Xue Gao

Shiheng Liang

Anthony Ferri

Weichuan Huang

Didier Rouxel

Xavier Devaux

Xiao-Guang Li

Hongxin Yang

Mairbek Chshiev

Rachel Desfeux

Antonio Da Costa

Guichao Hu

Mathieu Stoffel

Abir Nachawaty

Chunping Jiang

Zhongming Zeng

Jian-Ping Liu

Hui Yang

Yuan Lu
email: yuan.lu@univ-lorraine.fr

Enhancement of ferroelectric performance in PVDF:Fe 3 O 4 nanocomposite based organic multiferroic tunnel junctions

Keywords: poly(vinylidene fluoride), Fe3O4, nanocomposites, multiferroic, tunneling electroresistance

We report on the fabrication of organic multiferroic tunnel junction (OMFTJ) based on an organic barrier of Poly(vinylidene fluoride) (PVDF):Fe3O4 nanocomposite. By adding Fe3O4 nanoparticles into the PVDF barrier, we found that the ferroelectric properties of the OMFTJ are considerably improved compared to that with pure PVDF barrier. It can lead to a tunneling electroresistance (TER) of about 450% at 10K and 100% at room temperature (RT), which is much higher than that of the pure PVDF based device (70% at 10K and 7% at RT). OMFTJs based on the PVDF:Fe3O4 nanocomposite could open new functionalities in smart multiferroic devices via the interplay of the magnetism of nanoparticle with the ferroelectricity of the organic barrier.

The use of a ferroelectric thin film as barrier in a magnetic tunnel junction (MTJ) adds an additional level of functionality. In such a multiferroic tunnel junction (MFTJ), the tunneling electroresistance (TER) and tunneling magnetoresistance (TMR) effects coexist, [START_REF] Zhuravlev | Ferroelectric switch for spin injection[END_REF] which could possibly lead to new applications such as multi-level data storage devices. [START_REF] Garcia | Ferroelectric tunnel junctions for information storage and processing[END_REF][START_REF] Gajek | Tunnel junctions with multiferroic barriers[END_REF] Compared to inorganic spintronics, its organic counterpart is very appealing because of the long spin lifetime of charge carriers in addition to their relatively low cost, flexibility, and chemical diversity. [START_REF] Dediu | Spin routes in organic semiconductors[END_REF][START_REF] Sun | Active control of magnetoresistance of organic spin valves using ferroelectricity[END_REF][START_REF] Szulczewski | A spin of their own[END_REF] As one of the most typical ferroelectric polymers, poly (vinylidene fluoride) (PVDF) has been widely used in modern electronic systems and devices, whose ferroelectric performance relies mainly on its β phase content. [START_REF] Jiang | High β phase content in PVDF/CoFe2O4 nanocomposites induced by DC magnetic fields[END_REF] Moreover, PVDF and the related copolymers can form high quality ordered layers [START_REF] Lovinger | Ferroelectric Polymers[END_REF] and exhibit robust ferroelectricity down to monolayer thickness. [START_REF] Bune | Two-dimensional ferroelectric films[END_REF] Their performances are comparable to that of perovskite oxide ferroelectrics, [START_REF] Nakhmanson | Collective Polarization Effects in β-Polyvinylidene Fluoride and its Copolymers with Tri-And Tetrafluoroethylene[END_REF] making them suitable as tunneling barriers for organic multiferroic tunnel junctions (OMFTJs). 11 , 12 Recently, our group demonstrated the ferroelectric control of the "spinterface" spin-polarization in the PVDF or P(VDF-TrFE) based OMFTJs, [START_REF] Liang | Ferroelectric control of organic/ferromagnetic spinterface[END_REF][START_REF] Liang | Quenching of Spin Polarization Switching in Organic Multiferroic Tunnel Junctions by Ferroelectric 'Ailing-Channel' in Organic Barrier[END_REF] which opens new functionalities in controlling the injection of spin polarization into organic materials via the ferroelectric polarization of the barrier. Further improvement of the ferroelectric properties of the OMFTJ devices is urgently required to promote potential memristor and spintronics applications. Magnetite Fe3O4 has recently gained an increasing interest since bulk Fe3O4 has a high Curie temperature (Tc~850K) and is almost fully spin-polarized at room temperature (RT). Both properties are of great interests for applications in giant magneto-electronic and spin-valve devices. [START_REF] Goya | Static and dynamic magnetic properties of spherical magnetite nanoparticles[END_REF] It has been reported previously that ferroferric oxide (Fe3O4) spherical shaped nanoparticles are excellent fillers for high-dielectric-constant polymer composites. 16 , 17 , 18 Some researchers found that the ferroelectric properties of PVDF are improved by adding Fe3O4 nanoparticles. 19 , 20 , 21 , 22 This is generally explained by the interaction between the nanoparticles and the CH2 groups of the polymer chains, which promotes the nucleation of the polar β phase of PVDF. [START_REF] Goncalves | Magnetoelectric CoFe2O4/polyvinylidene fluoride electrospun nanofibres[END_REF][START_REF] Martins | Role of nanoparticle surface charge on the nucleation of the electroactive betapoly(vinylidene fluoride) nanocomposites for sensor and actuator applications[END_REF] However, up to now, there are still no reports on the impact of Fe3O4 nanoparticles on ferroelectric properties of PVDF based ferroelectric tunneling junction (FTJ) or OMFTJ.

In this Letter, we report on the fabrication of OMFTJs based on La0.6Sr0.4MnO3/PVDF:Fe3O4 nanocomposites/Co structures. By dispersing Fe3O4 nanoparticles into the PVDF barrier, we found that the ferroelectric properties of PVDF are much improved, showing a smaller polarizing voltage for polarization switching. Consequently, the OMFTJs based on the nanocomposites demonstrate superior performances: much larger amplitude of the TER and the improved thermal stability compared to the OMFTJs with a pure PVDF barrier.

OMFTJs based on La0.6Sr0.4MnO3/PVDF:Fe3O4 nanocomposites/Co/Au structures were prepared as follows. Firstly, a 50 nm thick La0.6Sr0.4MnO3 (LSMO) film was grown epitaxially on a SrTiO3 (STO) (001) substrate at 750ºC using DC magnetron sputtering. The LSMO layer was then etched by a hydrogen chloride solution (37%) to obtain a pattern consisting of 200 µm width bars as the bottom electrodes. Secondly, PVDF:Fe3O4 nanocomposite films were prepared by spin-coating with the following procedures. The PVDF solution was prepared by dissolving PVDF powder into a dimethylformamide (DMF) solution with a concentration of 20mg/mL. The Fe3O4 nanoparticles diluted in toluene (5nm nominal size purchased from Sigma-Aldrich) with a concentration of 5mg/mL were added into the PVDF solution with a ratio of 1:1 in volume. The mixture was sonicated (bathtype sonication) for 5h. The mixed suspension was then spin-coated onto the pre-patterned LSMO/STO substrate with a speed of 3000 RPM for 1 min. Subsequently, the as-coated film was annealed at 150ºC in Ar atmosphere for 2h to improve the crystallization of the ferroelectric β phase.

