Robustness of Voltage-induced Magnetocapacitance

One of the most important achievements in the field of spintronics is the development of magnetic tunnel junctions (MTJs). MTJs exhibit a large tunneling magnetoresistance (TMR). However, TMR is strongly dependent on biasing voltage, generally, decreasing with applying bias. The rapid decay of TMR was a major deficiency of MTJs. Here we report a new phenomenon at room temperature, in which the tunneling magnetocapacitance (TMC) increases with biasing voltage in an MTJ system based on Co40Fe40B20/MgO/Co40Fe40B20. We have observed a maximum TMC value of 102% under appropriate biasing, which is the largest voltage-induced TMC effect ever reported for MTJs. We have found excellent agreement between theory and experiment for the bipolar biasing regions using Debye-Fröhlich model combined with quartic barrier approximation and spin-dependent drift-diffusion model. Based on our calculation, we predict that the voltage-induced TMC ratio could reach 1100% in MTJs with a corresponding TMR value of 604%. Our work has provided a new understanding on the voltage-induced AC spin-dependent transport in MTJs. The results reported here may open a novel pathway for spintronics applications, e.g., non-volatile memories and spin logic circuits.

inferior to MgO-based MTJs. Overall, efforts in increasing V 1/2 have not been successful in MTJs or other spintronic devices.
Complementary to TMR effect, the tunneling magnetocapacitance (TMC) is also inherent to the capacitive MTJ structure [41][42][43][44] . Recently TMC has been increasingly studied due to their fascinating spin phenomena, such as spin capacitance [45][46][47][48] , frequency-dependent spin transport 42,43,49 and potential applications 41,50 . Though TMC and TMR share some similar origins and are correlated, TMC is unique in many aspects. For example, TMC is peaked at a specific frequency 43 , but is weakly dependent on the temperature 44 . Furthermore, V 1/2 of TMC is higher than that of TMR 44,47 . The highest V 1/2 of TMC in MgO-based MTJs is 0.7 V, which is almost twice as high as that of TMR in the same device 47 . Therefore, TMC is more robust against biasing than TMR, and the mechanism of this robustness remains unclear. It is beneficial to understand this mechanism as the TMC effect may lead to more spintronics applications as well as insight into fundamental spintronic behavior.
In this work we report a new phenomenon at room temperature in which the TMC increases with applying biasing voltage in an MTJ system based on Co 40 Fe 40 B 20 /MgO/Co 40 Fe 40 B 20 . This result means an unprecedented enhancement of V 1/2 with regard to TMC. We have observed a maximum TMC value of 102% under biasing, which is the largest voltage-induced TMC effect ever reported for MTJs. There is an excellent agreement between theory and experiment for the TMC in the bipolar bias regions using Debye-Fröhlich (DF) model combined with quartic barrier approximation (QBA) and spin-dependent drift-diffusion (SDD) model. Based on our calculations, we predict that the voltage-induced TMC ratio could reach 1100% in MTJs with a corresponding TMR ratio of 604%.

