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GaMnAs ferromagnetic semiconductor heterostructures
Physica E 13 (2002) 495 – 503
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Tunneling magnetoresistance in GaMnAs=AlAs=GaMnAs ferromagnetic semiconductor heterostructures M. Tanaka ∗ , Y. Higo Department of Electronic Engineering, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Abstract We have observed tunneling magnetoresistance (TMR) in epitaxially grown GaMnAs=AlAs=GaMnAs ferromagnetic semiconductor tunnel junctions. The TMR ratio, which is the change in tunnel resistance due to the change of magnetization con2guration from parallel to anti-parallel, was more than 70% (maximum 75%) in junctions with a very thin (6 1:6 nm) AlAs tunnel barrier, when the magnetic 2eld was applied along the [1 0 0] axis in the 2lm plane. Peculiar TMR characteristics were observed due to the magneto-crystalline anisotropy of GaMnAs. The TMR ratio was found to rapidly decrease with increasing barrier thickness, which is explained by calculations assuming that the parallel wave vector of carriers is conserved in tunneling. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 72.25.Dc; 73.40.Gk; 75.50.Pp; 75.70.Pa Keywords: Tunneling magnetoresistance; GaMnAs; Magnetic tunnel junction; Magnetic semiconductor
1. Introduction In the past few years, tunneling magnetoresistance (TMR) and related phenomena were extensively studied in magnetic tunnel junctions (MTJs) [1,2], leading to important applications such as magnetic 2eld sensors and magnetic random access memory (MRAM) [3,4]. In most of the experiments on spin-polarized tunneling in ferromagnet (FM)=insulator (I)=ferromagnet (FM) tunnel junctions, polycrystalline transition metals and amorphous oxides are used as FM and I layers, respectively. Ferromagnetic semiconductor heterostructures based on Ga1−x Mnx As can give a new interesting opportunity to study spin-dependent transport phenomena. Because Ga1−x Mnx As is a ferromagnetic p-type ∗ Corresponding author. Tel.: +81-3-5841-6728; fax: +81-35803-3975. E-mail address: [email protected] (M. Tanaka).
semiconductor with the zincblende-type crystal structure having almost the same lattice constant as GaAs and AlAs, Ga1−x Mnx As=(GaAs or AlAs) III–V based heterostructures can be epitaxially grown with abrupt interfaces and with atomically controlled layer thickness [5 –8]. Although the Curie temperature of GaMnAs is below room temperature so far (at most 110 K [7]), using GaMnAs-based III–V heterostructures as tunnel junctions would have several advantages: (1) One can form high-quality single-crystalline MTJs made of all-semiconductor heterostructures, which can be easily integrated with other III–V based structures and devices. (2) In principle, many parameters such as barrier height, barrier thickness, and the Fermi energy of FM electrodes are controllable. (3) Introduction of quantum heterostructures, such as double-barrier resonant tunneling diodes is probably easier than any other material system [9]. At this moment, however, little is understood on the spin-polarized tunneling in such a ferromagnetic
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semiconductor heterostructure system and little has been experimentally studied on all-epitaxial monocrystalline MTJs. We have recently observed TMR in a GaMnAs= AlAs=GaMnAs tunnel junction with the magnetic 2eld applied in plane along the [1 1 0] direction [10]. Although the total change in the tunnel resistance IR=R measured at 4:2 K was 44% including the slowly saturating negative component at a higher magnetic 2eld, the TMR ratio purely due to the spin-valve eJect was estimated to be only 15 –19% in our previous paper [10]. More recently, Chiba et al. [11] also reported a TMR ratio of 5.5% at 20 K in a GaMnAs tunnel junction. In this article, we describe our recent TMR study of Ga1−x Mnx As=AlAs=Ga1−x Mnx As heterostructures, in particular, for larger TMR ratios (¿ 70%; maximum 75%) at 8 K in Ga1−x Mnx As=AlAs=Ga1−x Mnx As tunnel junctions [12], which are purely due to the change of the magnetization direction of the two ferromagnetic electrodes. Peculiar anisotropic TMR characteristics were observed, which is caused by the magneto-crystalline anisotropy of GaMnAs with the easy magnetization axis of 1 0 0. We have also studied the dependence of the TMR on the barrier thickness in a wedge-type sample, and have found that the TMR ratio rapidly decreases with increasing barrier thickness dAlAs in junctions with dAlAs ¿ 1:5 nm. This barrier thickness dependence of the TMR can be explained by tight-binding calculations of tunneling assuming that the wave vector in the direction parallel to the interface is conserved. 2. Sample preparation Fig. 1 illustrates the sample structure and preparation process, using low temperature molecular beam epitaxy (LT-MBE) and patterning by photolithography. After a 100 nm-thick Be-doped ◦ GaAs buJer layer was grown at 580 C on a p+ GaAs (0 0 1) substrate, a Ga1−x Mnx As(x = 4:0%; 50 nm)=AlAs(dAlAs )=Ga1−x Mnx As(x = 3:3%; 50 nm) ◦ trilayer was grown at 250 C. By using a shutter linearly moving in front of the substrate, we changed the barrier thickness dAlAs ranging from 1:3 to 2:8 nm within a wafer of 20 × 20 mm2 . The slope of the wedge was estimated by the growth rate of AlAs,
Fig. 1. Preparation of a wedge-type ferromagnetic semiconductor trilayer heterostructure by LT-MBE and mesa-etched round-shaped MTJs 200 m in diameter.