The thickness of the PVDF:Fe3O4 barrier was checked by the profilometer to be about 18 nm. Thirdly, the sample is then loaded into a molecular beam epitaxy (MBE) system (with a base pressure of 1×10 - 10 Torr) for the growth of the top Co/Au electrodes. 10 nm thick Co and 10 nm thick Au were grown sequentially by e-beam evaporation with an in-situ shadow mask. To minimize the metal diffusion into organic materials, [START_REF] Probst | Diffusion of metals into organic films[END_REF][START_REF] Xiong | Giant magnetoresistance in organic spin-valves[END_REF] the temperature of the substrate was maintained at around 90K during the growth of the top electrode. The final junction, that is schematically shown in Fig. 3(a), has a typical size of about 200×200 µm [START_REF] Garcia | Ferroelectric tunnel junctions for information storage and processing[END_REF] .

The surface morphologies of both pure PVDF and PVDF:Fe3O4 nanocomposite films were compared by atomic force microscopy (AFM) (Fig. 1(a) and 1(b), respectively). The pure PVDF surface exhibits a needle-like crystalline feature with a typical width of about 20 nm and a typical length of about 50 nm, which is a characteristic of the ferroelectric β phase of PVDF. [START_REF] Mabuchi | Electric-Field-Induced Polarization Enhancement of Vinylidene Fluoride/Trifluoroethylene Copolymer Ultrathin Films[END_REF] The rootmean square (RMS) roughness is about 3.2 nm for a 0.8×0.8 μm 2 scanning area. For the PVDF:Fe3O4 nanocomposite film, the surface roughness increases to reach a RMS of 7.1nm for a 0.8×0.8 μm 2 scanning area. One can observe spherical shaped Fe3O4 nanoparticle inclusions, which are randomly distributed in the PVDF layer. The size of the Fe3O4 inclusion particles is not homogenous, ranging from nm to µm size due to the aggregation of the magnetic nanoparticles. Conductive AFM (c-AFM) measurement is the most direct way to identify the existence of pinholes. Nanoscale conductivity variations were probed through current mapping experiments using the conductive-AFM technique.

A Ti/Ir-coated silicon tip and cantilever with a stiffness of 3Nm -1 were used. DC bias voltages ranging from -10 and +10V between the grounded AFM tip and the bottom electrode were applied during scanning. The electrical conductivity map recorded over 20×20 µm² large area are displayed in Fig. 1(c) and 1(d) respectively for the samples with pure PVDF and PVDF:Fe3O4 nanocomposite films. No conducting path is obtained for an applied bias of +5V, as demonstrated by the uniform contrast associated to insignificant current. Such absence of conduction signal was confirmed in several places of the sample surface regardless the applied bias voltage when varying between -10 and +10V. This confirms that the contribution of pinhole on transport is very limited despite the inhomogeneity of particle size. In addition, it also proves that the polarizing voltage around 4V range does not induce a damage of organic barrier with the formation of pinholes and leakage currents.

The ferroelectric properties of both pure PVDF and PVDF:Fe3O4 nanocomposite films were compared by piezo-response force microscopy (PFM). In the PFM maps shown in Fig. 1(e) and 1(f), the films were firstly polarized with a positively biased tip over the area indicated with a dashed square. Then, a negative poling bias was subsequently applied in the middle area to reverse the polarization. As observed from the strong contrast of PFM phase in the two polarization states, the polarizations of both pure PVDF and PVDF:Fe3O4 nanocomposite films are quite homogenous.

Moreover, a complete switching of the polarization can be achieved in both cases. Nevertheless, the difference in ferroelectric properties are highlighted by the local PFM phase and amplitude hysteresis loops, which are shown in Fig. 1(g) and 1(h). As observed in Fig. 1(h), the coercivity of the polarizing voltage is about 0.2 V, that is much smaller than the corresponding value (1.2V) measured on the pure PVDF film (Fig. 1(g)). This indicates that the switching of the polarization is much easier in PVDF:Fe3O4 nanocomposite films due to the improvement of their ferroelectric properties.

To investigate the magnetic properties of the Fe3O4 particles dispersed inside the PVDF, we have measured the magnetization of a Si/Au/PVDF:Fe3O4 sample with a superconducting quantum interference device (SQUID) magnetometer. Fig. 2 shows the temperature dependent magnetic hysteresis loops measured of the Si/Au/PVDF:Fe3O4 sample. It clearly reveals a superparamagnetic behavior of the Fe3O4 particles with zero remnant magnetization. Although Fe3O4 particles form clusters due to aggregation, each particle still has its own magnetization and its direction can be randomly flipped under the influence of temperature. In the absence of an external magnetic field, the average magnetization is zero. At large field, the magnetizations of all particles are aligned along the direction of the applied magnetic field. The saturation of the magnetization is obtained for an applied field of about 0.2T at 10 K and 0.7T at 300K. The saturation magnetization increases when the temperature decreases. The field cooling (FC) and zero-field cooling (ZFC) measurements (see inset of Fig. 2) allow us to deduce the information of blocking temperature and estimate the nanoparticle size. [START_REF] Barrera | Fe3O4 nanoparticles and nanocomposites with potential application in biomedicine and in communication technologies: Nanoparticle aggregation, interaction, and effective magnetic anisotropy[END_REF] The moment is measured with a small field of +5mT for ZFC and FC (cooling with +5T) conditions. From the ZFC curve, the blocking temperature can be obtained to be around 15 K. This corresponds to a 5 nm size for the Fe3O4 nanoparticles, [START_REF] Barrera | Fe3O4 nanoparticles and nanocomposites with potential application in biomedicine and in communication technologies: Nanoparticle aggregation, interaction, and effective magnetic anisotropy[END_REF] which is in a good agreement with the nominal particle size of the purchased product.

