PHYSICAL REVIEW B 75, 155328 共2007兲

Quantum size effect and tunneling magnetoresistance in ferromagnetic-semiconductor
quantum heterostructures
Shinobu Ohya,1,2,* Pham Nam Hai,1 Yosuke Mizuno,1 and Masaaki Tanaka1,3,†
1Department of Electronic Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
2

PRESTO Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

3SORST Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

共Received 20 December 2006; revised manuscript received 19 February 2007; published 24 April 2007兲
We report on the resonant tunneling effect and the increase of tunneling magnetoresistance induced by it inferromagnetic-semiconductor GaMnAs quantum-well 共QW兲 heterostructures. The resonant tunneling effectwas observed when the GaMnAs QW thickness was from 3.8 to 20 nm, which indicates that highly coherent
tunneling occurs in these heterostructures. The observed quantum levels of the GaMnAs QW were successfully
explained by the valence-band k · p model and the p-d exchange interaction. It was also found that the Fermi
level of the electrode injecting carriers is important to observe resonant tunneling in this system.
DOI: 10.1103/PhysRevB.75.155328

PACS number共s兲: 72.25.Dc, 73.40.Gk, 75.50.Pp, 85.75.Mm

I. INTRODUCTION

III-V-based ferromagnetic-semiconductor heterostructurescontaining GaMnAs are one of the best model systems tostudy spin-dependent transport phenomena, which can beused for future spintronic devices. Large tunneling magnetoresistance 共TMR兲 of 75% 共8.0 K兲1 and 290% 共0.39 K兲2
were observed in the GaMnAs-based single-barrier heterostructures. Also, the GaMnAs-based quantum heterostructures are expected to realize new functions by combining aspin degree of freedom and the quantum-size effect 共resonant
tunneling effect兲.3–11 For example, a very large enhancementof TMR up to ⬃800%4 and to more than ⬃106%3 is expected in GaMnAs-based resonant tunneling diode 共RTD兲
structures. In magneto-optical measurements of the GaMnAs
quantum well 共QW兲, blueshifts of the magneto-optical spectra have been observed, suggesting the existence of thequantum-size effect in GaMnAs.12,13 However, there are noreports on the clear observation of the resonant tunneling
effect in ferromagnetic-semiconductor quantum heterostructures.3,14,15 In the metal-based magnetic tunnel junctions
共MTJs兲, the resonant tunneling effect and the TMR oscillation induced by it have been observed, though these phenomena appeared only when the QW thickness is extremely thin,less than 3 nm.16,17 Comparing with these metal systems, the
GaMnAs-based quantum heterostructures are fully epitaxial
single crystals and have atomically flat interfaces, where
highly coherent tunneling is expected. Therefore, this is amaterial system ideal for physical understanding of the spindependent resonant tunneling effect. Furthermore, it has
good compatibility with III-V-based semiconductor devices
and thus can lead to future three-terminal spin devices suchas resonant tunneling spin transistors. Hence, it is a very
important issue to observe resonant tunneling effect in III-Vbased ferromagnetic heterostructures. In this paper, we reporta successful detection of resonant tunneling effect and TMR
increase induced by it in semiconductor heterostructures.
II. SAMPLE PREPARATION

Figure 1共a兲 shows the schematic device structure containing a GaMnAs QW confined by AlAs and AlGaAs barriers
1098-0121/2007/75共15兲/155328共6兲

examined here. This heterostructure was grown by molecularbeam epitaxy 共MBE兲 with a layer structure from the surface
to the substrate; Ga0.95Mn0.05As共20 nm兲 / GaAs共1 nm兲 /Al0.5Ga0.5As共4 nm兲 / GaAs共1 nm兲 / Ga0.95Mn0.05As 共d nm兲 /GaAs共1 nm兲 / AlAs共4 nm兲 / Be-doped GaAs共100 nm兲 on ap-type GaAs共001兲 substrate, where the GaMnAs QW thickness d ranges from 3.8 to 20 nm. The Be concentration of the
Be-doped GaAs 共GaAs: Be兲 layer was 1 ⫻ 1018 cm−3. The
1-nm-thick GaAs layers were inserted to prevent the Mn diffusion into the barrier layers and to smooth the surface. The
GaAs: Be, AlAs, and the lowest GaAs spacer layers weregrown at 600, 550, and 600 ° C, respectively. The GaMnAs
layers were grown at 225 ° C, and GaAs/ AlGaAs/ GaAs layers below the top GaMnAs layer were grown at 205 ° C. We
grew four samples named A, B, C, and D. When growing
sample A, we moved the in-plane position of the main shutter equipped in our MBE chamber in front of the sample
surface during the growth of the GaMnAs QW, and changedd from 3.8 to 8.0 nm on the same sample wafer. In thegrowth of samples B–D, d was fixed at 12, 16, and 20 nm,
respectively.