which was obtained by reMection high-energy electron diJraction (RHEED) oscillations, and the moving speed of the shutter. Preparation of wedge-type samples is important in order to measure the dependence of the TMR of MTJs on the barrier thickness, because the electronic and magnetic properties of the GaMnAs layers are very sensitive to the growth conditions [13]. In addition, undoped 1 nm-thick GaAs spacers were inserted between GaMnAs and AlAs to avoid Mn diJusion into the barrier, which causes spin-Mip scattering, and makes the interfaces smooth. In order to measure tunneling transport, the sample was patterned by photolithography and mesa etching into arrays of round-shaped mesa junctions 200 m in diameter with various barrier thicknesses ranging from 1.3 to 2:8 nm. 3. Tunneling magnetoresistance (TMR) 3.1. Magnetization and TMR The magnetization of the Ga1−x Mnx As(x = 4:0%; 50 nm)=AlAs (3 nm)=Ga1−x Mnx As(x=3:3%; 50 nm)
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Fig. 2. (a) Magnetization of a Ga1−x Mnx As(x = 4:0%; 50 nm)= AlAs(3 nm)=Ga1−x Mnx As(x = 3:3%; 50 nm) trilayer measured by SQUID at 8 K. The specimen size was 3 × 3 mm2 . The vertical axis shows the normalized magnetization M=Ms , where Ms is the saturation magnetization. (b) TMR curves at 8 K of a Ga1−x Mnx As(x = 4:0%; 50 nm)=AlAs(1:6 nm)=Ga1−x Mnx As(x = 3:3%; 50 nm) tunnel junction. The tunnel junctions were mesa-etched diodes 200 m in diameter. Bold solid and dashed curves are major loops, with the magnetic 2eld sweep direction from positive to negative and negative to positive, respectively. A minor loop is shown by a thin solid curve. In both (a) and (b), the magnetic 2eld was applied along the [1 0 0] axis in the plane.
trilayer measured by SQUID at 8 K is shown in Fig. 2(a). In the SQUID measurements, the trilayer sample was cleaved into a square shape with the area of 3 × 3 mm2 . The magnetic 2eld was applied along the [1 0 0] axis in the plane. Pairs of arrows in the 2gure indicate the magnetization directions of the top and bottom GaMnAs layers at diJerent 2elds. Due to the diJerent coercivity of the two GaMnAs layers, we observed a double-step magnetization curve with coercive 2elds of about 60 and 100 Oe. The easy magnetization axis of the ferromagnetic GaMnAs layers lies in the 2lm plane. Fig. 2(b) shows tunnel resistance vs. magnetic 2eld, that is, TMR curves measured at 8 K on a junction
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with dAlAs = 1:6 nm when the magnetic 2eld was applied along the [1 0 0] axis in the plane. The measurements were taken at a constant bias of 1 mV, and so there is no hot carrier eJect. The TMR is de2ned here as (R(H ) − R(0))=R(0), where R(H ) is the resistance at the 2eld of H , and R(0) = 0:014 Pcm2 is taken from a major loop. Bold solid and dashed curves (major loops) in Fig. 2(b) were obtained by sweeping the 2eld from positive to negative and negative to positive, respectively. As shown by the bold solid curve, when the 2eld was swept from the positive saturation 2eld down to negative, R(H ) increased from 0.014 to 0:025 Pcm2 (corresponding TMR was 72%) at H = −110 Oe where the magnetization of one GaMnAs layer reversed and the magnetization con2guration changed from parallel to antiparallel. Sweeping the 2eld further to the negative direction, the R(H ) and the TMR decreased to the initial value (R(H ) = 0:014 Pcm2 ) at H = −125 Oe, where the magnetization of the other GaMnAs layer reversed and the magnetization con2guration became parallel again. The diJerence of the coercive 2elds between the M –H curve in Fig. 2(a) and the TMR curve in Fig. 2(b) is caused by the diJerence in the shape and size of the measured specimens. Note that the TMR value is over 70%, much higher than the TMR previously reported [10,11]. A thin solid curve in Fig. 2(b) shows a minor loop, indicating that the antiparallel con2guration as well as the parallel one are stable. 3.2. Barrier thickness dependence Fig. 3(a) shows the tunnel resistance R for the tunnel junctions measured at 8 K as a function of the barrier thickness dAlAs . The resistance exponentially increased over a wide range from 10−3 to 10 Pcm2 as dAlAs increased, which means that high-quality tunnel junctions were formed with a constant barrier height. In the WKB approximation, the slope of ln R − dAlAs characteristics is given by 2[2m∗ Vb ]1=2 =˜, thereby the product m∗ Vb is estimated to be 0:32m0 [kg eV], where m0 is the free-electron mass, m∗ is the eJective mass of holes, and Vb is the barrier height. The valence band oJset between GaMnAs and AlAs is unknown but it is considered to be close to that (∼ 0:55 eV) of GaAs and AlAs, and the Fermi energy of holes in GaMnAs is 0.1–0:2 eV, thus, the barrier height Vb is ∼ 0:45 eV. Therefore, the eJective mass m∗ of holes which is
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clear at present, this drop could be caused by the decrease of the eJective barrier height because of interface roughness or the image potential. Another possible reason is the ferromagnetic interlayer exchange coupling between GaMnAs layers separated by a very thin AlAs layer [11]. 3.3. Magneto-crystalline anisotropy
Fig. 3. Barrier thickness dependence of (a) the tunnel resistance and (b) the TMR in Ga1−x Mnx As(x = 4:0%; 50 nm)= AlAs(dAlAs )=Ga1−x Mnx As(x=3:3%; 50 nm) tunnel junctions measured at 8 K. In (b), the TMR values were measured with the magnetic 2eld applied along the [1 0 0] and [1 1 0] axes.