A scheme of the LSMO/PVDF:Fe3O4/Co/Au device used for the electrical measurements is schematically shown in Fig. 3(a). I-V measurements were performed using a two-terminal geometry by using a Keithley 2400 as a voltage source and a Keithley 6487 picoamperemeter to measure the current. To ferroelectrically polarize the PVDF barrier, we have applied different voltage pulses to the junction with a ramp of 0.1V/s and a duration of 1s. In Fig. 3(b), two distinct I-V curves associated with different junction resistances were obtained after applying opposite polarizing voltages. Good tunneling properties are obtained from the non-linear variation of the I-V characteristics, which also confirms that the Fe3O4 inclusions do not create short circuit or pinholes in the PVDF barrier. Fig. 3(c) and 3(d) show the magneto-resistance loops of the device after applying a positive and a negative polarization, respectively. While scanning the magnetic field, the magnetization of the LSMO and Co are switched separately to get either a parallel or an antiparallel magnetization configurations thus resulting in the magnetoresistance curves. The TMR is defined by the following relations: 𝑇𝑀𝑅 = 𝑅 𝐴𝑃 -𝑅 𝑃 𝑅 𝑃 × 100% for positive TMR, and 𝑇𝑀𝑅 = 𝑅 𝐴𝑃 -𝑅 𝑃 𝑅 𝐴𝑃 × 100% for negative TMR, where RP and RAP are the junction resistance for parallel and antiparallel magnetizations alignment of two electrodes, respectively. The device gives TMR values of +9.2% and -11.3% when it is positively and negatively polarized, respectively. The change of the TMR sign with different PVDF polarizations could be explained by the sign change of the spin-polarization at the organic/ferromagnetic "spinterface" depending on the ferroelectric polarization of the organic barrier. [START_REF] Liang | Ferroelectric control of organic/ferromagnetic spinterface[END_REF] Another possible explanation is that some oxygen atoms could exist at Co/PVDF interface.

Switching the ferroelectric polarization of PVDF shifts the Co-O antibonding state at the oxidized interface due to the screening of the polarization charges, which affects the interface transmission properties and reverses the spin-polarization at the Co/PVDF interface. [START_REF] Velev | Multiferroic Tunnel Junctions with Poly(Vinylidene Fluoride)[END_REF] In addition to the TMR effect, a clear difference between the two parallel resistances (RP) for the two polarizations can be observed. The tunneling electroresistance is defined as: 𝑇𝐸𝑅 = 𝑅 𝑃 𝐷𝑜𝑤𝑛 -𝑅 𝑃 𝑈𝑝 𝑅 𝑃 𝑈𝑝 × 100%, where 𝑅 𝑃 𝐷𝑜𝑤𝑛 and 𝑅 𝑃 𝑈𝑝 are the parallel resistance when the PVDF is in the "down" and "up" polarization states, respectively. The TER of the device reaches about 215%. The four resistance states associated with different magnetization and ferroelectric configurations prove the realization of the OMFTJ function with a PVDF barrier containing Fe3O4 nanoparticles. The TMR observed in PVDF:Fe3O4 OMFTJ is comparable to that of pure PVDF OMFTJ. [START_REF] Liang | Ferroelectric control of organic/ferromagnetic spinterface[END_REF] However, the TER measured in PVDF:Fe3O4 nanocomposite films is 3 times higher than that of pure PVDF OMFTJ (~75%), [START_REF] Liang | Ferroelectric control of organic/ferromagnetic spinterface[END_REF] which confirms the enhancement of the ferroelectric performance in PVDF:Fe3O4 nanocomposite based OMFTJs. compared to the first loop (293%). When the ferroelectric domains are not fully polarized with the applied electric field, a larger opposite field is necessary to switch back the polarization, thus making the loop more and more opened. [START_REF] Guo | Thermally Induced Cooperative Molecular Reorientation and Nanoscale Polarization Switching Behaviors of Ultrathin Poly(vinylidene fluoridetrifluoroethylene) Films[END_REF] This validates that the observed resistance switching is due to the ferroelectricity of PVDF and excludes other mechanisms, such as the migration of oxygen vacancy in LSMO surface [START_REF] Grünewald | Voltage-Controlled Oxide Barriers in Organic/Hybrid Spin Valves based on Tunneling Anisotropic Magnetoresistance[END_REF] or a reversible redox reaction of electrodes [START_REF] Rouco | Quasiparticle tunnel electroresistance in superconducting junctions[END_REF] . To further optimize the TER, we have fabricated several samples by varying the PVDF:Fe3O4 barrier thickness. Fig. 3(f) shows the TER as a function of the barrier thickness and the corresponding resistance for the negative polarization state. It is found that the optimized thickness is about 18 nm. Both a lower and a larger barrier thickness leads to a decreasing TER value. These results are in good agreement with our previous thickness dependent results in P(VDF-TrFE) OMFTJs. [START_REF] Liang | Quenching of Spin Polarization Switching in Organic Multiferroic Tunnel Junctions by Ferroelectric 'Ailing-Channel' in Organic Barrier[END_REF] We have shown that the decreasing TER value for the device with a thin barrier is mainly due to the incomplete ferroelectric polarization of the barrier. [START_REF] Liang | Quenching of Spin Polarization Switching in Organic Multiferroic Tunnel Junctions by Ferroelectric 'Ailing-Channel' in Organic Barrier[END_REF] For the thicker barrier, the tunneling mechanism is dominated by thermally activated hopping inside the barrier. [START_REF] Lu | Spin-polarized inelastic tunneling through insulating barriers[END_REF] Moreover, the larger interface roughness induced by the larger thickness is also detrimental to the ferroelectric properties. [START_REF] Liang | Ferroelectric control of organic/ferromagnetic spinterface[END_REF] Finally, we compare the temperature dependence of the TER for OMFTJs with a pure PVDF barrier and a PVDF:Fe3O4 nanocomposite barrier, as shown in Figs. 4(a) and 4(b). For both devices, we have polarized the junctions at 10K and separately measured the junction resistance with increasing temperature in both polarization states. For the device with pure PVDF (Fig. 4(a)), the resistance variations for both polarization states appear rather complicated, indicating that several mechanisms influencing the tunneling behavior are at work. These mechanisms could include thermal activation of the hopping process, thermal strain in the PVDF or thermal relaxation of ferroelectric domains. In the temperature range T>120K (indicated by dashed line), the resistance in the positive polarization state decreases, while it increases in the negative polarization state. The disappearing of the resistance difference for both polarization states results in a rapid drop of the TER from 80% at 120K to 7% at RT. This indicates that the thermal fluctuation of the ferroelectric domains is main mechanism to be responsible for the temperature dependence of resistance in the temperature range higher than 120K. [START_REF] Zhang | Thermal Fluctuations of Ferroelectric Nanodomains in a Ferroelectric-Dielectric PbTiO3=SrTiO3 Superlattice[END_REF] One can then estimate the energy barrier between the two polarization states to be about kBT=10meV from this characteristic temperature of 120K. As a comparison, the PVDF:Fe3O4 based OMFTJ shows a much better thermal stability of the ferroelectric properties.

Firstly, the characteristic temperature is shifted to 170K (indicated by the dashed line in Fig. 4(b)), indicating an increased energy barrier (corresponding to kBT=14meV) between the two polarization states. Secondly, the resistance contrast decrease is much less pronounced when the temperature increases. It is noteworthy that one can still obtain 100% TER at room temperature.

