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Strain-induced enhancement of electric quadrupole splitting in resistively detected nuclear magnetic resonance spectrum in quantum Hall systems

Applied Physics Letters (Impact Factor: 3.3). 01/2010; 96(3):032102. DOI: 10.1063/1.3291618
Source: arXiv
ABSTRACT
We show electrical coherent manipulation of quadrupole-split nuclear spin states in a GaAs/AlGaAs heterostructure on the basis of the breakdown of quantum Hall effect. The electric quadrupole splitting in nuclear spin energy levels is intentionally enhanced by applying an external stress to the heterostructure. Nuclear magnetic resonance spectra with clearly separated triple peaks are obtained, and Rabi oscillations are observed between the nuclear spin energy levels. The decay of the spin-echo signal is compared between the cases before and after the enhancement of quadrupole splitting. Comment: 4 pages, 4 figures

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Available from: Minoru Kawamura
arXiv:0912.4313v1 [cond-mat.mes-hall] 22 Dec 2009
Strain-induced enhancement of electric quadrupole splitting in resistively detected
nuclear magnetic resonance spectrum in quantum Hall systems
M. Kawamura,
1, 2, 3,
T. Yamashita,
1
H. Takahashi,
1
S. Masubuchi,
1
Y. Hashimoto,
4
S. Katsumoto,
4, 5
and T. Machida
1, 5,
1
Institute of Industrial Science, University of Tokyo,
4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
2
Advanced Science Institute, RIKEN, 2-1 Wako, Saitama 351-0198, Japan
3
PRESTO, Japan Science and Technology Agency, 4-1-8 Kawaguchi, Saitama 333-0012, Japan
4
Institute for Solid State Physics, University of Tokyo,
5-1-5 Kashiwanoha, Kashiwa 277-8581, Japan
5
Institute for Nano Quantum Information Electronics,
University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
(Dated: December 22, 2009)
We show electrical coherent manipulation of quadrupole-split nuclear spin states in a
GaAs/AlGaAs heterostructure on the basis of the breakdown of quantum Hall effect. The elec-
tric quadrupole splitting in nuclear spin energy levels is intentionally enhanced by applying an
external stress to the heterostructure. Nuclear magnetic resonance spectra with clearly separated
triple peaks are obtained, and Rabi oscillations are observed between the nuclear spin energy levels.
The decay of the spin-echo signal is compared between the cases before and after the enhancement
of quadrup ole splitting.
PACS numbers: 74.43.-f
Nuclear spins in semiconductors have recently at-
tracted considerable attention because their extremely
long coherence time is suitable for the implemen-
tation of quantum bits/memorie s
1,2,3
. In order to
manipulate nuclear spin quantum states coherently,
all-electrical
4,5,6
/optical
7,8,9
nuclear magnetic resonance
(NMR) techniques have been developed on the basis o f
the hype rfine interaction between nuclear s pins and elec-
tron spins. However, a ll of these new NMR techniques
have been successfully applied in GaAs. Since all the
constituent atoms in GaAs have nuclear spins I = 3/2,
the nuclear spin states split into four-level I
z
eigen states
| ± 3/2i and | ± 1/2i in a magnetic field as shown on the
left-hand side of Fig. 1(a). Such a four-level sy stem ca n
be regarded as coupled quantum bits if transitions be-
tween any pairs of the levels are contr olled selectively
10
.
In the presence of a local electric field gradient, the
electric quadrupole interaction produces non-equidistant
nuclear spin e nergy levels
11
as s hown on the right-hand
side of Fig. 1(a). Although the electric quadrup ole split-
ting e nergy
Q
is zero in GaAs because of the cubic sym-
metry of the GaAs crystal, it is possible to increase the
amplitude of
Q
by applying an external stress to the
crystal
12,13,14
, because
Q
is proportio nal to the local
electric field gradient. Such an external stress can be ap-
plied using pressure cells or piezoelectric devices
12,13
or
by coating the surface of GaAs with different material
14
.
