Abstract
Magnetic tunnel junctions (MTJs) in the field of spintronics have received enormous attention owing to their fascinating spin phenomena for fundamental physics and potential applications. MTJs exhibit a large tunnel magnetoresistance (TMR) at room temperature. However, TMR depends strongly on the bias voltage, which reduces the magnitude of TMR. On the other hand, tunnel magnetocapacitance (TMC), which has also been observed in MTJs, can be increased when subjecting to a biasing voltage, thus exhibiting one of the most interesting spin phenomena. Here we report a large voltageinduced TMC beyond 330% in MgObased MTJs, which is the largest value ever reported for MTJs. The voltage dependence and frequency characteristics of TMC can be explained by the newly proposed DebyeFröhlich model using Zhangsigmoid theory, parabolic barrier approximation, and spindependent drift diffusion model. Moreover, we predict that the voltageinduced TMC ratio could reach over 3000% in MTJs. It is a reality now that MTJs can be used as capacitors that are small in size, broadly ranged in frequencies and controllable by a voltage. Our theoretical and experimental findings provide a deeper understanding on the exact mechanism of voltageinduced AC spin transports in spintronic devices. Our research may open new avenues to the development of spintronics applications, such as highly sensitive magnetic sensors, high performance nonvolatile memories, multifunctional spin logic devices, voltage controlled electronic components, and energy storage devices.
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Introduction
Magnetic tunnel junctions (MTJs), which consist of a thin insulating layer sandwiched by two ferromagnetic (FM) layers, are among the key devices in the field of spintronics. Owing to the large tunneling magnetoresistance (TMR) at room temperature, MTJs have been utilized for hard disk drives, magnetic random access memories (MRAMs), and highly sensitive magnetic sensors^{1,2,3,4}. Other applications include straingauge sensors^{5,6}, MEMS microphone^{7,8}, flexible sensors^{9,10}, nuclear magnetic resonance (NMR) signal detectors^{11,12,13}, and neuromorphic computing devices^{14,15}. MTJs have been wlidely used in various fields of electronic devices.
Engineering the robustness of TMR against a bias voltage is one of the most important issues for the achievement of high magnetic sensitivity in MTJs^{16,17,18}. As is well known, TMR decreases with increasing bias voltage, which lowers sensitivity^{19,20}. This reduction is attributed to hotelectron properties in the antiparallel state of the biferromagnetic (FM) layers^{19}. For example, zerobias TMR of 377% and 89% are observed in MgO and AlObased MTJs using Co_{70}Fe_{30} FM layers, and it decreases to 75% and 20%, respectively, at a bias voltage of 0.5 V^{21}. The improvement of biasreduced TMR has been reported in MTJs with a small lattice mismatch (a few percent) between the FM and the insulating layers^{22,23,24,25,26,27}. Zerobias TMR is 92% in fully epitaxial Fe/MgO/GaO_{x}/Fe MTJs, and the half biasing voltage V_{1/2}, where the TMR is halved, can be raised to 0.5 V^{22}. Moreover, TMR is 117% near zero bias and V_{1/2} is relatively large, ranging from 1.0 to 1.3 V in latticematched Fe/spinel MgAl_{2}O_{4}/Fe MTJs^{23,24,25,26}. Further improvement has been reported. TMR is 240% near zero bias, and it keeps a large value of 180% at 0.5 V in MgAl_{2}O_{4}based MTJs^{27}. Nevertheless, a bias voltage always reduces TMR, which remains an essential problem in the applications of MTJs.
As a complementary effect to TMR, tunneling magnetocapacitance (TMC) is now actively being investigated due to its unique properties, such as high magnetic sensitivity, thermal stability, and robustness against bias voltage^{28,29,30,31,32}. Since the magnetocapacitance (MC) effect is observed in a system with broken timereversal and spaceinversion symmetry, the research of TMC is of particular importance for both practical applications and for fundamental physics^{28}. TMC is larger than TMR at a specific frequency, and it can be well accounted for by the Debye–Frölich (DF) model^{29}. The maximum TMC reported previously is 155% in MgObased MTJs featured with a TMR of 100%. In this case, the DF model calculation predicts a maximum TMC of 1000%. As a result of the presence of spin capacitance^{30}, TMC has been shown to be temperature independent. Perhaps more significantly, TMC is more robust against biasing than TMR. The V_{1/2} of TMC is almost twice as high as that of TMR in MgObased MTJs^{31}. Our recent work also demonstrates that TMC actually slightly increases from 98% up to 102% upon biasing, which correspondingly causes the TMR to decay from 100% to 50%^{32}.