III. TUNNELING MAGNETORESISTANCEMEASUREMENTS

In order to carry out the tunneling magnetoresistancemeasurements, circular mesa diodes 200 ␮m in diameter
were fabricated by chemical etching. We spin-coated an insulating negative resist on the sample, opened a contact hole
180 ␮m in diameter on the top of the mesa, and fabricated ametal electrode by evaporating Au on this surface. In thefollowing measurements, the bias polarity is defined by thevoltage of the top GaMnAs electrode with respect to thesubstrate. The schematic band diagrams when negative andpositive biases V are applied to this structure are shown in
Figs. 1共b兲 and 1共c兲, respectively. In this structure, TMR occurs by tunneling holes between the ferromagnetic GaMnAs
top electrode and the ferromagnetic GaMnAs QW. The following tunneling transport measurements were carried out ina cryostat cooled at 2.6 K with a conventional two-terminal

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OHYA et al.

FIG. 2. 共Color兲 共a兲 Tunneling magnetoresistance 共TMR兲 curves 关
共R − R0兲 / R0 vs magnetic field兴 measured at 2.6 K on a junction withd = 12 nm when the magnetic field was applied along the 关100兴 axis
in the plane, where R is the tunnel resistance and R0 is the one atzero magnetic field. The measurements were carried out at constantbias voltages of 10 mV 共red solid and broken curves兲 and −104 mV
共blue solid and broken curves兲. Solid and broken curves were obtained by sweeping the field from −10 to 10 kOe and 10 to−10 kOe, respectively. The obtained TMR ratios, defined as 共Rmax− R0兲 / R0, in this RTD junction with d = 12 nm at 10 mV and−104 mV were 18.9% and 14.1%, respectively. 共b兲 Bias dependence of TMR in Ga0.95Mn0.05As共20 nm兲 / GaAs共1 nm兲 / Al0.5
Ga0.5As共4 nm兲 / GaAs共1 nm兲 / Ga0.95Mn0.05As共d nm兲 / GaAs共1 nm兲
/ AlAs共4 nm兲 / GaAs: Be共100 nm兲 RTD junctions with various QW
thicknesses d when a magnetic field was applied in plane along the
关100兴 direction at 2.6 K, where the TMR ratios are normalized by
the maximum value of TMR in each curve shown in the parenthesis. These results were obtained by measuring TMR minor loops at
various bias voltages and the TMR 共estimated by the tunnel resistances in parallel and antiparallel magnetization states兲 at zero magnetic field was plotted as a function of bias voltage.

FIG. 1. 共Color兲 共a兲 Schematic device structure of theGa0.95Mn0.05As共20 nm兲 / GaAs共1 nm兲 / Al0.5Ga0.5As 共4 nm兲 / GaAs
共1 nm兲 / Ga0.95Mn0.05As 共d nm兲 / GaAs 共1 nm兲 / AlAs共4 nm兲 / GaAs:
Be共100 nm兲 RTD junction examined in this study. 共b兲 and 共c兲 Schematic band diagrams of the RTD junction when the bias polarity is
negative and positive, respectively. Here, the 1-nm-thick GaAs
spacer layers are omitted for simplicity. 共d兲 d2I / dV2-V characteristics of these RTD junctions with various QW thicknesses d in parallel magnetization at 2.6 K. Numbers in the parentheses express
the magnification ratio for the vertical axis. 共e兲 dI / dV-V characteristics of the junction with d = 12 nm at 2.6 K in parallel 共blue curve兲
and antiparallel 共red curve兲 magnetization.

direct-current 共dc兲 method. dI / dV-V and d2I / dV2-V characteristics were derived mathematically from the data of the IV characteristics measured at every 5 mV. The results of thebias dependence of TMR were obtained from the data of I-V
characteristics measured in parallel and antiparallel magnetizations. I-V characteristics in both parallel and antiparallel
magnetizations were obtained at zero-magnetic field.
Figure 1共d兲 shows d2I / dV2-V characteristics of these junctions in parallel magnetization at 2.6 K. Sharp features near
the zero bias are observed in all the curves with various d,corresponding to the zero-bias anomaly which is usually observed in GaMnAs-based heterostructures.18 The most important feature in Fig. 1共d兲 is the oscillations whose peakvoltages depend on d in the negative bias region of all thecurves. With increasing d, these peaks shift to smaller volt-