In this paper, we show intentional enhancement of elec-
tric quadrupole splitting and selective control of a four-
level nuclear spin system. Using the breakdown phe-
nomenon of quantum Hall effect, nuclear spins are po-
larized and NMR are detected. We apply an external
stress to a Hall-bar device by coating its surface with
a polyimide film. NMR spectra with clearly separated
FIG. 1: (a) Energy diagram of I = 3/2 nuclear spin system
for
Q
= 0 (left) and
Q
6= 0 (right). (b) Micrograph of the
Hall-bar device. A pulsed rf-magnetic field is irradiated using
the metal strip covering the 5-µm-wide conduction channel.
triple peaks are obtained in the polyimide-coated devices.
Splitting of NMR spectra enables us to s how the selec-
tive and coherent manipulation of a four-leve l nuclear
spin system using pulsed NMR techniques. Furthermore,
the decay of spin-echo signal is compare d between the
cases before and after the enhancement of quadrupo le-
splitting.
The exp eriments were performed using a
two-dimensional electron gas (2DEG) in a
GaAs/Al
0.3
Ga
0.7
As single heterostructure wafer grown
by molecular beam epitaxy on a (00 1) oriented GaAs
substrate. The 2DEG is located at 230 nm below the
surface. The mobility and density of the 2DEG at 4.2
K are 220 m
2
/Vs and 1.6 × 10
15
m
2
, respectively.
Figure 1(b) shows an optical micrograph of the Hall-bar
device used in the present study. A 10-µm-wide Ti/Au
Schottky gate electrode that was used for tuning electron
density also functioned as a local coil for ge nerating
radio-frequency (rf) magnetic fields B
rf
parallel to the
Page 1
2
FIG. 2: (a) - (c) NMR spectra obtained using the Hall-bar
device before it was coated with a polyimide film. B = 4.92 T
(ν = 1.08). Values of f
0
are 35.520 MHz (a), 49.808 MHz (b),
and 63.286 MHz (c). (d) - (f) N MR spectra obtained using
the Hall-bar device after it was coated with the polyimide
film. B = 5.82 T (ν = 1.00). Values of f
0
are 41.963 MHz
(d), 58.847 MHz (e), and 74.771 MHz (f). The solid curves
are the fitting curves.
2DEG. External s tatic magnetic field B was a pplied
perpendicular to the 2DEG, hence parallel to the [001]
direction of the GaAs crystal. All the measurements
were pe rformed at 50 mK using a
3
He-
4
He dilution
refrigerator. The sample chip (1 mm × 1 mm × 0.5 mm)
was glued backside to a ceramic chip carrier using silver
paste. After wiring to the Hall-bar device, the ceramic
package was held against the cold finger plate of the
dilution refrigerator to make a good thermal contac t.
NMR s ignals were obtained by dynamic nuclear polar-
ization (DNP) and resistive detection (RD) techniques
in a break down regime of integer quantum Hall effect
(QHE), as already demons trated in our earlier studies
15
.
As an initialization process, nuclear spins are dy nam-
ically polarized through the hyperfine interaction be-
tween nuclear spins and electron spins under a breakdown
regime of a q uantum Hall state w ith the Landau level fill-
ing factor ν = 1. By applying a bias c urrent larger than
the critical current of the QHE breakdown, electrons are
excited to the uppe r Landau subband, accompanied by
flips of electron spins. The flips of electron spins cause
flops of nuclear spins via the hyperfine interaction, re-
sulting in positive nuclear polarization
15
hI
z
i > 0. Then,
the nuclear spin sta tes are manipulated by applying B
rf
.
The manipulated nuclear spin state is read out by mea-
suring the longitudinal voltage V
xx
of the Hall-bar de-
vice. The read-out procedure is based on the fact that
the positively pola rized nuclear spins (hI
z
i >0) reduce
the Zeeman splitting energy of electrons, which increases
V
xx
.
First, we measured the NMR spectrum using an un-
coated Hall-bar device. In Figs. 2(a), (b), and (c), the
changes in the longitudinal voltage V
xx
induced by the
B
rf
irradiation a re plotted as a function of the B
rf
fre-
quency. Each curve corresponds to the NMR spectrum
for
75
As,
69
Ga, and
71
Ga. A single-peak spectrum is
observed fo r all the three nuclear species. These sing le -
peak sp e ctra indicate that the nuclear spin levels are dis-
tributed almost equidistantly as illustrated in the left-
hand panel in Fig. 1(a).