In this work, we report a new phenomenon of bias induced doubling of the magnitude of TMC in an MTJ system based on a stack of Co_{40}Fe_{40}B_{20}/MgO/Co_{40}Fe_{40}B_{20}. We have observed a maximum TMC value of 332% under a bias voltage, which is the largest TMC ever reported for MTJs. There is an excellent agreement between theory and experimental results for the TMC in the entire voltage regions at each frequency using DF model incorporating a parabolic barrier approximation (PBA), spindependent drift diffusion (SDD) model, and Zhangsigmoid theory. Based on our calculations, we predict that the voltageinduced TMC ratio could reach 3000% in MTJs, representing a dramatic spintronics effect which can potentially benefit applications in various areas.
Results and discussion
Device structure and measurement of TMC and TMR
We have prepared MTJ multilayer stack structures using a high vacuum magnetron sputtering system with a base pressure of 2 × 10^{–8} Torr, with the following layer sequence: SiO_{2}/Ta(5)/Co_{50}Fe_{50}(2)/IrMn(15)/Co_{50}Fe_{50}(2)/Ru(0.8)/Co_{40}Fe_{40}B_{20}(3)/MgO(2)/Co_{40}Fe_{40}B_{20}(3)/Contact layer (numbers referred to thickness in nm). Details of the device fabrication procedure are described in the Experimental Section. Using standard photolithography, we have patterned the multilayer MTJ stacks into a junction area of 1800 μm^{2} with an elliptical shape with physical Ar ionmilling and SiO_{2} insulation overlayer. The frequency characteristics and the bias voltage dependence of the TMC and TMR for MTJs were measured by an AC fourprobe method at room temperature. The AC voltage was set to 2.6 mV_{rms}. The magnetic field was applied along the magnetic easyaxis direction to 1.4 kOe.
Modeling of TMC
Figure 1a shows the schematic of calculation procedure for the analysis of the frequency characteristics and bias dependence of TMC. The calculation is performed based on a newly proposed DF model using Zhangsigmoid model in addition to the conventional models of PBA and SDD. Here, we describe each model in detail. The DF model describes the dielectric dispersion of electric dipoles, and it can be applied to various systems such as insulators, semiconductors, metals, or organic molecular liquids. The DF model can also be used as tools for explanation of frequency characteristics of magnetocapacitance effect^{33,34,35}. On the basis of the model, the capacitance \({C}_{{\rm P}\left(\text{AP}\right)}^{{\rm DF}}(f)\) as a function of frequency f for the Parallel (Antiparallel), P(AP), configuration in MTJs can be expressed by
where C_{∞,P(AP)} and C_{0,P(AP)} are the highfrequency and DC capacitances, τ_{P(AP)} is the relaxation time, and β_{P(AP)} is the exponent showing the distribution of relaxation time, respectively, for the P(AP) configuration. The equivalent circuit is shown in Fig. 1b. By calculating Eq. (1), we can obtain
The relation between τ_{P} and τ_{AP} in FM/insulator/FM is given by
where P_{TMC} is the spin polarization, contributing to TMC, inside the FM layer^{29,36}. Using these formulas, we can find frequency characteristics of TMC ratio, defined by
Then, we incorporate Zhang model to calculate TMC under bias voltage. According to Zhang model^{19}, the conductance can be expressed by G_{P(AP),V} = G_{P(AP),0} (1 + K_{P(AP)}V), where G_{P(AP),0} is a conductance at zero bias in the P(AP) configuration and K_{P(AP)} is parameter determined by Curie temperatures of FM layers, the density of states of itinerant electrons in FM layers_{,} and direct and spindependent transfers and spin quantum number within the framework of the transfer Hamiltonian in the system of FM/insulator/FM. Moreover, we introduce sigmoid function into Zhang model to express the weighting of the applied voltage. The sigmoid function is expressed by
where V_{0,P(AP)} indicates the voltage at which the value of the sigmoid function becomes 0.5 in the P(AP) configuration as shown in Fig. 1c. α_{P(AP)} is the constant parameter, indicating the broadening of the sigmoid function, in the P(AP) configuration. Here, we describe the physical picture behind the sigmoid function. By applying a voltage and approaching V_{0,P(AP)}, since the electrons gain energy, the spin flip is promoted. In the AP configuration, the spin accumulation occurs at the FM/insulator. Therefore, the voltage, contributed to the DFmodelled dynamic capacitance, in the AP configuration is smaller than that in the P configuration. For this reason, spin flip is more likely to occur in the P configuration than in the AP configuration at low voltages. This corresponds to the relationship of V_{0,P} < V_{0,AP} in sigmoid function. This means that the sigmoid function can express the spinflip voltage. A large difference between V_{0,P} and V_{0,AP} could contribute the enhancement of TMC with respect to the voltage. The combination with Zhang model and sigmoid function provides the relaxation time τ_{P(AP),V} with applied voltage, which can be written by
where τ_{P(AP),0} is the relaxation time at zero bias voltage in the P(AP) configuration, and κ is an adjustable positive parameter of much smaller than 1.0. Equation (6) is called Zhangsigmoid model. The relaxation time τ_{P(AP),V} in Eq. (6) should be used as the replacement of τ_{P(AP)} in Eq. (2) under the application of bias voltage.
