the Kondo resonance is gradually reduced, and the ob-
served double peak changes into a single peak at B = 1.2
T (blue curve in Fig. 2). This means that the Kondo ef-
fect is almost restored. From the ∆VSDof the Kondo res-
onance measured at B = 1.2 T, we can roughly estimate
the Kondo temperature TKof ∼ 5 K, which is consistent
with that of Au/Ti/InAs QD/Ti/Au systems.[3, 4] For

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240
200
160
120
I (pA)
-0.10-0.050.00 0.050.10
Magnetic field (T)
FIG. 3: (Color online) The magnetoconductance curve mea-
sured at VG = 1.25 V (N = 3).
further increase in applied magnetic fields, the Kondo
effect is suppressed again due to the lifting of the spin
degeneracy.
To examine the relationship between the zero-bias con-
ductance and the magnetic configuration of Ni electrodes,
we also investigate the magnetoconductance of the QDSV
at VG = 1.25 V (N = 3) in Fig.
blue curves correspond to the data for up-sweep and
down-sweep measurements, respectively. At ± ∼ 0.015
T we can see current changes due to the switching of the
magnetic configuration of the Ni electrodes from paral-
lel to anti-parallel:[9] we can see an enhancement in the
conductance for anti-parallel configurations, i.e., inverse
TMR effect. This means that the Kondo effect is sup-
pressed in a parallel magnetic configuration in the Ni
electrodes, while the Kondo effect is somewhat restored
in an anti-parallel magnetic configuration.[12, 15, 16, 17]
From these data, we regard the suppression of the N =
3 Kondo effect at B = 0 T as a consequence of the fer-
romagnetic electrodes with a parallel magnetic configu-
ration.
In Au(Co)/Au QD/Au(Co) metallic junctions, sup-
pression of the Kondo effect at B = 0 T has also been
observed.[18] The splitting of the Kondo resonance re-
sults from the competition between the Kondo effect and
the indirect RKKY interaction.[18] However, it is known
that the RKKY-like interaction between the spin of the
QD and the static spins of the Co impurities can not in-
duce evident hysteretic TMR curves,[18] as shown in Fig.
3. Accordingly, we can rule out the RKKY interaction
between the QD spin and the static spins of the Ni elec-
trodes. Next, we in turn need to consider an influence
of a local stray field from the ferromagnetic electrodes.
3.The red and
When the magnetic configuration of the ferromagnetic
electrodes is parallel, the local stray field can induce the
Zeeman splitting, where the direction of the local stray
field can be regarded as the same direction of external
magnetic fields. However, Fig. 2 clearly indicates that
an effective field inducing the suppression of the Kondo
effect works in the opposite direction of external mag-
netic fields. Thus, the splitting of the Kondo resonance
presented here can not be explained by the local stray
field.
From the above considerations, we now infer that the
suppression of the Kondo effect at B = 0 T is prob-
ably due to a local exchange field, which is similar to
Ni/C60/Ni SVs previously shown.[12] In theories,[15, 16,
17] for parallel magnetic configurations of ferromagnetic
electrodes in QDSV devices, the spin-dependent quan-
tum charge fluctuations occur, and then the QD’s lev-
els are renormalized. The renormalization for the spin-
down level is stronger than that for the spin-up level, so
that a level splitting between the two spin orientations
is generated.[15, 16, 17] It has been well discussed that
such effective field is compensated by applying magnetic
fields,[15, 16, 17] being consistent with the present data
in Fig. 2. For previous Ni/C60/Ni SVs,[12] since the
exchange field probably acted as an effective field paral-
lel to the magnetization orientation of the Ni electrodes,
restoration of the Kondo effect by applying external mag-
netic fields could not be detected. In the present case, the
exchange field works as an effective field anti-parallel to
the the magnetization orientation of the Ni electrodes,
so that the restoration of the Kondo effect can be ob-
served clearly by applying external magnetic fields, as
illustrated in Fig. 2.
In summary, we have studied the Kondo effect using
a laterally-fabricated semiconductor QDSV device. In a
parallel magnetic configuration of the ferromagnetic elec-
trodes, the Kondo resonance at N = 3 splits clearly in
the absence of external magnetic fields. With applying
magnetic fields, the splitting is gradually reduced, and
then the Kondo effect is almost restored at B = 1.2 T.
This means that, in the Kondo regime, an inverse effec-
tive magnetic field of B ∼ 1.2 T can be applied to the
QD in the parallel magnetic configuration of the ferro-
magnetic electrodes.
K. H. acknowledges Y. Utsumi for his fruitful discus-
sions. This work is supported by the Special Coordina-
tion Funds for Promoting Science and Technology, and
the Grant-in-Aid from MEXT, and Collaborative Re-
search Project of Materials and Structures Laboratory,
Tokyo Institute of Technology, and the Sumitomo Foun-
dation.
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