Next, the Hall-bar device was warmed up to room tem-
perature; at this temperature, a droplet of polyimide so-
lution was dropped onto the surface of the device. Then,
the po ly imide coating was ba ked in N
2
atmosphere at 180
C for 15 min. The polyimide-coated device was cooled
down again for the NMR mea surements.
16
Since the ther-
mal shrinkage rate of the polyimide film is considerably
higher than that of the GaAs film, the subsequent cool-
ing of the polyimide-coated device is expected to induce
a large strain in the device.
Figure 2(d) shows the NMR spectrum of
75
As after
it was coated with the poly imide film. The NMR spec-
trum is split into three peaks. These pe aks correspond to
transitions A, B, and C shown on the right-hand side o f
Fig. 1(a). The NMR spectra of
69
Ga and
71
Ga are als o
split as shown in Figs. 2(e) and (f), respectively. Ampli-
tudes of the splitting are f = 36 kHz, 18 kHz, and 11
kHz for
75
As,
69
Ga, and
71
Ga, respectively. The ratio of
f is in good agreement with the ratio of the quadrupole
moment Q: f(
69
Ga)/f(
71
Ga) = 1 .6 agrees with
Q(
69
Ga)/Q(
71
Ga) = 0.19 × 10
28
m
2
/0.12 × 10
28
m
2
=
1.6. This indicates that the splitting of the NMR spectra
is attributed to the electric quadrupole interaction. We
observed the splitting in the spectrum of
75
As in another
device; the single-peak spe c trum before the polyimide
coating is split to three peak s (∆f = 16 kHz) after the
polyimide coating. The NMR peak splitting of 7.5 kHz
for
75
As was also obse rved in yet another device after
coating its surface with PMMA electr on-bea m re sist
17
.
We consider that the polyimide film produces a strain
in the GaAs/AlGaAs heterostructure, resulting in the
generation of a large electric field gradient at nuclear spin
sites, and the induced electric field gradient enhances
Q
.
Comparing the observed splitting of 36 kHz in the NMR
sp e c trum of
75
As [Fig. 2(d)] with the earlier mea sure-
ments in GaAs quantum wells
12
, the strain in our device
is estimated as 1.7 × 10
4
. The estimated value of the
strain seems c onsistent with the results of electron trans-
port measurements of 2DEG under a strain-induced pe-
riodic potential modulation
18
. From the FWHM o f the
NMR spectrum of
75
As [Fig. 2(a)], the strain in the de-
vice before the polyimide film co ating is estimated to be
Page 2
3
FIG. 3: Changes in V
xx
induced by applying a pulse of B
rf
with various pulse durations τ
pulse
at B = 5.82 T (ν = 1.00).
The frequencies of B
rf
are 41.952 MHz (A), 41.987 MHz (B),
and 42.022 MHz (C) in (a), and 41.969 MHz (D) and 42.007
MHz (E) in (b). The curves are offset for clarity. The inset
in (a) shows schematic energy diagram for single- and two-
photon absorption/emission. The inset in (b) shows the NMR
spectrum of
75
As with the input rf-voltage V
rf
= 4.8 V.
not larger than 3.9 × 10
5
, even if the broadening of the
sp e c trum is attributed to
Q
. Therefore, contribution of
the other sources of strain, such as Ti/Au Schotky gate
or the silver paste on the backside of the sample chip, is
small compared to that of the polyimide film.