Results and Discussion
Device structure and TMR and TMC under no bias voltage. Figure 1a shows the device structure prepared by a magnetron sputtering system with a base pressure of 2 × 10 −8 Torr, with the following layer sequence: SiO 2 /Ta(5)/Co 50  . 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 Ar ion-milling and SiO 2 insulation overlayer. The frequency characteristics and the bias voltage dependence of the TMR and TMC for MTJs were measured by an AC four-probe method at room temperature. The AC voltage was set to 2.6 mV rms . The magnetic field was applied along the magnetic easy-axis direction to 1.4 kOe. Figure 1b,c show the TMR and TMC curves at 60 Hz. The DC applied voltage is 0 V. Clear TMR and TMC effects are observed, i.e., R P < R AP and C P > C AP . Large TMR and TMC ratios of approximately 100% are obtained at room temperature. Figure 1d,e shows the frequency characteristics of TMC, TMR and C P(AP) . We calculated the frequency characteristics of the TMC and C P(AP) using the DF model 43,51 . Based on the model, the capacitance C f ( ) P(AP) DF as a function of frequency f for the P(AP) configuration in MTJs can be expressed by where C ∞,P(AP) and C 0,P(AP) are the high-frequency and static capacitances, τ P(AP) is the relaxation time of electric dipoles, consisting of electrons and holes, formed near the interface between the FM layer and insulator, and β P(AP) is the exponent showing the distribution of the relaxation time, respectively, for the P(AP) configuration. After a straightforward calculation of Eq. (1), we can obtain β πτ The relation between τ P and τ AP in FM/insulator/FM is given by where P TMC is the spin polarization inside the FM layer 43,51 . Using these formula, we can calculate the frequency characteristics of the TMC ratio, defined by Fig. 1d,e, it is evident that the theoretical results of the TMC and C P(AP) fit the experimental data very well. The calculation was based on the following parameters: C ∞,P(AP) = 1.45 (1.5) nF, C 0,P(AP) = 630 (590) nF, β P(AP) = 0.998 (0.977), τ P = 0.0071 s and P TMC = 0.46. As for the magnetoresistance, we calculated the TMR ratio using the Julliere formula 52 , assuming a spin polarization P TMR of 0.59. The difference between P TMC and P TMR is attributed to the different penetration lengths of spin-dependent carriers (inside Co 40 Fe 40 B 20 ) contributing to TMC and TMR. Our previous paper reveals that the penetration length (λ TMC ) of TMC is longer than that (λ TMR ) of TMR 43 . Here, as is well known, the spin polarization of surface atoms in the FM layer or the interfacial FM atoms between FM/insulator is higher than that of inner atoms from the surface/interface due to the two-dimensional surface/interface effect [53][54][55] . This picture can be applied to our MTJ system. Namely, the spin polarization (P inter ) of the first interfacial atoms in Co 40 Fe 40 B 20 layers is considered to be higher than that (P inner ) of inner atoms from the Co 40 Fe 40 B 20 /MgO interface (See Fig. S1). In fact, according to the first-principles calculation using the Vienna Ab Initio Simulation Package (VASP), the spin polarization at the Co terminated interface is higher than that of the inner Co and Fe atoms in CoFeB/MgO system 56 . From these spin-polarization behavior, it is found that P TMC is low for a long λ TMC , and P TMR is high for a short λ TMR . According to the above fitting results, P TMC is 0.46, and P TMR is 0.59. The spin polarization P TMR of 0.59 is in good agreement with the experimental value (0.57-0.65) of CoFeB alloy obtained by point-contact Andreev reflection 57 . Also, we herein note that a negative TMC, i.e., C P < C AP , is observed in the high-frequency region. This can be understood from the fitting results, i.e., C ∞,P(AP) = 1. 45 Fig. 1d. This is due to the appearance of the spin capacitance originated from the accumulation of spin-polarized carriers at the two FM/insulator interfaces. The detailed results and discussion are described in the Supplementary Information section. The excellent agreement between theory and experiment reveals that the TMC shows a maximum value of 96% at 60 Hz. Hence, we will use operation frequency of 60 Hz to study the bias dependence of TMC effect. Here, it is noted that we reported a high TMC of 155% in our previous paper 43 . This result was obtained near zero bias voltage. In contrast, it is found that MTJs showing such high TMC tend to bring about the breakdown under the bias voltage. MTJs showing about 100% do not break down under the bias voltage, and the reproducibility is also good. From this reason, we have studied the bias dependence of TMC using MTJs with a TMC of about 100%. Figure 2 shows the bias dependence of TMC and TMR curves at 60 Hz.

Voltage-induced TMC and TMR.
The TMC ratio under the applied bias voltage V DC at the frequency f is defined by Interestingly, the TMC increases from 96% to 102% as the magnitude of bias voltage increases from 0 to 184 mV, whereas TMR rapidly decreases from 105% to 53%. As described earlier, the enhancement of V 1/2 TMR is an important issue in the development of high-performance TMR devices. The  remain robust against bias voltage which weakens the corresponding TMR quickly. Both the large TMC and its robustness are highly beneficial to spintronics applications associated with the TMC effect. Figure 3 shows the bias voltage dependence of R P(AP) , C P(AP) and the modeling of the voltage-induced TMC. According to Zhang's theory 27 , the tunnel conductance in FM/insulator/ FM strongly depends on the bias voltage, especially within the order of a few hundred millivolts, due to hot electrons producing spin excitations. The conductance G P(AP) (V DC ) at the bias voltage V DC in the P(AP) configuration can be expressed by