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QUANTUM SIZE EFFECT AND TUNNELING…

ages and the period of the oscillation becomes short. Suchoscillatory behavior has not been observed in
GaMnAs-based single-barrier MTJs, indicating that these oscillations are induced by the resonant tunneling effect. The
peaks HHn and LHn 共n = 1, 2, 3 , . . .兲 are assigned to resonant
tunneling through the nth level of the heavy hole 共HH兲 bandand light hole 共LH兲 band in the GaMnAs QW, respectively,
as will be described later. Figure 1共e兲 shows the dI / dV-V
curves of the junction with d = 12 nm at 2.6 K in parallel
共blue curve兲 and antiparallel 共red curve兲 magnetization.
These two curves are almost the same, but there is a little
voltage shift which is most obvious at LH1.
TMR was clearly observed in the junctions with d from
3.8 to 12 nm. Figure 2共a兲 shows 共R − R0兲 / R0 vs magnetic
field characteristics 共TMR curves兲 measured at 2.6 K on ajunction with d = 12 nm when the magnetic field was appliedalong the 关100兴 axis in plane, where R is the tunnel resistanceand R0 is the one at zero magnetic field. These measurements
were carried out at constant bias voltages of 10 mV 共redsolid and broken curves兲 and −104 mV 共blue solid and broken curves兲. Solid and broken curves were obtained bysweeping the field from −10 to 10 kOe and 10 to −10 kOe,
respectively. When the magnetic field H was swept from thepositive saturation field down to negative 共broken curves兲,the tunnel resistance R increased from the low-resistance
共R0兲 state to the high-resistance 共Rmax兲 state at around H =−165 Oe where the magnetization of one GaMnAs layer reversed and the magnetization configuration changed fromparallel to antiparallel. Sweeping the field further to thenegative direction, R decreased to the initial value at around
H = −200 Oe where the magnetization of the other GaMnAs
layer reversed and the magnetization configuration became
parallel again. This is a typical TMR behavior usually observed in GaMnAs-based MTJs.19–21 The obtained TMR ratios, defined as 共Rmax − R0兲 / R0, in this RTD junction with d= 12 nm at 10 and −104 mV were 18.9% and 14.1%, respectively.
Figure 2共b兲 shows the bias dependence of the TMR ratioof these junctions at 2.6 K with a magnetic field applied inplane along the 关100兴 direction, where the TMR ratios arenormalized by the maximum value of TMR in each curve
shown in the parenthesis. TMR oscillations can be seen in
the negative bias region of all the curves. With increasing d,
the TMR peaks 共except for those near zero bias兲 shift tosmaller voltages as is the case of the d2I / dV2-V characteristics shown in Fig. 1共d兲, which indicates that these TMR increases are induced by the resonant tunneling effect. Especially, a large TMR increase occurs at LH1, which is causedby the magnetization-dependent peak’s shift at LH1 observedin the dI / dV-V characteristics shown in Fig. 1共e兲. Also, Fig.
2共b兲 indicates that the bias voltage of Vhalf, at which TMR is
reduced by half, can be significantly increased by the resonant tunneling effect. In the negative-bias region of d
= 12 nm, 兩Vhalf兩 was increased to 124 mV 关shown by a redarrow in Fig. 2共b兲兴 due to the TMR increase at LH1, whereas
Vhalf in the positive bias was 76 mV 关shown by a blue arrow
in Fig. 2共b兲兴. This value is much higher than those of
GaMnAs-based single-barrier structures which are usuallyaround 50 mV.2,22,23 On the other hand, the origin of theunusual sharp decrease of TMR near the zero bias is not

FIG. 3. Switching field 共coercivity兲 as a function of d observedin the TMR curve of these RTD junctions at 2.6 K with a bias
voltage of 10 mV and the magnetic field applied in plane along the
关100兴 axis. The closed circles and triangles are the switching fieldsof the GaMnAs QW and the top GaMnAs electrode, respectively.
Both of them tend to increase with decreasing d.