responsible for tunneling is roughly estimated to be ∼ 0:7m0 . Fig. 3(b) shows barrier thickness dependence of TMR at 8 K when the magnetic 2eld was applied in-plane along the [1 0 0] and [1 1R 0] axes. The maximum TMR was 75% at dAlAs =1:46 nm when the 2eld was applied along the [1 0 0] axis. In both 2eld directions, with increasing dAlAs (¿ 1:5 nm), the TMR was found to rapidly decrease. At all the values of dAlAs , the TMR was higher when the 2eld was applied along the [1 0 0] axis than along the [1 1 0] axis. The diJerence in the TMR between the two directions of the 2eld is due to the cubic magneto-crystalline anisotropy induced by the zincblende-type GaMnAs crystal structure, where the easy magnetization axis of GaMnAs is 1 0 0, the details of which are reported elsewhere [14]. Although the reason for the drop in the TMR for the junction with dAlAs ¡ 1:4 nm is not
When we measured TMR on many round-shaped mesa tunnel junctions, a variety of diJerent characteristics were observed, as shown in Figs. 4(a) – (d). Here, the magnetic 2eld was applied in plane along the [1 0 0] axis. Since the present tunnel junctions are totally monocrystalline and GaMnAs is considered to have the magneto-crystalline anisotropy with the easy magnetization axis of 1 0 0 [14], the magnetization direction of the top and bottom GaMnAs layers favors to be along one of the four directions ([1 0 0]; [0 1 0]; [1R 0 0], and [0 1R 0]) in the 2lm plane. We attributed these TMR behaviors to the diJerent magnetization con2gurations, as illustrated in the lower panel of Fig. 4. Here, solid and gray arrows are the magnetization directions of the two GaMnAs layers, and time evolutions of magnetization con2guration are depicted when the applied magnetic 2eld is changed from positive (+200 Oe) to negative (−200 Oe). These TMR behaviors are well explained by the analysis of magnetization rotation based on the single domain theory [15]. The multi-value characteristics of TMR due to the magnetocrystalline anisotropy could lead to interesting applications such as multi-value recording and novel logic circuitry. 3.4. Temperature dependence We measured temperature dependence of the TMR for various junctions with diJerent dAlAs , and plotted in Fig. 5 the normalized conductance diJerence IG = IG(T )=IG(8 K), where T is temperature, IG(T ) = GP (T ) − GAP (T ); GP (T ) and GAP (T ) are the junction conductances at T [K] for parallel and antiparallel magnetization, respectively. IG (equivalently, TMR) basically decreased with increasing temperature and vanished at ∼ 50 K, which is the Curie temperature of one of the GaMnAs layers. IG dropped once at ∼ 20 K, because the coercivity of the top and bottom GaMnAs layers is so close (almost same) that the
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Fig. 4. A variety of TMR characteristics of round-shaped mesa tunnel junctions at 8 K. The magnetic 2eld was applied in plane along the [1 0 0] axis. In the lower panel, time evolutions of magnetization con2guration are depicted when the applied magnetic 2eld is changed from positive (+200 Oe) to negative (−200 Oe). Solid and gray arrows are the magnetization directions of the two GaMnAs layers.
window for antiparallel magnetization is too small, which was con2rmed by temperature-dependent magnetization measurements, thus IG was diScult to be observed at around 20 K. A solid line in Fig. 5 is the 2t to the theory IG(T ) = IG0 (1 − T 3=2 )2 , where IG0 is a constant and is 2tted to 1:5 × 10−3 [K −3=2 ], based on thermal spin-wave excitations [16]. The theory can explain the present data, as it did for conventional Co=Al2 O3 =Co(NiFe) MTJs. This means that the dominant contribution to the tunnel conductance is a direct elastic tunneling with the tunneling carrier spin-polarization P decreasing as 1 − T 3=2 . Both the excellent scaling of the junction resistance with the AlAs barrier thickness (Fig. 3(a)) mentioned earlier
and this temperature dependence of IG give strong evidence for TMR junctions.
4. Tight-binding calculation of TMR 4.1. Spin-dependent tunneling with k conservation In conventional Julliere’s model [17], the TMR depends only on the spin-dependent density of states in the two FM electrodes and does not depend on the barrier thickness d, so that the Julliere model cannot explain our experimental results. Since the present GaMnAs=AlAs=GaMnAs heterostructures are
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Fig. 5. Temperature dependence of the normalized conductance diJerence IG (equivalently TMR) for various junctions with diJerent dAlAs = 1:46; 1:58; 1:70; 1:82 nm. The solid line is the 2t to the theory based on thermal spin wave excitations.
epitaxially grown single crystals, the wave vector k of carriers parallel to the interface should be conserved in tunneling. Calculations using the tight-binding theory including k conservation by Mathon [18] seem consistent with our experimental results of the barrier thickness dependence of the TMR. Our experimental results can be qualitatively explained as follows: Fig. 6 shows the Fermi surfaces for up and down spins in two FM electrodes, calculated by the single-orbital tight-binding model, when the magnetization con2guration is (a) parallel and (b) antiparallel. Also, the dispersion of the decaying factor z in the barrier layer was calculated and shown in the middle of the 2gure. The wave vector kz (EF ; k ) normal to the interface in the FM electrodes is determined from EF = E0 + 2t cos(kz a) + w(k ), and the decaying factor z (EF ; k ) in the barrier layer is determined from EF = E0 + 2t cosh(z a) + w(k ), where w(k ) = 2t[cos(kx a) + cos(ky a)]; k = (kx ; ky ) is the wave vector parallel to the 2lm plane, EF is the Fermi energy, E0 is the on-site energy in each layer, t is the nearest-neighbor hopping parameter, and a is the lattice constant [18]. We simply regard spin-polarization in the FM electrodes as the diJerence of E0 between the majority and minority carriers. When the magnetizations of the two FM electrodes are parallel as shown in Fig. 6(a), the majority (minority) spin is the up (down) spin in the both electrodes, so that the carriers can tunnel through all the channels (k ; ). When the magnetizations of the two FM electrodes are antiparallel as shown in Fig. 6(b), the down spin is the majority spin in the right electrode, thus the carriers
with k = |k | ¿ kcut-oJ cannot tunnel, where kcut-oJ is the cut-oJ wave vector which is the largest k in the minority spin band. This diJerence of tunneling between the parallel and antiparallel con2gurations indicates that the TMR is mainly caused by the carriers with large k (¿ kcut-oJ ). However, these carriers with larger k exponentially decay more rapidly during tunneling in the barrier because of larger z , as shown in the middle of Fig. 6. Due to this in-plane dispersion of z (k ), when the barrier thickness d is large, the tunneling conductance is dominated by the carriers with smaller k , which do not much contribute to the TMR. Therefore, the TMR decreases as d increases. 4.2. Calculation of TMR and comparison with the experimental results In order to compare our experimental TMR obtained in the GaMnAs=AlAs=GaMnAs tunnel junctions, we calculated the dependence of TMR on dAlAs using the spin–orbit nearest-neighbor sp3 s∗ model [19,20]. We used tight-binding parameters in Ref. [21] to obtain the realistic band structures of GaAs and AlAs. The eJect of Mn ions in GaMnAs was simpli2ed by introducing an additional term IJx into the intralayer coupling matrices in the sp3 s∗ Hamiltonian. Here, Jx is a 10 × 10 matrix derived from the x component of the total angular momentum J in the planar-orbital basis. We used Jx because the magnetization was along the [1 0 0] axis. This additional term causes the changes of the on-site energies proportional to Jx . The scalar proportional coeScient corresponds to the spin-splitting energy between the two holes | 32 ; 12 and | 32 ; − 12 at the point. In order to calculate TMR, tunneling probability T was 2rst calculated, as shown in Fig. 7, and plotted in the k plane (−0:3 =a 6 kx 6 0:3 =a; −0:3 =a 6 ky 6 0:3 =a), both for parallel and antiparallel magnetizations. The k dependence of T is complex because of the complexity of the valence band of GaMnAs and AlAs. The band parameters used here are shown in the inset of Fig. 8. Despite the complexity, the essential point is as follows. When the AlAs barrier thickness is as thin as 1 monolayer (ML), T has some nonzero values even at large k for the parallel magnetization whereas T is zero at large k for the antiparallel magnetization (see the upper panels of Fig. 7). This diJerence in T between the parallel and antiparallel
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Fig. 6. Fermi surfaces of the simple cubic lattice calculated by the single orbital tight-binding model for up and down spins with the spontaneous spin-splitting in (a) parallel and (b) antiparallel magnetization con2gurations. Dependence of the decaying factor z in the barrier on k is also shown in the middle of the 2gure.