The improvement of the ferroelectric properties of PVDF by adding Fe3O4 nanoparticles can be explained by the following reasons. Firstly, the interaction between the negatively charged surface of the nanoparticles and the positively charged polymer CH2 groups can promote the nucleation of the polar β phase of PVDF, [START_REF] Goncalves | Magnetoelectric CoFe2O4/polyvinylidene fluoride electrospun nanofibres[END_REF][START_REF] Martins | Role of nanoparticle surface charge on the nucleation of the electroactive betapoly(vinylidene fluoride) nanocomposites for sensor and actuator applications[END_REF] which gives the main contribution to the ferroelectricity of the PVDF barrier. Secondly, the addition of Fe3O4 nanoparticles brings more position for charge accumulation at the internal interfaces. The migration and accumulation of charge carriers can result in a homogenous polarization and a high dielectric constant. 20, 36 , 37 , 38 Thirdly, PVDF:Fe3O4 nanocomposite exhibits multiferroic properties with significant magneto-electric (ME) coupling at PVDF/particle interfacial regions, that could result in the enhancement of the ferroelectric properties. [START_REF] Prabhakaran | Ferroelectric and magnetic studies on unpoled Poly (vinylidine Fluoride)/Fe3O4 magnetoelectric nanocomposite structures[END_REF][START_REF] Li | Nanocomposites of ferroelectric polymers with TiO2 nanoparticles exhibiting significantly enhanced electrical energy density[END_REF] In addition, due to the ME coupling between the PVDF host and the Fe3O4 magnetic nanoparticles, the polarizing electric field could also alter the orientation of magnetization of Fe3O4 particles and affect the spin-dependent interface transmission probabilities. [START_REF] Merodio | Electric Field Control of the Resistance of Multiferroic Tunnel Junctions with Magnetoelectric Antiferromagnetic Barriers[END_REF] In summary, we have fabricated La0.6Sr0.4MnO3/PVDF:Fe3O4 nanocomposite/Co OMFTJ. It is found that the ferroelectric properties of the OMFTJs can be considerably improved by adding Fe3O4 nanoparticles to the PVDF barrier. The PVDF:Fe3O4 OMFTJ shows a high TER of about 450% at 10K, which is six times larger than that of a pure PVDF based device. In addition, the higher energy barrier (14meV) between two polarization states ensures a better thermal stability of the OMFTJ with Fe3O4 nanoparticles, which can maintain a TER about 100% even at room temperature. The enhanced ferroelectricity of OMFTJ based on the PVDF:Fe3O4 nanocomposite will promote the OMFTJ for memristor and spintronics applications. V and -2 V for the two PVDF polarization states. The polarizing voltage is only applied at 10 K before increasing the temperature.

Fig. 3 (

 3 Fig. 3(e) shows the two successive loops of the parallel junction resistance RP as a function of

FiguresFIG. 1 .FIG. 2 .FIG. 3 .FIG. 4 .

 1234 Figures

Acknowledgements

We acknowledge the support from the French National Research Agency (ANR) FEOrgSpin project (Grant No. ANR-18-CE24-0017) and SIZMO2D project (Grant No. ANR-19-CE24-0005-02). We also thank the PHC CAI YUANPEI 2017 (N° 38917YJ) program, ICEEL (INTER-Carnot) BlueSpinLED and ICEEL (international) SHATIPN projects. The Région Hauts-de-France and FEDER (EU) under the CPER project "Chemistry and Materials for a Sustainable Growth" is


Bingshan Tao

Caihua Wan

Ping Tang

Jiafeng Feng

Hongxiang Wei

Xiao Wang

Stéphane Andrieu

Hongxin Yang

Mairbek Chshiev

Xavier Devaux

Thomas Hauet

François Montaigne

Stéphane Mangin

Michel Hehn

Daniel Lacour

Xiufeng Han
email: xfhan@iphy.ac.cn

Yuan Lu
email: yuan.lu@univ-lorraine.fr

Coherent Resonant Tunneling through Double Metallic Quantum-Well States

Keywords: quantum well, magnetic tunnel junction, resonant tunneling, magnetoresistance

Study of resonant tunneling through multi-metallic quantum well (QW) structure is not only important for the fundamental understanding of quantum transport, but also for the great potential to generate advanced functionalities of spintronic devices. However, it remains challenging to engineer such structure due to the short electron phase coherence length in metallic QW system. Here, we demonstrate the successful fabrication of double-QW structure in a single fully epitaxial MTJ heterostructure, where two Fe QW layers are sandwiched between three MgAlOx tunnel barriers. We show clear evidence of the coherent resonant tunneling through the discrete QW states in the two QWs. The coherent resonant tunneling condition is fulfilled only when the middle barrier between the two QWs is thin enough and available QW states are present simultaneously in both QWs under a certain bias. Compared to the single QW structure, the resonant tunneling in double-QW MTJ produces strong conductivity oscillations with much narrower peak width (about half) owing to the enhanced energy filtering effect. This study presents a comprehensive understanding of the resonant 2 tunneling mechanism in MTJ with multiple QWs, which is essential for future development of new spintronic devices operating in the quantum tunneling regime.