clear, but it is probably partly due to the band offset of the
GaMnAs QW as discussed below.
Figure 3 shows the switching field 共coercivity兲 as a function of d observed in the TMR curve of these RTD junctions
at 2.6 K with the bias voltage of 10 mV and the magnetic
field applied in plane along the 关100兴 axis. The closed circles
and triangles are the switching fields of the GaMnAs QW
and the top GaMnAs electrode, respectively. The switching
field of the GaMnAs QW roughly tends to increase withdecreasing d. 共We note that a strong increase of coercivity bysize reduction has been reported also in magnetic
nanoclusters.24兲 The small peak at around d = 8 nm is due tothe degradation of the crystal quality 共or of the surface flatness兲 of the GaMnAs QW, which can be seen also in Fig.
2共b兲, where the TMR ratio decreases with increasing d whend is less than 8 nm.25 The reason why the switching field of
the top GaMnAs layer also changes with d has not beenclarified, yet, but it is probably due to the ferromagnetic
coupling between the GaMnAs top electrode and the
GaMnAs QW.

IV. COMPARISON WITH THEORETICALCALCULATIONS

To understand the experimental results, we calculated thequantum levels of GaAs/ Al0.5Ga0.5As共4 nm兲 / GaMnAs⫻共d nm兲 / AlAs共4 nm兲 / GaAs using the transfer matrix
method26 with the valence-band 4 ⫻ 4 k · p Hamiltonian27 andthe p-d exchange Hamiltonian28 for including the in-planemagnetization of the GaMnAs QW. The valence band lineup
assumed in this calculation is shown in Fig. 4共a兲. We assumed that the splitting energy ⌬ of the GaMnAs QW, whichcorresponds to the spin splitting energy for the LH valenceband at the ⌫ point, is 共3 meV, 0, 0兲 along the in-plane 关100兴
direction parallel to the magnetic field applied in our experiments. The center energy of the spin-split valence band of
the GaMnAs QW was set at 28 meV above the valence bandof GaAs in terms of hole energy. 共Later, we will discuss thevalidity of this energy position of the valence band of the
GaMnAs QW.兲 Figure 4共b兲 shows the calculated result of theresonant-peak bias voltages for the heavy hole tunneling 共redpoints and curves assigned to HHn兲 and the light hole tunneling 共blue points and curves assigned to LHn兲 at k储 = 0,155328-3

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OHYA et al.

FIG. 4. 共Color兲 共a兲 Valence-band lineup assumed in our calculation of the quantum levels in GaAs/ Al0.5Ga0.5As
共4 nm兲 / GaMnAs共d nm兲 / AlAs共4 nm兲 / GaAs. EF, EV, and ⌬ mean
the Fermi level, the valence band edge, and the spin-splitting energyof the light-hole band of the GaMnAs QW at the ⌫ point, respectively. 共b兲 Calculated and experimentally obtained resonant peakvoltage vs the GaMnAs QW thickness d. The black solid rectangles
and triangles denote the experimentally obtained resonant-peakvoltages assigned as HH and LH quantum levels in the d2I / dV2-V
characteristics of Ga0.95Mn0.05As共20 nm兲 / GaAs共1 nm兲 / Al0.5Ga0.5
As共4 nm兲 / GaAs共1 nm兲 / Ga0.95Mn0.05As共d nm兲 / GaAs共1 nm兲 / AlAs
共4 nm兲 / GaAs: Be共100 nm兲 RTD junctions in parallel magnetization, respectively. Here, these voltages are expressed in the absolutevalues. The small red and blue points 共curves兲 denote the calculated
resonant voltages of HH and LH, respectively. The quantum levelsof LH1 and LH2 are spin-split by the in-plane magnetization introduced by the p-d exchange Hamiltonian. The calculated voltages of
the LH quantum levels shown in this figure are those in parallel
magnetization.