magnetizations leads to large TMR. In contrast, when the AlAs barrier thickness is thicker (5 MLs), T is signi2cantly suppressed at large k for the parallel magnetization due to large z , as described above, thus the diJerence in T between the parallel and antiparallel magnetizations is smaller, resulting in smaller TMR (see the lower panels of Fig. 7). Fig. 8 shows the calculated (solid curve) and measured (solid circles) barrier thickness dependences of the TMR in the present GaMnAs=AlAs=GaMnAs tunnel junctions. We assumed that EF ; V , and were 0.2 [eV], 0.67 [eV], and 0.08 [eV], respectively. The Fermi energy EF and the valence band oJset V were measured from the top of the valence band in the calculated GaMnAs band structure, as shown in the inset of Fig. 8. V = 0:67 [eV] gives the valence band
oJset of 0.55 [eV] when = 0, that is, the case for normal GaAs=AlAs interfaces, which is a reasonable value. Compared with the experimental results, the calculated TMR decreases rapidly in the thinner barrier region. The barrier thickness was evaluated from RHEED oscillations and the moving speed of the shutter, as mentioned before. Since completely accurate alignment of the moving shutter with the substrate in our MBE chamber is diScult, the absolute values of the estimated barrier thickness may not be reliable (though the relative values are reliable), thus, we horizontally shifted the calculated dependence towards right by 0:7 nm (only 2:5 ML) to 2t the experimental results, as shown by a dashed curve in Fig. 8. The 2tting is fairly good, but not perfect partly because the band structure of GaMnAs is still unknown and
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Fig. 7. Tunneling probability T in GaMnAs=AlAs(dAlAs )=GaMnAs tunnel junctions plotted in the k plane (−0:3 =a 6 kx 6 0:3 =a; −0:3 =a 6 ky 6 0:3 =a), both for parallel and antiparallel magnetization con2gurations, when the AlAs barrier thickness dAlAs = 1, and 5 ML.
the model is simple compared with the more complex band structure and=or partly because there could be spin scattering at the interfaces or in the tunnel barrier which is not taken into account. However, the present spin-orbit nearest-neighbor sp3 s∗ model is found to explain the most essential part of the experimental barrier thickness dependence of the TMR. Note that there are three essential points in this model: (1) The cut-oJ wave vector kcut-oJ in the plane exists in the antiparallel con2guration. (2) The decaying factor z in the barrier increases with increasing k . (3) k is con-
served in tunneling. Although these points may not be valid in the conventional MTJs with polycrystalline metallic electrodes, we think that they are valid in the present Ga1−x Mnx As=AlAs=Ga1−x Mnx As tunnel junctions, which are epitaxially grown single crystals. 5. Summary We have grown Ga1−x Mnx As(x = 4:0%; 50 nm)= AlAs(dAlAs )=Ga1−x Mnx As(x = 3:3%; 50 nm) single-
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work, and Prof T. Nishinaga (President of Toyohashi University of Technology) and Prof. S. Naritsuka (Meijo Univ.) for their support. This work was partially supported by the JSPS Research for the Future Program (JSPS-RFTF 97P00202), by the PRESTO project of JST, Toray Science Foundation, and by a Grant-in-Aid for Scienti2c Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan. References Fig. 8. Solid curve represents the calculated dependence of TMR on the barrier thickness dAlAs when the Fermi energy EF = 0:2 eV, the band oJset V = 0:67 eV (both measured from the top of the valence band of GaMnAs), and the spin-splitting = 0:08 eV between the two light holes | 32 ; 12 and | 32 ; − 12 at the point. Inset shows the band dispersion and the relationship of these parameters. The solid curve is horizontally shifted to the dashed curve by 0:7 nm (only 2:5 ML) to 2t the experimental results (solid circles, the magnetic 2eld was along the [1 0 0] axis), because the absolute barrier thicknesses of the junctions are nominal.