Introduction

Resonant tunneling in quantum well (QW) structures has been extensively studied because of its importance in the field of nanoelectronic science and technology. [START_REF] Tsu | Tunneling in a finite superlattice[END_REF] Recently, in metallic QW system, the combination of the tunneling magnetoresistance (TMR) [START_REF] Julliere | Tunneling between ferromagnetic films[END_REF][START_REF] Moodera | Large magnetoresistance at room temperature in ferromagnetic thin film tunnel junctions[END_REF] effect with resonant tunneling through metallic QW states in magnetic tunnel junctions (MTJs) has triggered considerable interest in the new functionality of spintronic devices. [START_REF] Yuasa | Spin-polarized resonant tunneling in magnetic tunnel junctions[END_REF][START_REF] Chshiev | Magnetic Diode Effect in Double Barrier Junctions[END_REF][START_REF] Kalitsov | Impurity-induced tuning of quantum well states in spin-dependent resonant tunneling[END_REF][START_REF] Lu | Spin-dependent resonant tunneling through quantum-well states in magnetic metallic thin films[END_REF][START_REF] Wang | First-principles theory of quantum well resonance in double barrier magnetic tunnel junctions[END_REF] In these structures, the discrete spin-dependent QW states can be formed in the middle metallic QW layer sandwiched between two barriers. The QW potential barrier can be formed either by metallic layer using the symmetry dependent Bloch state orbital band structure, [START_REF] Teixeira | Observation of spindependent quantum well resonant tunneling in textured CoFeB layers[END_REF][START_REF] Sheng | Detailed analysis of spin-dependent quantum interference effects in magnetic tunnel junctions with Fe quantum wells[END_REF][START_REF] Greullet | Evidence of a symmetry-dependent metallic barrier in fully epitaxial MgO based magnetic tunnel junctions[END_REF][START_REF] Niizeki | Enhanced tunnel magnetoresistance due to spin dependent quantum well resonance in specific symmetry states of an ultrathin ferromagnetic electrode[END_REF] or by a double oxide tunneling barriers with a much higher barrier height for better electron confinement. [START_REF] Zeng | Oscillatory tunnel magnetoresistance in double barrier magnetic tunnel junctions[END_REF][START_REF] Nozaki | Quantum oscillation of the tunneling conductance in fully epitaxial double barrier magnetic tunnel junctions[END_REF][START_REF] Liu | CoFe alloy as middle layer for strong spin dependent quantum well resonant tunneling in MgO double barrier magnetic tunnel junctions[END_REF] Since the QW states are often formed in the majority spin channel, [START_REF] Yuasa | Spin-polarized resonant tunneling in magnetic tunnel junctions[END_REF][START_REF] Wang | First-principles theory of quantum well resonance in double barrier magnetic tunnel junctions[END_REF] the conductance in parallel magnetic configuration can be enhanced when the injector Fermi level is aligned with the QW state at resonance, resulting in an enhanced TMR ratio. [START_REF] Yuasa | Spin-polarized resonant tunneling in magnetic tunnel junctions[END_REF] A record high resonant TMR (4000%) has been reported for a double barrier MTJ measured with point-contact technique at 4.2K. [START_REF] Iovan | Spin diode based on Fe/MgO double tunnel junction[END_REF] In semiconductor materials, multi-QW structures have already been extensively studied, [START_REF] Esaki | Resonant tunneling in semiconductor double barriers[END_REF] such as resonant-tunneling diode, [START_REF] Brown | Oscillations up to 420 GHz in GaAs/AlAs resonant tunneling diodes[END_REF] multi-quantum well light emitting diode and laser [START_REF] Zory | Quantum Well Lasers[END_REF] etc. When the thickness of the barrier and QW is thin enough, the multi-QWs form the superlattice structure and the QW states in different wells can hybridize with each other to create new sub-band structure, [START_REF] Esaki | New transport phenomenon in a semiconductor "superlattice[END_REF][START_REF] Davies | Tunneling between two strongly coupled superlattices[END_REF] which gives rise to many novel features for electronic and optronic properties. However, up to now, no experimental results have been reported for the metallic multi-QW structures. The general reason is due to the difficulty to keep a good electron phase coherence when resonant tunneling through multi metallic QWs. The decoherence process is originated from interface roughness, [START_REF] Chshiev | Influence of quantum well states on transport properties of double barrier junctions[END_REF] or inelastic scattering in the QW and at the interface, [START_REF] Jonsonand | Effect of inelastic scattering on resonant and sequential tunneling in double barrier heterostructures[END_REF] which can absorb and re-emit electrons losing their phase information. In addition, the small electron mean-free path in the metals (Fe: 1.5nm) [START_REF] Gurney | Direct Measurement of Spin-Dependent Conduction-Electron Mean Free Paths in Ferromagnetic Metals[END_REF] also results in a rapid energy thermalization due to the electron-electron or electron-phonon scattering, which prevents electrons dwelling on the QW states before tunneling into a second QW. Those are the reason why elaborating efficient multi-QW structures is very challenging.

In our previous work, [START_REF] Tao | Long-range phase coherence in doublebarrier magnetic tunnel junctions with a large thick metallic quantum well[END_REF] by using MgAlOx as barrier [START_REF] Tao | Perpendicular magnetic anisotropy in Ta|Co40Fe40B20|MgAl2O4 structures and perpendicular CoFeB|MgAl2O4|CoFeB magnetic tunnel junction[END_REF][START_REF] Belmoubarik | MgAl2O4(001) based magnetic tunnel junctions made by direct sputtering of a sintered spinel target[END_REF][START_REF] Ikhtiar | Giant tunnel magnetoresistance in polycrystalline magnetic tunnel junctions with highly textured MgAl2O4(001) based barriers[END_REF][START_REF] Zhang | Spinel oxides: Δ1 spin-filter barrier for a class of magnetic tunnel junctions[END_REF] to form the QW, we demonstrated the long-range phase coherence in thick Fe QW up to 12 nm, which was attributed to the minimizing of interfacial strain at the Fe/MgAlOx interface due to the small lattice mismatch between Fe and MgAlOx. [START_REF] Sukegawa | Tunnel magnetoresistance with improved bias voltage dependence in lattice-matched Fe/spinel MgAl2O4/Fe(001)MgAl2O4/Fe(001) junctions[END_REF][START_REF] Sukegawa | Enhanced tunnel magnetoresistance in a spinel oxide barrier with cation-site disorder[END_REF] In this work, by taking advantage of the long-range phase coherence in Fe/MgAlOx QW structure, we have successfully fabricated fully epitaxial double-QW MTJs with three MgAlOx tunnel barriers. The resonant tunneling through two QW states in a specifically designed double-QW structure has been evidenced by magneto-transport measurements. The understanding of the resonant tunneling mechanism in multi-QW MTJ provides efficient ways to engineer new functionalities for quantum resonant tunneling spintronic devices.

Results and Discussion

The single and double quantum-well (SQW and DQW) samples namely MgO substrate//MgO (10nm)/Fe (45 nm)/SQW or DQW/Fe (10 nm)/Co (10nm)/Au (10nm) were grown in a molecular beam epitaxy (MBE) chamber. Three types of DQW structures were designed in this study with the stack structures from bottom to top as following: Sample I: MgAlOx(3 MLs)/Fe(9 nm)/MgAlOx( 6MLs, etching stop layer)/Fe(9 nm)/MgAlOx(3 MLs), Sample Ⅱ: MgAlOx(6 MLs, etching stop layer)/Fe(9 nm)/MgAlOx (6 MLs)/Fe(7.7 nm)/MgAlOx (6 MLs) and Sample Ⅲ: MgAlOx(6 MLs, etching stop layer)/Fe(7.7 nm)/MgAlOx(3 MLs)/Fe(7.7 nm)/MgAlOx(6 MLs). One SQW sample (Sample IV) was grown to compare with DQW Sample III with the structure: MgAlOx(6 MLs)/Fe(7.7 nm)/MgAlOx(6 MLs, etching stop layer). Here, ML indicates atomic monolayer and the thickness of barrier was controlled by the high-energy electron diffraction (RHEED) intensity oscillation recorded during growth. The detailed condition can be found in Methods section and Supplementary S1. After elaboration, E-beam lithography was used to form the nanopillar junctions, with elliptical shape of 120240nm 2 (shown in the inset of Fig. 1(a)). During the fabrication of nanopillar structure for SQW or DQW MTJ, the ion milling etching was stopped in a certain layer named stop layer. Please see in Supplementary S2 the effect of the position of the stop layer. For the two-terminal magneto-transport measurements, the negative bias voltage corresponds to the injection of electrons from top to bottom electrodes.

Scanning transmission electron microscope (STEM) characterizations was performed to verify the structure of the DQW MTJs. Fig. 1

Demonstration of the formation of double QWs in one MTJ

Our first goal is to demonstrate the successful realization of DQW states in one MTJ structure.