where k储 is the wave vector parallel to the film plane. These
resonant peak bias voltages were derived by multiplying the
calculated energy values of the quantum levels by 2.5 关ideally, this value is 2 共Ref. 29兲兴 for better fit, which means that
20% of the applied bias voltage is consumed in the electrodes. Since the heavy hole spins are oriented along thetunneling direction and the p-d exchange Hamiltonian is proportional to s · S, the quantum levels of HH are not spin split
but those of LH are split by the in-plane magnetization,30
where s and S are spins of the carrier and the Mn atom,
respectively. Holes tunnel through the lower and upper statesof the spin-split LH quantum levels in parallel and in anti-

parallel magnetization, respectively. The calculated voltagesof the LH quantum levels shown in Fig. 4共b兲 are those inparallel magnetization.
Figure 4共b兲 also shows the experimental peak voltages
assigned to HH and LH quantum levels observed in thed2I / dV2-V curves in parallel magnetization by black solid
rectangles and triangles, respectively. Here, the peak voltages
are expressed in the absolute values. Although there is a little
deviation between the experimental and calculated results,
the experimental results are well-fitted by the present model.
Possible origins of these deviations are considered as follows. When d is thinner than 5 nm, Mn diffusion from the
GaMnAs QW layer to the adjacent GaAs spacer layer yields
lowering of the resonant tunneling energy. The deviations
may also come from the point defects incorporated into
GaMnAs such as Mn interstitials31 and As antisite defects,32
whose concentrations are very sensitive to the growth condition of GaMnAs.33 These defects can influence the spinsplitting energy, band offset, and strain, leading to such deviations. We note that the spin-splitting energy 共3 meV, 0, 0兲
is consistent with our results of the temperature dependenceof TMR, where TMR disappeared at around 20 K when increasing temperature.34,35 Also, this spin-splitting energy canwell-explain the quantity of the peak voltage shift of
7共±2兲 mV observed in the dI / dV-V curves with parallel andantiparallel magnetizations at LH1 shown in Fig. 1共e兲 共i.e.,7 ⬇ 3 ⫻ 2.5兲. Our result that the quantum levels of the
GaMnAs QW can be described by the spin-split valenceband model indicates that the tunneling phenomena throughthe GaMnAs QW are strongly associated with the valenceband feature.
V. DISCUSSION

In our experiment, the resonant peaks were observed onlyin the negative bias region, where holes are injected from the
GaAs: Be layer to the GaMnAs QW. We think that it is attributed to the difference of the Fermi energy EF between the
top GaMnAs and the bottom GaAs: Be electrodes.34 Figure
5共a兲 shows the schematic valence-band diagrams of the
GaMnAs electrode 共left graph兲 and the hole subband structure of AlAs共1 nm兲 / GaAs QW 共5 nm兲 / AlAs共1 nm兲 共rightgraph兲 calculated by the k · p model. For simplicity, we ignored the spin splitting and used an AlAs barrier instead of
AlGaAs. Also, a single band is assumed in the GaMnAs
electrode. GaMnAs has a large hole concentration of the order of 1020 to 1021 cm−3, thus a large EF around 200 meV.
共Here, we assumed that EF exists in the valence band. Even
if EF exists in the impurity band as mentioned in the next
paragraph, the result of this discussion does not change.36兲
Considering the freedom in the kz direction of holes in thebulk GaMnAs electrode, this high EF means that the holes
occupy a wide k储 region. Now, we consider that holes are
injected to the GaMnAs QW from the GaMnAs electrode
whose energy is increased by the bias voltage, as shown in
Fig. 5共a兲. If k储 is conserved during tunneling, holes are injected to the subbands of the GaMnAs QW within the grayregion. The circular points correspond to the states of the
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PHYSICAL REVIEW B 75, 155328 共2007兲

GaMnAs QW

HH1 level兲 of the GaMnAs QW is higher than EF
共⬇7 meV兲. This means that there are almost no holes in the
GaMnAs QW when the bias voltage is small. Under the general concept of the carrier-mediated ferromagnetism where
the ferromagnetism of GaMnAs is induced by the valenceband holes,37 the GaMnAs QW in our RTD devices would
not become ferromagnetic because there is no holes in its
valence band. In our experiment, however, the GaMnAs QW
is ferromagnetic because TMR was observed even when thebias voltage is small. At present, this discrepancy is not perfectly understood, but we think it might be partly due to the
low Curie temperature of the GaMnAs QW in our RTD
samples 共⬃20 K兲. It is well-known that the ferromagnetic
GaMnAs films with a low Curie temperature often show
strong insulating behavior even when the temperature is below its Curie temperature.38 In this case, mobile valenceband holes are not likely to exist there. Recently, Burchet al.39 indicated that EF of GaMnAs exists not in the valenceband but in the impurity band in the band gap of GaMnAs bymeasuring the infrared optical spectroscopy. Although there
is a little difference of the energy positions of EF obtained intheir results 共around 100– 200 meV from the valence band兲and in our results 共28− 7 = 21 meV from the valence band of
GaMnAs兲, their results seem to qualitatively support ourpresent understanding of the quantum levels in the GaMnAs
QW. Note also that EF of GaMnAs strongly depends on thegrowth conditions.
In our experiment, a very large TMR enhancement as predicted in the theories3,4 was not obtained. The possible reason of this is the small spin splitting 共3 meV兲 obtained in the
GaMnAs QW of our RTD devices. If a GaMnAs QW with alarger spin-splitting energy can be obtained by using a better
growth condition 共i.e., more appropriate growth temperature
and arsenic pressure兲 where the concentration of the interstitial Mn defects is minimized, a larger TMR enhancement
will be obtained. Also, if a high-quality epitaxial QW composed of a single-crystal ferromagnetic metal with larger spin
splitting can be obtained, TMR will be largely enhanced.