barrier tunnel junctions by LT-MBE. In junctions with dAlAs 6 1:6 nm, the TMR of more than 70% (the highest value was 75%) was obtained when the 2eld was applied along the [1 0 0] axis in the plane. The various TMR characteristics were shown and explained by the magnetocrystalline anisotropy of GaMnAs having the easy magnetization axis of 1 0 0. The TMR rapidly decreased as the barrier thickness dAlAs increased for the junctions with dAlAs ¿ 1:5 nm. This barrier thickness dependence of the TMR was explained by calculations assuming that the parallel wave vector of carriers was conserved in tunneling. Acknowledgements We would like to thank Dr. T. Hayashi (now at NTT) for his contribution at the initial stage of this
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Tunneling magnetoresistance in GaMnAs=AlAs=GaMnAs ferromagnetic semiconductor heterostructures M. Tanaka ∗ , Y. Higo Department of Electronic Engineering, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Abstract We have observed tunneling magnetoresistance (TMR) in epitaxially grown GaMnAs=AlAs=GaMnAs ferromagnetic semiconductor tunnel junctions. The TMR ratio, which is the change in tunnel resistance due to the change of magnetization con2guration from parallel to anti-parallel, was more than 70% (maximum 75%) in junctions with a very thin (6 1:6 nm) AlAs tunnel barrier, when the magnetic 2eld was applied along the [1 0 0] axis in the 2lm plane. Peculiar TMR characteristics were observed due to the magneto-crystalline anisotropy of GaMnAs. The TMR ratio was found to rapidly decrease with increasing barrier thickness, which is explained by calculations assuming that the parallel wave vector of carriers is conserved in tunneling. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 72.25.Dc; 73.40.Gk; 75.50.Pp; 75.70.Pa Keywords: Tunneling magnetoresistance; GaMnAs; Magnetic tunnel junction; Magnetic semiconductor
1. Introduction In the past few years, tunneling magnetoresistance (TMR) and related phenomena were extensively studied in magnetic tunnel junctions (MTJs) [1,2], leading to important applications such as magnetic 2eld sensors and magnetic random access memory (MRAM) [3,4]. In most of the experiments on spin-polarized tunneling in ferromagnet (FM)=insulator (I)=ferromagnet (FM) tunnel junctions, polycrystalline transition metals and amorphous oxides are used as FM and I layers, respectively. Ferromagnetic semiconductor heterostructures based on Ga1−x Mnx As can give a new interesting opportunity to study spin-dependent transport phenomena. Because Ga1−x Mnx As is a ferromagnetic p-type ∗ Corresponding author. Tel.: +81-3-5841-6728; fax: +81-35803-3975. E-mail address: [email protected] (M. Tanaka).
semiconductor with the zincblende-type crystal structure having almost the same lattice constant as GaAs and AlAs, Ga1−x Mnx As=(GaAs or AlAs) III–V based heterostructures can be epitaxially grown with abrupt interfaces and with atomically controlled layer thickness [5 –8]. Although the Curie temperature of GaMnAs is below room temperature so far (at most 110 K [7]), using GaMnAs-based III–V heterostructures as tunnel junctions would have several advantages: (1) One can form high-quality single-crystalline MTJs made of all-semiconductor heterostructures, which can be easily integrated with other III–V based structures and devices. (2) In principle, many parameters such as barrier height, barrier thickness, and the Fermi energy of FM electrodes are controllable. (3) Introduction of quantum heterostructures, such as double-barrier resonant tunneling diodes is probably easier than any other material system [9]. At this moment, however, little is understood on the spin-polarized tunneling in such a ferromagnetic
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semiconductor heterostructure system and little has been experimentally studied on all-epitaxial monocrystalline MTJs. We have recently observed TMR in a GaMnAs= AlAs=GaMnAs tunnel junction with the magnetic 2eld applied in plane along the [1 1 0] direction [10]. Although the total change in the tunnel resistance IR=R measured at 4:2 K was 44% including the slowly saturating negative component at a higher magnetic 2eld, the TMR ratio purely due to the spin-valve eJect was estimated to be only 15 –19% in our previous paper [10]. More recently, Chiba et al. [11] also reported a TMR ratio of 5.5% at 20 K in a GaMnAs tunnel junction. In this article, we describe our recent TMR study of Ga1−x Mnx As=AlAs=Ga1−x Mnx As heterostructures, in particular, for larger TMR ratios (¿ 70%; maximum 75%) at 8 K in Ga1−x Mnx As=AlAs=Ga1−x Mnx As tunnel junctions [12], which are purely due to the change of the magnetization direction of the two ferromagnetic electrodes. Peculiar anisotropic TMR characteristics were observed, which is caused by the magneto-crystalline anisotropy of GaMnAs with the easy magnetization axis of 1 0 0. We have also studied the dependence of the TMR on the barrier thickness in a wedge-type sample, and have found that the TMR ratio rapidly decreases with increasing barrier thickness dAlAs in junctions with dAlAs ¿ 1:5 nm. This barrier thickness dependence of the TMR can be explained by tight-binding calculations of tunneling assuming that the wave vector in the direction parallel to the interface is conserved. 2. Sample preparation Fig. 1 illustrates the sample structure and preparation process, using low temperature molecular beam epitaxy (LT-MBE) and patterning by photolithography. After a 100 nm-thick Be-doped ◦ GaAs buJer layer was grown at 580 C on a p+ GaAs (0 0 1) substrate, a Ga1−x Mnx As(x = 4:0%; 50 nm)=AlAs(dAlAs )=Ga1−x Mnx As(x = 3:3%; 50 nm) ◦ trilayer was grown at 250 C. By using a shutter linearly moving in front of the substrate, we changed the barrier thickness dAlAs ranging from 1:3 to 2:8 nm within a wafer of 20 × 20 mm2 . The slope of the wedge was estimated by the growth rate of AlAs,
Fig. 1. Preparation of a wedge-type ferromagnetic semiconductor trilayer heterostructure by LT-MBE and mesa-etched round-shaped MTJs 200 m in diameter.