To do that, one has to be able to grow the QW structure on relative thick tunneling barrier in order to measure a sizable tunneling resistance. In our previous work, [START_REF] Tao | Long-range phase coherence in doublebarrier magnetic tunnel junctions with a large thick metallic quantum well[END_REF] the QW layer has been grown on the thin 3ML thick MgAlOx or MgO bottom barriers. This thickness was too thin to obtain a reasonable junction resistance even with a nanopillar structure. The bottom barrier thickness should be further increased. Nevertheless, in that case the QW states are found to be attenuated rapidly when increasing the thickness of the bottom MgAlOx layer (see Supplementary S3). This could be due to the increase of the surface roughness with the thickness of the oxide layer, resulting in the decoherence of electron phase at the MgAlOx/Fe interface. [START_REF] Chshiev | Influence of quantum well states on transport properties of double barrier junctions[END_REF] Fortunately, we have found that the 6ML thick MgAlOx could be a good compromise to obtain both the QW states and a measurable resistance for the nanopillar junctions. Based on the aforementioned reasons, we have designed the triple-barrier MTJ (Sample I) to demonstrate the formation of the double QW states. The core structure comprises two thin barriers at both sides and one thick barrier in the middle separated by two Fe QW layers with identical thicknesses, as schematically shown in Fig. 2(a). In this structure, the resistance of the thin barrier is 100 times lower than that of the thick barrier, so that most of bias voltage drop occurs within the thick barrier. The QW energy levels of the bottom and top Fe QW layers are almost aligned with the Fermi levels (EF) of the under and upper bulk Fe electrodes, respectively. As shown in Fig. 2(b), when the negative bias is applied, EF of the upper Fe electrode and the top QW energy levels are lifted up together. When the energy of electrons matches with the discrete QW states in the bottom QW layer under a specific bias, it results in the resonant tunneling and a local maximum of conductance. Thus, the oscillations of the conductance under the negative bias reflects the QW states formed in the bottom Fe QW layer. In a similar way, the QW states within the top QW layer can be detected by applying a positive bias, as schematically shown in Fig. 2(c). If the QW states can be formed in both QW layers, we expect to observe symmetric conductivity oscillation with bipolar bias (both positive and negative applied bias). the Fe[100] easy axis direction and the TMR ratio is calculated by (RAP-RP)/RP×100%, where RAP and RP are the resistances of the antiparallel (AP) and parallel (P) magnetization configurations of the two adjacent QW layers, respectively. Since the middle thick barrier mainly dominates the junction resistance, the TMR ratio is indeed determined by the P and AP states of the two QW layers. From the TMR curve, it is found that the full AP state is difficult to reach due to the similar coercivity of the two Fe QW layers. Nevertheless, we still get a TMR ratio of 51% at RT due to the dipolar coupling between the two Fe QW layers within the nanopillar structure. [START_REF] Matsumoto | Spin-torque-induced switching and precession in fully epitaxial Fe/MgO/Fe magnetic tunnel junctions[END_REF] Remarkably, quite symmetric oscillations in the differential conductance are observed under negative and positive bias in both P and AP states, as shown in Fig. 2(d) and (e). The amplitude of oscillation is much stronger in P state than that in AP state, while the oscillation periodicity can be well matched in both magnetization configurations and the oscillation is still detectable up to RT. The observation of conductivity oscillation in the AP state can be understood due to the band folding effect in the spinel MgAl2O4 MTJ, resulting in the existence of 1 conductive channel in the minority spin states, as demonstrated by the ab-initio calculation. [START_REF] Miura | First-principles study of tunneling magnetoresistance in Fe/MgAl2O4/Fe(001) magnetic tunnel junctions[END_REF] In Fig. 2(g), the differential TMR (DTMR), calculated from the differential conductance defined as

DTMR = [(𝑑𝐼 𝑑𝑉) ⁄ -(𝑑𝐼 𝑑𝑉 ⁄ ) ] (𝑑𝐼 𝑑𝑉 ⁄ ) ⁄
, shows clear oscillations with the same periodicity as those of the conductivity oscillations.

To prove that the oscillations originate from the formation of the QW states, we performed simulations using a phase accumulation model (PAM). [START_REF] Smith | Quantum-well and tight-binding analyses of spin-polarized photoemission from Ag/Fe(001) overlayers[END_REF] The PAM describes the quantization condition for the existence of a QW state as:

2𝑘 𝑑 -Φ -Φ -Φ = 2𝜋𝑛 (1)
where 𝑘 = 2𝑚 * (𝐸 -𝐸 )/ℏ is the crystal momentum wave vector in the direction perpendicular to the interface, d indicates the Fe QW thickness, and Φ = Φ = 2sin (𝐸 -𝐸 )/(𝐸 -𝐸 ) -𝜋 are the reflection phase shift at the two Fe/MgAlOx interfaces which confine the QW structure. m * is the effective mass of majority Δ1 electron in Fe, and EL and EU are the energies of the lower and upper edges of the barrier band gap. Here, we set m * =1, EL =-1.0eV and EU =3.9eV similar to Ref. [8].

The parameter Φinf taking into account the additional phase shift at interfaces is set to 0 for simplification. By injecting all parameters into Eq. ( 1), we obtain the following expression:

𝑛 = 1.63𝑑√𝑉 + 1 -0.637 sin . + 1 -𝑛 (2)
Where 𝑛 is the index of the first QW state close to EF. As displayed in the inset of Fig. From the periodicity of the oscillation, it is reasonable to suppose that the conductance oscillations at positive and negative bias are attributed to the top and bottom QW states, respectively, due to their different QW thickness. The possible explanation is that the electrons are rapidly dephased and thermalized [START_REF] Lyon | Thermalization of hot carriers in quantum wells[END_REF][START_REF] Esmaielpour | Enhanced hot electron lifetimes in quantum wells with inhibited phonon coupling[END_REF] inside the first QW before they can resonantly tunnel into the second QW, as schematically drawn in Fig. 3(b) and (c). In semiconductor QW, hot electrons typically thermalize in a picosecond time scale, dissipating energy via various phonon-mediated relaxation pathways. [START_REF] Esmaielpour | Enhanced hot electron lifetimes in quantum wells with inhibited phonon coupling[END_REF] In metallic QW, electron thermalization is even enhanced due to the smaller electron mean-free path compared to the semiconductor. Therefore, the electrons will quickly lose their phase and energy coherence if they are confined in a QW for a longer time and the reception side with another QW structure has no available resonant QW energy level under that bias. In the end, the MTJ with QWs in series only reveals the resonant tunneling characters of the last QW which the electrons tunnel through.