Modeling of voltage-induced TMC.
is the conductance at zero bias in the P(AP) configuration and γ P(AP) is a parameter determined by the Curie temperatures of FM, the density of states (DOS) of itinerant electrons in FM, direct and spin-dependent transfers and spin quantum number within the framework of the transfer Hamiltonian. The resistance R P(AP) (V DC ) can be calculated from As shown in Fig. 3a, the experimental data of R P(AP) (V DC ) are in good agreement with the calculation using Zhang's model, where γ P(AP) is set to 0.0188 (1.87). This means that Zhang's model is effective for explaining the bias dependence of TMR under both AC and DC mode.
The calculation of C P (f, V DC ) is performed using the DF model combined with QBA. In the QBA, the potential profile of the barrier is assumed to be a quartic function, which is considered to be a good approximation to describe an AC tunneling transport 51 . The potential function φ η ( ) P under the bias voltage V DC in the P configuration can be expressed by , where η = x d / is the reduced spatial variable, x is the distance from the center of the barrier, d and φ 0,P are the barrier thickness and height in the absence of the bias voltage, respectively, and e is the electron charge. The potential profile is depicted in Fig. 3b. The solution of φ η = eV ( ) P D C is η 1 = −1/2, η 2 , η 3 and η 4 (for η 2 < 0, η 3 and η 4 > 0, η 3 < η 4 ). Since the values of η 2 , η 3 and η 4 can be calculated by the Cardano's method, the effective barrier thickness d eff can be represented by d eff = (1/2 + η 3 )d, where η 3 depends on V DC and φ 0,P . Therefore, C P (f, V DC ) at the applied DC voltage in the P configuration can be written by   The QBA is used to calculate the effective barrier thickness, which contributes to the measured capacitance. DC voltage dependence of (c) the capacitance C P in the P configuration. The C P is calculated using DF model under the QBA, described by Eq.
, where x i is the distance from the interface between the Co 40 Fe 40 B 20 and MgO, λ is a characteristic screening length and en 0,AP is a screening charge density at the interface in the AP configuration. The spin capacitance can be expressed by where ΔQ AP is the screening charge for the AP configuration and ΔV DC is the electrical potential difference applied in the charging space. Therefore, the spin capacitance can be obtained as , where S is a junction area and V DC (x i ) is an electrical potential as a function of x i in the charging space, i.e., . V eff is an effective applied voltage, which is expressed by κV, where κ is an adjustable positive parameter of much smaller than 1.0. Consequently, the spin capacitance can be represented by ,  Fig. 3d. The bias voltage dependence of the capacitance C AP in the AP configuration is shown in Fig. 3e. The capacitance C AP increases at around zero bias and then it decreases at higher voltages. This behavior is in good agreement with the results calculated by Eqs (4)−(6) with parameters of C ∞,AP = 1.5 nF, C 0,AP = 590 nF, β AP = 0.977, τ P = 0.0075 s, P TMC = 0.46, f = 60 Hz, κ = 0.1, S = 1800 μm 2 and λ = 0.1 nm. φ 0,AP is 0.144 (0.153) eV and n 0,AP is 0.94 (0.92) × 10 23 cm −3 for the positive (negative) bias region. The increase of C AP near zero bias is attributed to the decrease of the effective barrier thickness d eff . As seen from the potential profile φ P (x) of MTJs shown in Fig. 3b, d eff decreases with increasing bias voltage V DC . This corresponds to the decrease of η 3 . According to our calculation, η 3 is 0.5, 0.35 and 0.28 for V DC of 0, 50 and 100 mV, respectively. From Eq. (6), it is found that AP DF QBA DC increases with decreasing η 3 . Therefore, C AP (f, V DC ) increases with increasing V DC . The reduction of C AP at higher voltages is attributed to the spin capacitance, described in Eq. (4), i.e., the spin capacitance decreases with increasing V DC . Figure 4 shows the bias-voltage dependence of the TMC and TMR ratios. The calculation of the TMC is performed using Eqs (3)(4)(5)(6) for setting the same parameters used in the calculation of C P(AP) (f, V DC ) in Fig. 3c,e. The TMR is obtained from the Zhang formula. The calculation results of the TMC and TMR provide excellent fits to experimental data in bipolar bias regions. The reduction of TMR can be easily understood from the experimental  results of both no significant change of R P (V DC ) and the reduction of R AP (V DC ) in higher voltages, as shown in Fig. 3a. In particular, the reduction of R AP (V DC ) is due to the existence of hot electrons tunneling through the barrier, which brings about the decrease of TMR. The enhancement of TMC can also be clearly understood from the results of both the increase of C P (f, V DC ) and the reduction of C AP (f, V DC ) in higher voltages, as shown in Fig. 3c,e. The reduction of C AP (f, V DC ) is attributed to the emergence of the spin capacitance, which promotes the increase of TMC. Thus, the spin capacitance gives a significant influence on TMC, and it will play an important role on future application.
Though the application of the interesting TMC effect is not well understood at this stage, we venture to discuss the application potential of TMC devices. As can be seen from Fig. 4, TMR is larger than TMC in the low bias region. In considering the application, the important factor in sensing is an electric sensitivity. The electric sensitivity is generally expressed by the signal-to-noise (S/N) ratio, which is defined as 20logV S /V N . Here V S is a signal voltage and V N is a noise voltage. In the case of TMR sensing under the applied voltage V DC , since V S is given by ⋅ TMR V DC and V N is proportional to V DC , V S /V N is proportional to ⋅ TMR V DC . Therefore, the increase of V DC is necessary for the improvement of the S/N ratio. In fact, magnetic read heads, sensors, or MRAMs are designed for operation under a bias of a few hundred mV 61 . Additionally, the enhancement of TMR at a higher voltage is of importance. As shown in Fig. 4, the TMR decreases with increasing V DC , whereas TMC increases at higher voltages. Since V S /V N is proportional to ⋅ TMC V DC in TMC sensing, the TMC is superior to TMR from the viewpoint of the S/N ratio. Furthermore, the impedance Z of TMC devices can be reduced in the high frequency region since the impedance of the capacitor is expressed as Z = 1/jωC, where ω is the angular frequency. This means that the noise voltage V N could be reduced. The high V S and low V N lead to the enhancement of the S/N ratio. Also, the AC technique allows for the performance of various functions such as modulation/demodulation, filtering, oscillation and resonance. In fact, magnetoimpedance devices using the AC technique have enabled the application to geomagnetic sensors or positioning sensors of GPS [62][63][64][65] . Also, a capacitive magnetic sensing, in which an RC parallel circuit module consisting semiconductor magnetoresistance device and capacitor was used in the feedback loop of a Hartley or Colpitts oscillator, has been proposed and demonstrated by our group [66][67][68] . In short, TMC devices may pave a new way for various applications to the next generation of magnetic read heads, MRAMs, logic circuits, and highly sensitive magnetic sensors (including geomagnetic sensors, positioning sensors, etc.).