PBA model is taken into account to describe the bias voltage dependence of the effective barrier thickness. The potential profile in the barrier is based on parabolic function, which is often used as an approximation for tunneling process, such as ac nonmagnetic and magnetic tunneling transport^{37,38}. In this PBA, the potential function \(\phi \left( u \right) = 4\phi _{0} (1  u)u + eVu,\) where \(u = x/d\) is the reduced spatial variable, \(x\) is the distance from the surface of the one side electrode, \(d\) is the barrier thickness, \(\phi _{0}\) is the barrier height in the absence of the bias voltage and e is the electron charge. The solution of \(\phi (u) = eV\) is \(u_{1} = eV/4\phi _{0}\) and \(u_{2} = 1\) (for \(u_{1} < u_{2}\)), the effective barrier thickness d_{eff} can be represented by
The calculation of \(C_{{\rm AP}}(f,V)\) is performed using the SDD model in addition to DF model combined with PBA and Zhangsigmoid model. SDD model illustrates that the accumulation of minority spins and the depletion of majority spins occur at the interface between the ferromagnetic layer and insulating layer in the AP configuration^{37}. The spin accumulation gives rise to the creation of tiny screening charge dipoles, which act as an additional serial capacitance. This capacitance is called spin capacitance^{37}, which can be represented by
where S is a junction area, \(n_{{0,{\rm AP}}}\) is a screening charge density and λ is a characteristic screening length at the interface in the AP configuration. Since this screening charge acts as a serial capacitance, the capacitance \({{C}}_{\text{AP}}({f}, V)\) under the applied DC voltage V in the AP configuration,
where the capacitance \({C}_{{\rm AP}}^{{\rm DFZSP}}\)(\(f, V\)) based on the DF model combined with Zhangsigmoid model and PBA in the AP configuration is represented by
TMC and TMR under no bias voltage
Figure 2a, b shows the TMC and TMR curves at 160 Hz. The DC applied voltage is 0 V. Clear TMC and TMR are observed, i.e., and C_{P} > C_{AP} and R_{P} < R_{AP.}
TMC and TMR ratios are 172% and 100%, respectively, at room temperature. Figure 2c, d shows the frequency characteristics of TMC, TMR and C_{P(AP)}. We calculated the frequency characteristics of the TMC and C_{P(AP)} using Eqs. (2)–(4). The calculation results of TMC and C_{P(AP)} under no bias voltage fit to the experimental data well. The calculation was performed using the following parameters: C_{∞,P(AP)} = 0.80 (0.90) nF, C_{0,P(AP)} = 1037 (1221) nF, β_{P(AP)} = 0.986 (0.999), τ_{P} = 0.0118 s and P_{TMC} = 0.477. According to the fitting result, P_{TMC} is 0.477, and P_{TMR} is 0.577. Here, P_{TMR} is the spin polarization of FM layer, contributing to TMR. The excellent agreement between theory and experiment reveals that the TMC shows a maximum value of 172% at 160 Hz.