which was obtained by reMection high-energy electron diJraction (RHEED) oscillations, and the moving speed of the shutter. Preparation of wedge-type samples is important in order to measure the dependence of the TMR of MTJs on the barrier thickness, because the electronic and magnetic properties of the GaMnAs layers are very sensitive to the growth conditions [13]. In addition, undoped 1 nm-thick GaAs spacers were inserted between GaMnAs and AlAs to avoid Mn diJusion into the barrier, which causes spin-Mip scattering, and makes the interfaces smooth. In order to measure tunneling transport, the sample was patterned by photolithography and mesa etching into arrays of round-shaped mesa junctions 200 m in diameter with various barrier thicknesses ranging from 1.3 to 2:8 nm. 3. Tunneling magnetoresistance (TMR) 3.1. Magnetization and TMR The magnetization of the Ga1−x Mnx As(x = 4:0%; 50 nm)=AlAs (3 nm)=Ga1−x Mnx As(x=3:3%; 50 nm)
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Fig. 2. (a) Magnetization of a Ga1−x Mnx As(x = 4:0%; 50 nm)= AlAs(3 nm)=Ga1−x Mnx As(x = 3:3%; 50 nm) trilayer measured by SQUID at 8 K. The specimen size was 3 × 3 mm2 . The vertical axis shows the normalized magnetization M=Ms , where Ms is the saturation magnetization. (b) TMR curves at 8 K of a Ga1−x Mnx As(x = 4:0%; 50 nm)=AlAs(1:6 nm)=Ga1−x Mnx As(x = 3:3%; 50 nm) tunnel junction. The tunnel junctions were mesa-etched diodes 200 m in diameter. Bold solid and dashed curves are major loops, with the magnetic 2eld sweep direction from positive to negative and negative to positive, respectively. A minor loop is shown by a thin solid curve. In both (a) and (b), the magnetic 2eld was applied along the [1 0 0] axis in the plane.
trilayer measured by SQUID at 8 K is shown in Fig. 2(a). In the SQUID measurements, the trilayer sample was cleaved into a square shape with the area of 3 × 3 mm2 . The magnetic 2eld was applied along the [1 0 0] axis in the plane. Pairs of arrows in the 2gure indicate the magnetization directions of the top and bottom GaMnAs layers at diJerent 2elds. Due to the diJerent coercivity of the two GaMnAs layers, we observed a double-step magnetization curve with coercive 2elds of about 60 and 100 Oe. The easy magnetization axis of the ferromagnetic GaMnAs layers lies in the 2lm plane. Fig. 2(b) shows tunnel resistance vs. magnetic 2eld, that is, TMR curves measured at 8 K on a junction
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with dAlAs = 1:6 nm when the magnetic 2eld was applied along the [1 0 0] axis in the plane. The measurements were taken at a constant bias of 1 mV, and so there is no hot carrier eJect. The TMR is de2ned here as (R(H ) − R(0))=R(0), where R(H ) is the resistance at the 2eld of H , and R(0) = 0:014 Pcm2 is taken from a major loop. Bold solid and dashed curves (major loops) in Fig. 2(b) were obtained by sweeping the 2eld from positive to negative and negative to positive, respectively. As shown by the bold solid curve, when the 2eld was swept from the positive saturation 2eld down to negative, R(H ) increased from 0.014 to 0:025 Pcm2 (corresponding TMR was 72%) at H = −110 Oe where the magnetization of one GaMnAs layer reversed and the magnetization con2guration changed from parallel to antiparallel. Sweeping the 2eld further to the negative direction, the R(H ) and the TMR decreased to the initial value (R(H ) = 0:014 Pcm2 ) at H = −125 Oe, where the magnetization of the other GaMnAs layer reversed and the magnetization con2guration became parallel again. The diJerence of the coercive 2elds between the M –H curve in Fig. 2(a) and the TMR curve in Fig. 2(b) is caused by the diJerence in the shape and size of the measured specimens. Note that the TMR value is over 70%, much higher than the TMR previously reported [10,11]. A thin solid curve in Fig. 2(b) shows a minor loop, indicating that the antiparallel con2guration as well as the parallel one are stable. 3.2. Barrier thickness dependence Fig. 3(a) shows the tunnel resistance R for the tunnel junctions measured at 8 K as a function of the barrier thickness dAlAs . The resistance exponentially increased over a wide range from 10−3 to 10 Pcm2 as dAlAs increased, which means that high-quality tunnel junctions were formed with a constant barrier height. In the WKB approximation, the slope of ln R − dAlAs characteristics is given by 2[2m∗ Vb ]1=2 =˜, thereby the product m∗ Vb is estimated to be 0:32m0 [kg eV], where m0 is the free-electron mass, m∗ is the eJective mass of holes, and Vb is the barrier height. The valence band oJset between GaMnAs and AlAs is unknown but it is considered to be close to that (∼ 0:55 eV) of GaAs and AlAs, and the Fermi energy of holes in GaMnAs is 0.1–0:2 eV, thus, the barrier height Vb is ∼ 0:45 eV. Therefore, the eJective mass m∗ of holes which is
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clear at present, this drop could be caused by the decrease of the eJective barrier height because of interface roughness or the image potential. Another possible reason is the ferromagnetic interlayer exchange coupling between GaMnAs layers separated by a very thin AlAs layer [11]. 3.3. Magneto-crystalline anisotropy
Fig. 3. Barrier thickness dependence of (a) the tunnel resistance and (b) the TMR in Ga1−x Mnx As(x = 4:0%; 50 nm)= AlAs(dAlAs )=Ga1−x Mnx As(x=3:3%; 50 nm) tunnel junctions measured at 8 K. In (b), the TMR values were measured with the magnetic 2eld applied along the [1 0 0] and [1 1 0] axes.