Prediction of an extremely large voltage-induced TMC.
Finally, the spin polarization dependence of the voltage-induced TMC is calculated for the prediction of an extremely large TMC. Figure 5a,b shows the calculated frequency dependence of the TMC under no bias voltage and the bias dependence of the TMC with varying P, respectively. Here, P TMC is assumed to be equal to P TMR , which is denoted by P. The assumed maximum value of P is 0.87, which is estimated experimentally for high-performance MgO-based MTJs at room temperature 12 Figure 5c shows the calculated frequency dependence of the TMC at V DC = 200 mV 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 sub-μs scale. According to the DF model, τ p can be tuned by changing the oscillation speed of electric dipoles formed near the FM/insulator interfaces; τ p is short for a high oscillation speed. From the viewpoint of MTJ device structure, τ p can be tuned by changing the thickness of the insulating barrier; τ p could shorten in MTJs with a thinner barrier. Although this realization in MTJs is future work, the recent study using FeCo-MgF nanogranular films has demonstrated that the TMC peak is observed at a high frequency of 220 MHz, which corresponds to τ p of 0.72 ns 69 . Our calculations predict that a large TMC of over 1100% could be possibly observed using MTJs with a realistic P of 0.87. Furthermore, this large TMC can be tuned from low to high frequencies by shortening τ P .
In summary, we observed a new phenomenon in which the TMC increases with the bias voltage in MgO-based MTJs at room temperature. The enhancement of TMC is attributed to the emergence of the spin capacitance in the AP configuration of MTJs. The voltage-induced TMC increases to 102%, which is the largest value ever reported for MTJs. We also found the voltage-induced TMC can be well explained by a newly proposed theoretical calculation using DF model combined with QBA and SDD model. This calculation predicts that the voltage-induced TMC could potentially reach 1100% in MTJs with a corresponding TMR value of 604%. These theoretical and experimental findings provide a deep insight into the voltage-induced AC spin transport in MTJs. We demonstrated that the complementary TMR and TMC effects must be treated on equal footing. The large TMC effect and the associated robustness against biasing may open up new avenues for spintronics applications and electrical modeling.

Measurements of the voltage-induced TMC.
The frequency characteristics and the bias voltage dependence of the TMR and TMC for MTJs were measured by an AC four-probe method using an Agilent Technologies 4284 A 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 easy-axis direction to 1.4 kOe. The calculation result predicts that the voltage-induced TMC could potentially reach 1100% in MTJs with a P of 0.87, which is within the realm of high-performance MTJs (See ref. 12 ). (c) Calculated frequency dependence of the voltage-induced TMC with varying τ P . The peak position of the TMC is shifted to a high frequency region for a short τ P .