To further confirm our supposition, we have performed the analysis of the periodicity with the PAM model. To correctly take into account the electron thermalization effect, we have added a factor of F in Eq. ( 2):

𝑛 = 1.63𝑑√𝑉 * 𝐹 + 1 -0.637 sin * . + 1 -𝑛 (3)
This F factor represents the true voltage drop on the QW to probe the unoccupied QW states. As shown in the inset of Fig. 3(d), with the factor F=0.56, the periodicity at positive and negative bias can be well fitted with the states in the 7.3 nm and 8.7 nm thick QWs, respectively, which well correspond to the top and bottom QWs. In the situation of a full thermalization down to EF in the first QW, one should obtain a F=1/3 by taking into account the voltage drop on one barrier. On the contrary, if the electrons maintain their energy when tunneling into the second QW, F factor should be equal to 2/3 due to the voltage drop on the two barriers. Therefore, our fitted factor F=0.56 between 1/3 and 2/3 indicates that the electrons are partially thermalized in the first QW before tunneling into the second QW. One remarkable feature in this kind of DQW MTJ is that with the design of different thickness for the two QWs, one can achieve different oscillation periodicities with bipolar bias, which could be of interests to generate new functionality with the multi-QW MTJs.

Fig. 3(g) displays the DTMR curves calculated from the different conductance in P and AP states.

Although clear oscillations can be observed in both positive and negative bias, the amplitude of oscillation is smaller than that of Sample I. This can be understood by noticing that the influence of junction resistance in Sample II due to the QW resonant tunneling only occurs in one QW, while the total junction resistance should take into account three tunneling barriers. Therefore, the oscillation amplitude is reduced by a factor of 3 compared to Sample I.

Evidence of coherent resonant tunneling through double QWs

As mentioned above, to achieve the coherent resonant tunneling through two QWs, one must accelerate the tunneling of electrons through QWs and minimize their energy thermalization inside the QWs. To fulfill the conditions for such kind of coherent resonant tunneling, the discrete QW energy levels in the two QWs should be aligned under a certain bias. The following three aspects were considered to design such DQW structure. Firstly, the two QW layers must have an identical thickness so that their whole set of QW states can be matched with each other at zero bias to fulfill the resonant tunneling condition. Secondly, the QW states should be decoupled with the EF of thick electrodes so that one can adjust the bias to probe different unoccupied QW states. Thirdly, to ensure the energy alignment between the two QWs' states, the voltage drop between the two QWs should be minimized. Based on these considerations, we have designed a DQW MTJ structure (Sample Ⅲ) with two thick barriers (6MLs) at both sides and one thin barrier (3MLs) in the middle, as schematically shown in Fig. 4(a). The two QW layers have identical thickness of 7.7nm. The difference in resistance between the thick and thin barriers (100 times) ensures that the main voltage is dropped on the two thick barriers and very small bias is applied across the two QWs when performing bias dependence measurements. Fig. 4(a) schematically shows the diagrams of the resonant tunneling through two QWs under a negative bias.

Fig. 4(b) shows the bias dependence of the differential conductance in P state. Oscillations in conductance can be clearly observed in the bipolar bias condition. However, the amplitude of oscillation under negative bias is stronger than that under positive bias. This could reflect a certain asymmetric growth condition for the MgAlOx/Fe interface and the Fe/MgAlOx interface. [START_REF] Nozaki | Quantum oscillation of the tunneling conductance in fully epitaxial double barrier magnetic tunnel junctions[END_REF] To prove that the observed quantum oscillation is originated from the coherent resonant tunneling between the two QWs, we have fabricated one reference sample (Sample IV) with SQW structure [MgAlOx( 6MLs)/Fe(7.7 nm)/MgAlOx(6 MLs)], which is schematically shown in Fig. 4(c). In this sample, since the etching is stopped in the top thick MgAlOx barrier, the applied bias is totally dropped across the top barrier due to its dominated resistance in the junction. In comparison, in the DQW sample, only half of bias is applied across one thick barrier to probe the unoccupied QW states. Therefore, to quantitively compare the QW state positions for both samples, we have intentionally multiplied by a factor of 2 for the bias voltage of Sample IV. To enhance coherent resonant tunneling through the two QWs, two conditions are crucial.

Indeed both the thin middle barrier and the available energy levels in the second QW must ensure the electrons rapid tunneling into the second QW states without too much time dwelling in the first QW.

Another remarkable feature for such coherent resonant tunneling appears in the resonant peak width.

As clearly seen in Fig. 4(b) and 4(d), the width of the oscillation peak for the DQW Sample III is about half of SQW Sample IV. Since the QW states act as an energy filter, double QW structure can enhance this energy selection effect for the tunneling electrons, which results in narrower oscillation peak width. This finding also reinforces our conclusion that the observed oscillation features in Sample III are originated from the coherent resonant tunneling through the double QWs. One could also expect that the DQW must have stronger oscillation amplitude than that of SQW. Indeed the QW states in Fe are formed by majority 1 electron band. [START_REF] Yuasa | Spin-polarized resonant tunneling in magnetic tunnel junctions[END_REF][START_REF] Wang | First-principles theory of quantum well resonance in double barrier magnetic tunnel junctions[END_REF] The QW can select not only the energy of tunneling electrons but also the Bloch state symmetry feature linked to the band structures. Therefore, the DQW can effectively suppress the conduction channels from other electron bands than the majority 1 band, resulting in an enhanced oscillation amplitude. However, the oscillation amplitude It is well known from quantum theory that in the multi-QW system, when the middle barrier is sufficient thin, the two sets of QW states in the two wells can hybridize with each other and create new set of QW states. [START_REF] Horn | Electronic structure[END_REF] For a qualitative description of such physics in our DQW structure, we calculated the tunneling ratio of MTJ by using classic transfer matrix method on two DQW structures:

Thin barrier/QW/Thick barrier/QW/Thin barrier and Thick barrier/QW/Thin barrier/QW/Thick barrier. Please see details of calculation in Supplementary S4.

  (a) and (d) show dark-field STEM images for Sample III in a large and magnified scale, respectively. In Fig. 1(a), one can observe sharp interfaces between MgAlOx barriers (in black contrast) and Fe layers (in grey contrast). The QW and barrier layers appear quite flat and continuous, indicating a high quality of the triple-barrier MTJ structure. The magnifiedscale image further confirms that the two Fe QW layers have an identical thickness of 7.7nm. Energydispersive X-ray (EDS) spectroscopy has been performed to examine the chemical composition of the barriers. Fig. 1(b) and (c) show respectively the mapping of Al and Mg elements, indicating their homogenous distribution in the barriers. Fig. 1(e) displays the intensity profiles of Mg, Al and O elements with the corresponding STEM image. From the ratio of different elements, the chemical composition is confirmed to be consistent in the three MgAlOx barriers.