responsible for tunneling is roughly estimated to be ∼ 0:7m0 . Fig. 3(b) shows barrier thickness dependence of TMR at 8 K when the magnetic 2eld was applied in-plane along the [1 0 0] and [1 1R 0] axes. The maximum TMR was 75% at dAlAs =1:46 nm when the 2eld was applied along the [1 0 0] axis. In both 2eld directions, with increasing dAlAs (¿ 1:5 nm), the TMR was found to rapidly decrease. At all the values of dAlAs , the TMR was higher when the 2eld was applied along the [1 0 0] axis than along the [1 1 0] axis. The diJerence in the TMR between the two directions of the 2eld is due to the cubic magneto-crystalline anisotropy induced by the zincblende-type GaMnAs crystal structure, where the easy magnetization axis of GaMnAs is 1 0 0, the details of which are reported elsewhere [14]. Although the reason for the drop in the TMR for the junction with dAlAs ¡ 1:4 nm is not
When we measured TMR on many round-shaped mesa tunnel junctions, a variety of diJerent characteristics were observed, as shown in Figs. 4(a) – (d). Here, the magnetic 2eld was applied in plane along the [1 0 0] axis. Since the present tunnel junctions are totally monocrystalline and GaMnAs is considered to have the magneto-crystalline anisotropy with the easy magnetization axis of 1 0 0 [14], the magnetization direction of the top and bottom GaMnAs layers favors to be along one of the four directions ([1 0 0]; [0 1 0]; [1R 0 0], and [0 1R 0]) in the 2lm plane. We attributed these TMR behaviors to the diJerent magnetization con2gurations, as illustrated in the lower panel of Fig. 4. Here, solid and gray arrows are the magnetization directions of the two GaMnAs layers, and time evolutions of magnetization con2guration are depicted when the applied magnetic 2eld is changed from positive (+200 Oe) to negative (−200 Oe). These TMR behaviors are well explained by the analysis of magnetization rotation based on the single domain theory [15]. The multi-value characteristics of TMR due to the magnetocrystalline anisotropy could lead to interesting applications such as multi-value recording and novel logic circuitry. 3.4. Temperature dependence We measured temperature dependence of the TMR for various junctions with diJerent dAlAs , and plotted in Fig. 5 the normalized conductance diJerence IG = IG(T )=IG(8 K), where T is temperature, IG(T ) = GP (T ) − GAP (T ); GP (T ) and GAP (T ) are the junction conductances at T [K] for parallel and antiparallel magnetization, respectively. IG (equivalently, TMR) basically decreased with increasing temperature and vanished at ∼ 50 K, which is the Curie temperature of one of the GaMnAs layers. IG dropped once at ∼ 20 K, because the coercivity of the top and bottom GaMnAs layers is so close (almost same) that the
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Fig. 4. A variety of TMR characteristics of round-shaped mesa tunnel junctions at 8 K. The magnetic 2eld was applied in plane along the [1 0 0] axis. In the lower panel, time evolutions of magnetization con2guration are depicted when the applied magnetic 2eld is changed from positive (+200 Oe) to negative (−200 Oe). Solid and gray arrows are the magnetization directions of the two GaMnAs layers.
window for antiparallel magnetization is too small, which was con2rmed by temperature-dependent magnetization measurements, thus IG was diScult to be observed at around 20 K. A solid line in Fig. 5 is the 2t to the theory IG(T ) = IG0 (1 − T 3=2 )2 , where IG0 is a constant and is 2tted to 1:5 × 10−3 [K −3=2 ], based on thermal spin-wave excitations [16]. The theory can explain the present data, as it did for conventional Co=Al2 O3 =Co(NiFe) MTJs. This means that the dominant contribution to the tunnel conductance is a direct elastic tunneling with the tunneling carrier spin-polarization P decreasing as 1 − T 3=2 . Both the excellent scaling of the junction resistance with the AlAs barrier thickness (Fig. 3(a)) mentioned earlier
and this temperature dependence of IG give strong evidence for TMR junctions.
4. Tight-binding calculation of TMR 4.1. Spin-dependent tunneling with k conservation In conventional Julliere’s model [17], the TMR depends only on the spin-dependent density of states in the two FM electrodes and does not depend on the barrier thickness d, so that the Julliere model cannot explain our experimental results. Since the present GaMnAs=AlAs=GaMnAs heterostructures are
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Fig. 5. Temperature dependence of the normalized conductance diJerence IG (equivalently TMR) for various junctions with diJerent dAlAs = 1:46; 1:58; 1:70; 1:82 nm. The solid line is the 2t to the theory based on thermal spin wave excitations.
epitaxially grown single crystals, the wave vector k of carriers parallel to the interface should be conserved in tunneling. Calculations using the tight-binding theory including k conservation by Mathon [18] seem consistent with our experimental results of the barrier thickness dependence of the TMR. Our experimental results can be qualitatively explained as follows: Fig. 6 shows the Fermi surfaces for up and down spins in two FM electrodes, calculated by the single-orbital tight-binding model, when the magnetization con2guration is (a) parallel and (b) antiparallel. Also, the dispersion of the decaying factor z in the barrier layer was calculated and shown in the middle of the 2gure. The wave vector kz (EF ; k ) normal to the interface in the FM electrodes is determined from EF = E0 + 2t cos(kz a) + w(k ), and the decaying factor z (EF ; k ) in the barrier layer is determined from EF = E0 + 2t cosh(z a) + w(k ), where w(k ) = 2t[cos(kx a) + cos(ky a)]; k = (kx ; ky ) is the wave vector parallel to the 2lm plane, EF is the Fermi energy, E0 is the on-site energy in each layer, t is the nearest-neighbor hopping parameter, and a is the lattice constant [18]. We simply regard spin-polarization in the FM electrodes as the diJerence of E0 between the majority and minority carriers. When the magnetizations of the two FM electrodes are parallel as shown in Fig. 6(a), the majority (minority) spin is the up (down) spin in the both electrodes, so that the carriers can tunnel through all the channels (k ; ). When the magnetizations of the two FM electrodes are antiparallel as shown in Fig. 6(b), the down spin is the majority spin in the right electrode, thus the carriers
with k = |k | ¿ kcut-oJ cannot tunnel, where kcut-oJ is the cut-oJ wave vector which is the largest k in the minority spin band. This diJerence of tunneling between the parallel and antiparallel con2gurations indicates that the TMR is mainly caused by the carriers with large k (¿ kcut-oJ ). However, these carriers with larger k exponentially decay more rapidly during tunneling in the barrier because of larger z , as shown in the middle of Fig. 6. Due to this in-plane dispersion of z (k ), when the barrier thickness d is large, the tunneling conductance is dominated by the carriers with smaller k , which do not much contribute to the TMR. Therefore, the TMR decreases as d increases. 4.2. Calculation of TMR and comparison with the experimental results In order to compare our experimental TMR obtained in the GaMnAs=AlAs=GaMnAs tunnel junctions, we calculated the dependence of TMR on dAlAs using the spin–orbit nearest-neighbor sp3 s∗ model [19,20]. We used tight-binding parameters in Ref. [21] to obtain the realistic band structures of GaAs and AlAs. The eJect of Mn ions in GaMnAs was simpli2ed by introducing an additional term IJx into the intralayer coupling matrices in the sp3 s∗ Hamiltonian. Here, Jx is a 10 × 10 matrix derived from the x component of the total angular momentum J in the planar-orbital basis. We used Jx because the magnetization was along the [1 0 0] axis. This additional term causes the changes of the on-site energies proportional to Jx . The scalar proportional coeScient corresponds to the spin-splitting energy between the two holes | 32 ; 12 and | 32 ; − 12 at the point. In order to calculate TMR, tunneling probability T was 2rst calculated, as shown in Fig. 7, and plotted in the k plane (−0:3 =a 6 kx 6 0:3 =a; −0:3 =a 6 ky 6 0:3 =a), both for parallel and antiparallel magnetizations. The k dependence of T is complex because of the complexity of the valence band of GaMnAs and AlAs. The band parameters used here are shown in the inset of Fig. 8. Despite the complexity, the essential point is as follows. When the AlAs barrier thickness is as thin as 1 monolayer (ML), T has some nonzero values even at large k for the parallel magnetization whereas T is zero at large k for the antiparallel magnetization (see the upper panels of Fig. 7). This diJerence in T between the parallel and antiparallel
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Fig. 6. Fermi surfaces of the simple cubic lattice calculated by the single orbital tight-binding model for up and down spins with the spontaneous spin-splitting in (a) parallel and (b) antiparallel magnetization con2gurations. Dependence of the decaying factor z in the barrier on k is also shown in the middle of the 2gure.