Figure 3(a) shows the changes in V
xx
induced by apply-
ing a pulse o f B
rf
with various pulse durations τ
pulse
at B
= 5.82 T (ν = 1). We note that the amplitude of B
rf
in
the pulsed NMR measurements (Fig. 3) is 12 times larg e r
than that used to obtain the c ontinuous-wave NMR spec-
tra (Fig. 2)
19
. The B
rf
frequencies for the curves A, B,
and C are 41.952 MHz, 4 1.987 MHz, and 42.022 MHz,
respectively, as indica ted in the inset in Fig. 3(b). The
oscillatory changes in V
xx
denoted A, B, and C cor-
respond the Rabi oscillations of
75
As for transitions A
(| + 3/2i | + 1/2i), B (| + 1/2i | 1/2i), and C
(| 1/2i | 3/2i), respectively. These results clearly
show that the intentional enhancement of
Q
enables the
selective and c oherent contr ol of the four-level nuclear
spin system. Additional two peaks (D and E) are s e en in
the spectrum at the middle frequencies between the peaks
A a nd B, and B and C as similar to the work by Yusa
et al
5
. These additional peaks correspond to the two-
photon absorption/emission pr ocesses (| +3/2i |1/2i
and | + 1/2i | 3/2i) induced by the irra diation of
B
rf
with a large amplitude. The oscillations D and E in
Fig. 3(b) corres pond to the two-photon Rabi oscillations
taken at the B
rf
frequencies of 41.969 MHz and 42.007
MHz, respectively. The observed freq uency of the two-
photon Rabi oscillation
m=2
= 3.8 kHz nearly agrees
with the calculated value
20
m=2
2
m=1
/2∆
Q
=
(12.5 kHz)
2
/36 kHz = 4.3 kHz.
FIG. 4: (a) Decay of spin-echo signal obtained in the Hall-bar
device before the polyimide coating. B = 4.92 T (ν = 1.08).
(b)-(c) Decays of spin-echo signals obtained in the Hall-bar
device after the polyimide coating. B = 5.82 T (ν = 1.00). In
the case of (c), the electrons were depleted during t he rf p ulse
irradiation. The inset of (a) shows a schematic of the pulse
sequence for the spin-echo measurements. The inset of (b)
shows a representative spin-echo signal obtained by changing
τ
2
with a fixed τ
1
= 100 µs.
We verify the effect of electric quadrupole splitting
on the nuclear spin coherence time by performing spin-
echo experiments. We applied a sequence of π/2-π-π/2
rf pulses
21
, as shown in the inset of Fig. 4(a). The in-
set of Fig. 4(b) shows a representative spin-echo signal
in the device after the polyimide film coating obtained
by changing the seco nd waiting time τ
2
with a fixed first
waiting time τ
1
= 100 µs with the B
rf
frequency of 42.022
MHz. The coherence time T
2
is estimated from the decay
of the spin-echo signal by changing the total waiting time
τ
1
+τ
2
under the condition τ
1
= τ
2
. Figure 4(a) shows the
decay o f the spin-echo signals for
75
As in the device before
the polyimide film coating. The B
rf
frequency was tuned
to 41.963 MHz, the peak frequency in Fig. 2(a), where
all the three NMR transitions occur simultaneously. The
value of T
2
is estimated to be no longer than 0.2 ms,
and the signal decays non-monotonically. In c ontr ast, af-
ter coating the Hall-bar device with the polyimide film,
the spin-echo signal decays exponentially as shown in
Fig. 4(b). The B
rf
frequency was tuned to 42.022 MHz,
the peak C in the inset of Fig. 3(b). The value of T
2
is
estimated as 0.42 ms, which is almost twice longer than
that obtained before the polyimide film coating. The de-
cay time of the Rabi oscillations is also increased after
the polyimide film coating (not shown). In addition, as
shown in Fig. 4(c), the value of T
2
is further increased to
1.1 ms by decoupling the nuclear system from the elec-
tron system during nuclear-spin manipulation
22,23
; elec-
trons are depleted by applying negative dc voltage to the
Page 3
4
Schottky gate electrode during the rf-pulse irradiation.
In summary, we have demonstrated strain-induced en-
hancement of the electric quadrupole splitting and elec-
trical coherent manipulation in I = 3/2 nuclear spin en-
ergy levels in GaAs/GaAs heterostructure. The DNP
and RD techniques used in the present study can be em-
ployed at temperatures higher than 1 K and even in a
2DEG with a re latively low electron mobility
6,15
, because
the techniques are based on the bre akdown phenomena
of QHE.
This work was supported by a Grant-in-Aid fro m
MEXT, the Sumitomo Foundation, and the Special Co-
ordination Funds for Promoting Science a nd Technology.
Electronic address: minoru@riken.jp
Electronic address: tmachida@iis.u-tokyo.ac.jp
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