Voltageinduced TMC and TMR
Figure 3 shows the voltageinduced TMC and TMR curves at 160 Hz. The TMC ratio under the applied bias voltage \(V\) at the frequency f is defined by \(\text{TMC}(f, V) = (C_{{\rm P}}(f, V)C_{{\rm AP}}(f, V{))}/C_{{\rm AP}}(f, V)\). At around 0 mV, the TMC ratio decreases with the increase of the bias voltage. After that, the TMC ratio increases, and it reaches 332% at 92 mV. A TMC of 332% is the largest value ever reported for MTJs. As increasing the voltage higher than 92 mV, the TMC ratio decreases. On the other hand, TMR rapidly decreases from 100% to 40%. As described in the introduction, the enhancement of \(V_{{1/2}}^{{\rm TMR}}\) is important to develop highperformance TMR devices. In our devices, \(V_{{1/2}}^{{\rm TMR}}\) is around 138 mV. In contrast, TMC tends to increase with increasing the voltage, and especially at around 92 mV, TMC reaches 332%, which is the double value of TMC near zero bias. This means that \(V_{{1/2}}^{{\rm TMC}}\) is not so important in TMC. Instead of this, it is essential to set an appropriate voltage, in which TMC is peaked. One more interesting point is that the noise of the TMC in the high bias region is smaller than that of the TMC in the low bias region. The noise reduction in the high bias voltage is due to the decrease of the effective barrier thickness. The effective MgO thickness decreases with increasing the voltage due to the parabolic shape of potential barrier. Since the capacitance is proportional to the inverse of the thickness, the capacitance increases with increasing the voltage. This behaviour can be easily understood from Fig. 3a. The impedance of the capacitor is expressed by Z = 1/jωC, where ω is the angular frequency. Therefore, the applied voltage reduces the impedance, resulting in a low noise. This fact is consistent with previous works in MTJs, where the noise can be reduced in the high frequency region due to the low impedance^{29,39}. From these results, we can realize a large TMC and low noise, i.e. a high signaltonoise (SN) ratio by setting an appropriate voltage.
We also discuss the scalability of TMC devices. The junction area of fabricated MTJs in this study is 1800 μm^{2}. The typical capacitance is about 20 nF (see Fig. 3a). Since the capacitance is proportional to the junction area, for example, the capacitance is 0.1 pF in a junction area of 100 nm × 100 nm. The capacitance is 1 fF in a junction area of 10 nm × 10 nm. These values can be detected using current circuit technology (1 aF is possible to detect). Since the TMR of MTJs used in magnetic read heads or MRAM is about 100%, a TMC of 100% is considered to be necessary in TMC devices. For example, in the case of C = 0.1 pF and TMC = 100%, the capacitance C_{P} in the P configuration is 0.2 pF and C_{AP} in the AP configuration is 0.1 pF. Also, in C = 1 fF and TMC = 100%, C_{P} is 2 fF and C_{AP} is 1 fF. As mentioned above, these values can be detected using current circuit technology. Therefore, TMC heads or memories can work in nanoscale MTJs for readout.
Bias dependence of voltageinduced TMC
Figure 4 shows the experimental and calculation results of the bias voltage dependence of R_{P(AP)}, C_{P(AP)}, TMR and TMC ratio. TMR ratio is calculated using Zhang’s theory^{19}. As shown in Fig. 4a, the experimental data of \(R_{{\text{P(AP)}}}(V)\) are in good agreement with the calculation using Zhang’s model, where \({K}_{\text{P}\left(\text{AP}\right)}\) is set to 0 (2.48). This means that Zhang’s model is effective for explaining the bias dependence of TMR under both AC and DC model. The calculation of \({C}_{{\rm P(AP)}}(f, V)\) is performed using Eqs. (1)–(10). As shown in Fig. 4b, the measured capacitance \(C_{{\rm P(AP)}}(f,V)\) exhibiting a bowllike behavior is very well described by the theoretical calculations. Here, we used the same parameters of C_{∞,P(AP)}, C_{0,P(AP)}, β_{P(AP)}, τ_{P(AP)} and P_{TMC} as those used in the investigation of the frequency characteristics of TMC under no bias voltage. The other parameters are shown in Supplementary Table S1 at 160 Hz. The excellent agreement between theory and experiments indicates that the PBA is a good approximation for the expression of the potentialbarrier profile in MTJs based on Co_{40}Fe_{40}B_{20}/MgO/Co_{40}Fe_{40}B_{20} in calculating the bias dependence of C_{P(AP)} under AC field. This fact corresponds to the gradual increase of capacitance with applying the voltage due to the decrease of the effective MgO thickness under PBA. The combination of DF model and Zhangsigmoid theory also proves the validity of spin dynamics of electron–hole dipoles inside the MgO insulator. The Zhangsigmoid model describes that the spin flip occurs at an applied voltage larger than around V_{0} in the sigmoid function. In AP configuration, the spin capacitance appears in the MgO/Co_{40}Fe_{40}B_{20} interface as shown in Fig. 4c. The presence of the spin capacitance leads to the reduction of the applied voltage inside MgO barrier, where DFmodelled dynamic capacitance is dominant. On the other hand, in P configuration, a sufficiently large voltage is applied inside MgO barrier due to no spin capacitance in the MgO/Co_{40}Fe_{40}B_{20} interface. Therefore, the capacitance in P configuration rapidly increases at around V_{0,P}, which is smaller than V_{0,AP}. The difference between V_{0,P} and V_{0,AP} causes a large voltageinduced TMC, reaching 332%. This means that the voltage to bring about spin flip is quite different in P and AP configurations, respectively, that is, the energy that electrons acquire for spin flip differs from each other in P or AP, respectively. The threshold voltage V_{0,P(AP)} can be described by Zhangsigmoid model.