Fig. 2 (

 2 Fig. 2(d)-(g) show the transport properties of Sample I. The magneto-response TMR-H curves

Fig. 3 (

 3 Fig.3(d) and (e) show the bias dependence of the differential conductance in P and AP states,

Fig. 4 (

 4 d) shows the parallel conductance as a function of the converted bias voltage for Sample IV. Strong oscillations can be observed only for negative bias voltage. This is due to the fact that the Fermi level EF of the bottom electrode cannot be lifted to probe the unoccupied QW states under the positive bias due to the small resistance of the bottom barrier with large micron size of area. Remarkably, the four main peaks (indicated with dash lines) at negative bias correspond perfectly to those of Sample III. The slight difference in position is enlarged for the QW states at larger bias, which is due to a smaller QW thickness in Sample IV [7.0 nm estimated by PAM simulation in the inset of4(d)]. This gives a strong argument that although the DQW structure possesses double 7.7nm thick QWs, it really acts as the same behavior of a single 7.7nm thick QW. The QW state positions can be well fitted in the inset of Fig.4(b). This also proves that the electrons can coherently resonantly tunnel through the two QWs without energy thermalization in one of the QWs. These results would not have been observed if the electrons had thermalized in the QWs. The situation would have been similar to what we have observed for the SQW reference sample under positive bias condition.

  could also be influenced by many other factors, such as QW thickness and the etching stop layer (see Supplementary S2). A slight change in the QW layer thickness and the different etching stop layer in the SQW sample could effectively increase the oscillation amplitude and make the direct comparison with the DQW sample difficult. Undoubtedly, future reduction of the QW thickness in the DQW structure should exponentially increase the oscillation amplitude.

Fig. 5

 5 displays the calculated energy dependence of the tunneling ratio (T) in the two kinds of DQW junctions. Evidently, the DQW junctions with three tunnel barriers exhibit peak splitting effect due to the hybridization between the QW states in the two wells. In the Thin barrier/QW/Thick barrier/QW/Thin barrier junction (Fig.5(a)), the QW states weakly interact with each other and the splitting appears clearly at high bias voltage when the electron waves start overlaping through the barriers. On the contrary, in the Thick barrier/QW/Thin barrier/QW/Thick barrier junction (Fig.5(b)), QW states strongly interact with each other and one QW state can be completely split into two states. Generally, the splitting of the satellite peaks can be controlled by the thickness of the central barrier. In our experiments (Fig.4(c)), the splitting in the resonant peaks cannot be detected. This could be due to two reasons. Either the middle barrier could be still too thick so that the hybridization of QW states is too weak. Or, the energy distribution of tunneling electrons is too large and the splitting of peak is submerged by the overlap of two satellite QW states. In the future, the optimization of middle barrier thickness will allow us to observe such hybridization between two QWs.ConclusionIn summary, the spin-dependent resonant tunneling properties have been studied in fully epitaxial MgAlOx MTJ with double quantum well structures. Strong oscillations in conductance have been observed in the nanopillar structured DQW MTJ. It is found that the middle barrier plays a critical role on the resonant tunneling through the two QWs in series. When it is too thick, the electrons are partially thermalized in the first QW, consequently the periodicity of the conductance oscillations are only determined by the second QW. When the resonant tunneling condition is fulfilled, the DQW MTJ can produce strong conductance oscillations with much narrower peak width (about half) owing to the enhanced energy selection effect compared to the SQW MTJ. The realization of multiple QWs in single MTJ paves an efficient way to engineer quantum resonant tunneling to control the magnetoresistance with bias in addition to the conventional magnetization manipulation.

Figures:Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure 2: (a) Schematics of the double QW MTJ with core structure of Fe/MgAlOx(3

Figure 3 :

 3 Figure 3: (a) Schematics of the double QW MTJ with core structure of Fe/MgAlOx(6

Figure 4 :

 4 Figure 4: (a) Schematics of double QW MTJ with core structure of Fe/MgAlOx(6

Figure 5 :

 5 Figure 5: Simulation of energy dependence of tunneling ratio for double QW MTJs with structure of

Acknowledgement This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFA0206200), the National Natural Science Foundation of China (NSFC) (Grant No.11434014, 51620105004, 11674373, 51701203), the Strategic Priority Research Program (B) (Grant No. XDB07030200), the Key Research Program of Frontier Sciences (Grant No. QYZDJ-SSW-SLH016), and the International Partnership Program of the Chinese Academy of Sciences (CAS) (No.112111KYSB20170090). We also acknowledge the support by the joint French National Research Agency (ANR)-NSFC SISTER project (Grants No. ANR-11-IS10-0001 and No. NNSFC 61161130527), ENSEMBLE (Grants No. ANR-14-0028-01 and No. NNSFC 61411136001). We thank the ANR FEOrgSpin project (Grants No. ANR-18-CE24-0017-01) and the French PIA project "Lorraine Université d'Excellence" (No. ANR-15-IDEX-04-LUE). Experiments were performed using equipment from the platform TUBE-DAUM funded by FEDER (EU), ANR, the Region Lorraine and Grand Nancy.

Methods

Sample preparation:

The fully epitaxial MTJs with different configurations of MgAlOx barriers were grown by MBE on MgO(001) substrate. Firstly, the substrate was annealed at 650°C for 60 mins and 10 nm MgO seed layer was deposited at RT to prevent the carbon diffusion during subsequent annealing process. [START_REF] Lu | Spin-orbit coupling effect by minority interface resonance states in singlecrystal magnetic tunnel junctions[END_REF] Then 45 nm Fe was grown at RT as bottom electrode and annealed at 500°C for 30 mins to improve the crystalline quality and flatten the surface. Double QW structures of MgAlOx/Fe/MgAlOx/Fe/MgAlOx with different thickness of barriers and wells were then deposited, where each Fe layer was annealed at 400°C for 20 mins. The layer-by-layer growth of the MgAlOx barriers at RT was monitored by the oscillation of in-situ RHEED intensity. Finally, the samples were capped with Fe(10 nm)/Co(20 nm)/Au(10 nm) as the top electrode, where only Fe layer was annealed at 400°C for 20 mins. The Co layer is used to enhance the coercivity of top Fe and the Au layer is used to prevent the sample from oxidation. The multilayers were patterned into nanopillar junctions with elliptical size of 120240 nm 2 by E-beam lithography combined with Ar ion etching technique.

The etching process was monitored by secondary ion mass spectrometry (SIMS) and can be precisely stopped in the desired MgAlOx barrier.

TEM characterization:

Thin lamella TEM samples were prepared by Focused Ion Beam (FIB) lift up method (FEI-FIB-Helios). Ex-situ microstructural characterization was performed with probe aberration-corrected STEM microscopes (FEI-Titan-Themis) operated at 300kV equipped with the super X energy dispersive X-ray spectrometer (EDS).

TOC figure:

We demonstrate the successful fabrication of double quantum well (QW) structure in a single fully epitaxial magnetic tunnel junction heterostructure, where two Fe QW layers are sandwiched between three MgAlOx tunnel barriers. We show clear evidence of the coherent resonant tunneling through the discrete QW states in the two QWs.