Electrode(a)hole energy [eV]

0.5

holes

0.3
EF

0.2

-0.3

(b)

holes

0
k|| [π/a]0.3 -0.3

0k|| [π/a]

0.3

GaMnAs QWElectrode

0.5
hole energy [eV]

Increase
of V

holes

0.1
0

holes

EF

0.4

0.4
0.3

EF

0.2
0.1
0

holes

Increase
of V
EF

-0.3

0
k|| [π/a]holes

0.3 -0.3

0k|| [π/a]0.3

FIG. 5. 共a兲 Schematic valence-band diagrams of the GaMnAs
electrode 共left graph兲 and the hole subband structure of
AlAs共1 nm兲 / GaAs QW 共5 nm兲 / AlAs共1 nm兲 共right graph兲 calculated by the k · p model. For simplicity, we ignored the spin splitting
and used an AlAs barrier instead of AlGaAs, respectively. Also, a
single band is assumed in the electrode. EF is assumed to be
200 meV. The gray regions in the GaMnAs QW bandstructure correspond to the k储 regions where tunneling can occur, and the blackbands on the right side are corresponding energy regions. The circular points correspond to the states of the maximum and minimum
energies in each subband within the gray region. The broken lines
are maximum and minimum energies of each subband within thegray region. 共b兲 The case when holes are injected from the electrodewith a small hole concentration like GaAs: Be. EF is assumed to be
7 meV.

region. The black bands shown on the right side are theenergy regions corresponding to these subbands in the grayregion. We can see that these energy regions of the subbands
are energetically overlapped, thus these subbands cannot be
detected separately in tunneling transport measurements. On
the other hand, if carriers are injected from GaAs: Be with asmaller carrier concentration of 1 ⫻ 1018 cm−3 whose Fermi
level is estimated to be about 7 meV, the tunneling occurs
only within a small k储 region. Figure 5共b兲 shows the schematic valence-band diagrams of the GaAs: Be electrode 共left
graph兲 and the subbands in the GaMnAs QW 共right graph兲.
When carriers are injected from such an electrode with asmall Fermi level, these carriers are injected into the grayregions and black bands of the GaMnAs QW in Fig. 5共b兲,
where these energy regions are energetically separated.
Therefore, the resonant peaks are observed only in the negative bias region. Our result indicates that electrodes with alow carrier concentration are appropriate for clear detectionof the resonant tunneling effect in GaMnAs QW heterostructures.
Here, we discuss the validity of the energy position of the
GaMnAs QW assumed in our calculation. As can be seen in
Fig. 4共a兲, the energy of the valence-band bottom 共or of the

VI. SUMMARY

We have observed the resonant tunneling effect and TMR
increase induced by it in GaMnAs-QW double-barrier heterostructures with the QW thickness from 3.8 to 20 nm, indicating highly coherent tunneling occurs in these heterostructures. The observed quantum levels of the GaMnAs QW
were successfully explained by the coherent tunneling modelwith the valence-band k · p model and the p-d exchange interaction. It was also found that electrodes with a low carrier
concentration are appropriate for clear detection of the resonant tunneling effect in this system.

ACKNOWLEDGMENTS

This work was partly supported by PRESTO/SORST ofJST, Grant-in-Aids for Scientific Research, IT Program of
RR2002 of MEXT, and Kurata-Memorial Hitachi Science &Technology Foundation.

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*Electronic address: ohya@cryst.t.u-tokyo.ac.jp†

Electronic address: masaaki@ee.t.u-tokyo.ac.jp
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TMR not to tunneling anisotropic magnetoresistance 共TAMR兲
共Ref. 21兲.
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