Figure 4d shows the bias dependence of TMC and TMR at 160 Hz. As shown in Fig. 3a already, TMC decreases at around zero bias, and then it has a maximum value of 332% at 92 mV. This tendency can be observed in the forward and reverse bias region. It is also noted that TMC ratio is larger than TMR ratio in the entire bias region. This means that TMC is superior to TMR by setting an appropriate frequency for practical use. Figure 4e shows the bias dependence of TMC ratio at 30, 160 and 400 Hz. In the frequency ranging from 30 to 400 Hz, the same tendency can be seen in.
TMCV curves, and TMC is larger than TMR at any bias voltage. As can be seen in this figure, the maximum TMC is 332% at 160 Hz with the application of 92 mV. We emphasize that the TMC of 332% is the highest value ever reported for MTJs. The solid lines in Fig. 4e represent calculation results. The fitting parameters are listed in Supplementary Table S1. Here, C_{∞,P(AP)}, C_{0,P(AP)}, β_{P(AP)}, and τ_{P(AP)} are the same parameters in fitting the frequency dependence of TMC under no bias voltage, shown in Fig. 2c. The other parameters, appeared in Zhangsigmoid, PBA, and SDD models, are newly fitted to experimental data. As one can see, there is an excellent agreement between theory and experiment. The detailed results on the frequency dependence of TMC under bias voltage are shown in Supplementary Fig. S1.
Prediction of an extremely large voltageinduced TMC
Finally, we show the prediction of an extremely large TMC. Figure 5a shows the calculated frequency dependence of the TMC at a zero bias voltage with varying spin polarization P. The assumed maximum value of P is 0.83, which is estimated experimentally for highperformance MgObased MTJs at room temperature^{40}. The parameters used in the calculation of the TMC under no bias voltage are C_{∞,P(AP)} = 0.80 (0.90) nF, C_{0,P(AP)} = 1037 (1221) nF, β_{P(AP)} = 0.986 (0.999) and τ_{P} = 0.0118 s. As can be seen from Fig. 5a, the maximum TMC increases from 363% to 1906% with increasing P from 0.63 to 0.83. The f_{peak}, at which the TMC ratio is peaked at maximum, is 33, 55 and 74 Hz, respectively. Figure 5b shows the calculated frequency dependence of the TMC under no bias voltage with varying τ_{P}. The maximum peak of the TMC is shifted to a high frequency region on the order of MHz for a short τ_{P} in the subμs scale. The DF model suggests that the relaxation time is determined by the oscillation speed of electric dipoles formed near the FM/insulator interfaces. The relaxation time is short in a high oscillation speed. For a short relaxation time, the thickness of the insulator should be thinner. Therefore, the formation of a thinner MgO layer is necessary for a high frequency operation. In fact, the recent paper demonstrates a high frequency operation of ~ 100 MHz, corresponding to a relaxation time of sub ns, in FeCoMgF nanogranular system^{41}. Figure 5c, d shows the calculated voltageinduced TMC with varying P at 160 Hz and f_{peak}, respectively. The parameters used in the calculation of the bias dependence of the voltageinduced TMC are κ = 0.1, S = 1800 μm^{2}, λ = 0.1 nm. \(\phi\)_{0,P(AP)} is 2.0 (0.046) eV, n_{0,AP} is 0.354 × 10^{23} cm^{−3}, K_{0,P(AP)} = 26.7 (22.4) V^{−1}, V_{0,P(AP)} = 0.047 (0.085) V, and β_{P(AP)} = 64.7 (29.8). The maximum voltageinduced TMC increases from 788% to 3114% with increasing P from 0.63 to 0.83. The prospect of achieving TMC of more than 3000% is attractive for the development of spintronics. It will have profound impact on spinbased circuit designs, nonvolatile memories, magnetic sensing, spin logic devices, and voltage controlled electronic components. Traditionally, variable capacitors are bulky, mechanical, or narrowly ranged. Comparatively, the MTJs as capacitors are small in size, broadly ranged under the voltage control, and fully electronic and nonmechanical.