magnetizations leads to large TMR. In contrast, when the AlAs barrier thickness is thicker (5 MLs), T is signi2cantly suppressed at large k for the parallel magnetization due to large z , as described above, thus the diJerence in T between the parallel and antiparallel magnetizations is smaller, resulting in smaller TMR (see the lower panels of Fig. 7). Fig. 8 shows the calculated (solid curve) and measured (solid circles) barrier thickness dependences of the TMR in the present GaMnAs=AlAs=GaMnAs tunnel junctions. We assumed that EF ; V , and were 0.2 [eV], 0.67 [eV], and 0.08 [eV], respectively. The Fermi energy EF and the valence band oJset V were measured from the top of the valence band in the calculated GaMnAs band structure, as shown in the inset of Fig. 8. V = 0:67 [eV] gives the valence band
oJset of 0.55 [eV] when = 0, that is, the case for normal GaAs=AlAs interfaces, which is a reasonable value. Compared with the experimental results, the calculated TMR decreases rapidly in the thinner barrier region. The barrier thickness was evaluated from RHEED oscillations and the moving speed of the shutter, as mentioned before. Since completely accurate alignment of the moving shutter with the substrate in our MBE chamber is diScult, the absolute values of the estimated barrier thickness may not be reliable (though the relative values are reliable), thus, we horizontally shifted the calculated dependence towards right by 0:7 nm (only 2:5 ML) to 2t the experimental results, as shown by a dashed curve in Fig. 8. The 2tting is fairly good, but not perfect partly because the band structure of GaMnAs is still unknown and
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Fig. 7. Tunneling probability T in GaMnAs=AlAs(dAlAs )=GaMnAs tunnel junctions plotted in the k plane (−0:3 =a 6 kx 6 0:3 =a; −0:3 =a 6 ky 6 0:3 =a), both for parallel and antiparallel magnetization con2gurations, when the AlAs barrier thickness dAlAs = 1, and 5 ML.
the model is simple compared with the more complex band structure and=or partly because there could be spin scattering at the interfaces or in the tunnel barrier which is not taken into account. However, the present spin-orbit nearest-neighbor sp3 s∗ model is found to explain the most essential part of the experimental barrier thickness dependence of the TMR. Note that there are three essential points in this model: (1) The cut-oJ wave vector kcut-oJ in the plane exists in the antiparallel con2guration. (2) The decaying factor z in the barrier increases with increasing k . (3) k is con-
served in tunneling. Although these points may not be valid in the conventional MTJs with polycrystalline metallic electrodes, we think that they are valid in the present Ga1−x Mnx As=AlAs=Ga1−x Mnx As tunnel junctions, which are epitaxially grown single crystals. 5. Summary We have grown Ga1−x Mnx As(x = 4:0%; 50 nm)= AlAs(dAlAs )=Ga1−x Mnx As(x = 3:3%; 50 nm) single-
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work, and Prof T. Nishinaga (President of Toyohashi University of Technology) and Prof. S. Naritsuka (Meijo Univ.) for their support. This work was partially supported by the JSPS Research for the Future Program (JSPS-RFTF 97P00202), by the PRESTO project of JST, Toray Science Foundation, and by a Grant-in-Aid for Scienti2c Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan. References Fig. 8. Solid curve represents the calculated dependence of TMR on the barrier thickness dAlAs when the Fermi energy EF = 0:2 eV, the band oJset V = 0:67 eV (both measured from the top of the valence band of GaMnAs), and the spin-splitting = 0:08 eV between the two light holes | 32 ; 12 and | 32 ; − 12 at the point. Inset shows the band dispersion and the relationship of these parameters. The solid curve is horizontally shifted to the dashed curve by 0:7 nm (only 2:5 ML) to 2t the experimental results (solid circles, the magnetic 2eld was along the [1 0 0] axis), because the absolute barrier thicknesses of the junctions are nominal.
barrier tunnel junctions by LT-MBE. In junctions with dAlAs 6 1:6 nm, the TMR of more than 70% (the highest value was 75%) was obtained when the 2eld was applied along the [1 0 0] axis in the plane. The various TMR characteristics were shown and explained by the magnetocrystalline anisotropy of GaMnAs having the easy magnetization axis of 1 0 0. The TMR rapidly decreased as the barrier thickness dAlAs increased for the junctions with dAlAs ¿ 1:5 nm. This barrier thickness dependence of the TMR was explained by calculations assuming that the parallel wave vector of carriers was conserved in tunneling. Acknowledgements We would like to thank Dr. T. Hayashi (now at NTT) for his contribution at the initial stage of this
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