In summary, we have successfully observed a large TMC effect in MgObased MTJs at room temperature. The voltageinduced TMC increases up to 332%, which is the largest value ever reported for any MTJs. We have understood the full mechanism of this dramatic effect both qualitatively and quantitatively by our explained newly proposed DF model incorporating PBA, SDD, and the Zhangsigmoid model. This calculation predicts that the voltageinduced TMC could potentially reach 3114% in MTJs with a spin polarization of 83%. Our theoretical and experimental findings provide new insights into the exact mechanism of the voltageinduced AC spin transports in MTJs. The works will produce a new platform for the development of spintronics applications and electrical engineering.
Methods
Preparation of the samples
The MTJs were prepared by using a homemade high vacuum magnetron sputtering system with a base pressure of 2 × 10^{–8} Torr. The MTJs have the following layer sequence: SiO_{2}/Ta(5)/Co_{50}Fe_{50}(2)/IrMn(15)/Co_{50}Fe_{50}(2)/Ru(0.8)/Co_{40}Fe_{40}B_{20}(3)/MgO(2)/Co_{40}Fe_{40}B_{20}(3)/Contact layer (thickness in nm). We deposited all the metallic layers in DC mode under a sputtering Ar gas pressure of 1.5 mTorr, and the MgO layer deposited with radio frequency (RF) magnetron sputtering under an Ar gas pressure of 1.1 mTorr. Using standard photolithography, we have patterned the multilayer MTJ stacks into a junction area of 1800 μm^{2} with an elliptical shape with Ar ionmilling and SiO_{2} insulation overlayer. Afterwards, we annealed the MTJs at 310 °C for 4 h in a vacuum of 10^{–6} Torr under magnetic field of about 4.5 kOe to define the pinning axis for the bottom Co_{40}Fe_{40}B_{20} ferromagnetic electrode.
Measurements of the voltageinduced TMC
The frequency characteristics and the bias voltage dependence of the TMC and TMR for MTJs were measured by an AC fourprobe method using an Agilent Technologies 4284A LCR meter at room temperature. The frequency ranged from 50 Hz to 1 MHz and the bipolar bias voltage was applied up to 200 mV. The AC voltage was set to 2.6 mV_{rms}. The magnetic field was applied along the magnetic easyaxis direction to 1.4 kOe.
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Acknowledgements
This research was supported by the GrantinAid for Scientific Research (B) (under Grant No.18H01485) and Challenging Exploratory Research Program (No. 19K22093) funded by the Japan Society for the Promotion of Science (JSPS), the Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials and the Cooperative Research Program of “Network Joint Research Center for Materials and Devices” funded by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Research Project funded by the Center for Spintronics Research Network (CSRN) at Keio and Tohoku University. The work at Brown was supported by the U.S. National Science Foundation (NSF) under Grant No. OMA1936221.
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H.K. and G.X. conceived and designed the experiments using the help of other authors. G.X. performed the sample preparation and structural analysis. H.K., and Y.N. performed ac impedance measurements. K.O., H.K., and G.X. performed the theoretical analysis and calculation. All the authors contributed to analyzing and interpreting the data, and to writing the manuscript.
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Ogata, K., Nakayama, Y., Xiao, G. et al. Observation and theoretical calculations of voltageinduced large magnetocapacitance beyond 330% in MgObased magnetic tunnel junctions. Sci Rep 11, 13807 (2021). https://doi.org/10.1038/s41598021932264
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DOI: https://doi.org/10.1038/s41598021932264
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