Voltage-induced magnetization dynamics in CoFeB/MgO/CoFeB magnetic tunnel junctions

Recent progress in magnetic tunnel junctions (MTJs) with a perpendicular easy axis consisting of CoFeB and MgO stacking structures has shown that magnetization dynamics are induced due to voltage-controlled magnetic anisotropy (VCMA), which will potentially lead to future low-power-consumption information technology. For manipulating magnetizations in MTJs by applying voltage, it is necessary to understand the coupled magnetization motion of two magnetic (recording and reference) layers. In this report, we focus on the magnetization motion of two magnetic layers in MTJs consisting of top layers with an in-plane easy axis and bottom layers with a perpendicular easy axis, both having perpendicular magnetic anisotropy. According to rectified voltage (Vrec) measurements, the amplitude of the magnetization motion depends on the initial angles of the magnetizations with respect to the VCMA direction. Our numerical simulations involving the micromagnetic method based on the Landau-Lifshitz-Gilbert equation of motion indicate that the magnetization motion in both layers is induced by a combination of VCMA and transferred angular momentum, even though the magnetic easy axes of the two layers are different. Our study will lead to the development of voltage-controlled MTJs having perpendicular magnetic anisotropy by controlling the initial angle between magnetizations and VCMA directions.

magnetic layers under applied voltage, we conduct rectified voltage (V rec ) measurements 27,28 in MTJs that have a relatively thicker top CoFeB layers with an in-plane magnetic easy axis and ultrathin bottom CoFeB layers with a perpendicular magnetic easy axis 8 , and conduct numerical micromagnetic simulations based on the Landau-Lifshitz-Gilbert (LLG) equation of motion by taking into account VCMA on a model sample consisting of two CoFeB layers.

Results and Discussion
We prepare MTJs having 3-nm-thick top CoFeB layers (reference layer) with the in-plane magnetic easy axis and 1.3-nm-thick bottom CoFeB layers (free layer) with the perpendicular magnetic easy axis 8 (see Methods), as schematically shown in Fig. 1(a), along with the coordinate system. The CoFeB layers are separated by a 2.0-nm-thick MgO layer.
The reason for having PMA in the thin CoFeB layers has been attributed to the hybridization of Fe 3d and O 2p orbitals from the first-principles calculation 29 . The basic idea of VCMA is the modulation of the charge or spin density in the 3d orbitals by voltage or electric field [30][31][32] . Relative changes in spin density in the occupied orbitals can cause a change in PMA.
Both (top and bottom) ferromagnetic layers in our MTJs have interfacial PMA because they have an interface with the MgO layer. However, the direction of the easy axis strongly depends on the thickness of the ferromagnetic layer (inversely proportional to thickness) 33 . For the bottom layer, the PMA field overcomes the demagnetizing field to have net effective PMA. Therefore, the bottom layer has a perpendicular magnetic easy axis. However, the PMA value in the top layer is less than the demagnetizing field. Therefore, the top layer has an in-plane magnetic easy axis 33 .
To evaluate the VCMA field, we measure the differential resistance (dV/dI) of the MTJ as a function of an external magnetic field along the y-axis (H y ) under various bias voltages (V b ) ranging from − 0.4 to + 0.4 V. A positive voltage means the bottom electrode has positive potential with respect to the top electrode of the MTJ.
The curves of normalized dV/dI at V b = − 0.4 V (red line) and + 0.4 V (blue line) are plotted as functions of H y in Fig. 1(b). At μ 0 H y = − 2.0 T, the two curves show their minimum values after saturation, indicating that the magnetizations in both (top and bottom) CoFeB layers are along the negative y-axis. As H y increases to zero, the curves of dV/dI under |V b | = 0.4 V increase and reach maximum values at the zero magnetic field, indicating that the magnetization in the bottom CoFeB layer is almost aligned along the out-of-plane direction. When H y turns to a positive value, the magnetization in the top CoFeB layer starts to align towards the positive y-axis. Then, the curves of dV/dI decrease with the increase in H y for both bias voltages and reach minimum values again, indicating that the magnetizations of both CoFeB layers again lie along the in-plane direction (+ y-axis).
The difference between the two curves in Fig. 1(b) is clear. The difference comes from the modulation of an interfacial PMA field (H k ) by V b through the VCMA effect. From the difference in H k due to the applied V b , the Scientific RepoRts | 7:42511 | DOI: 10.1038/srep42511 magnitude of VCMA, i.e., μ 0 Δ H k /V, can be determined. We evaluate Δ H k , which are defined by the difference between H k (V b ) and H k (0) (by using the method mentioned in pervious studies 24,34), at |V b | = 0, 0.2, and 0.4 V, and Fig. 1(c) plots Δ H k as a function of V b . The gradients of μ 0 Δ H k are different for positive and negative V b . At positive (negative) V b , μ 0 Δ H k /V b is 127.1 (26.0) mT/V. The possible reason behind the difference between gradients under positive and negative V b has been discussed 29,34 . According to these reports, the different thicknesses of the two CoFeB layers in the MTJs may show asymmetric dependence of PMA on positive and negative V b . Figure 2(a) shows the dependencies of V rec on the excitation frequency (f RF ) at an amplitude of RF voltage V RF = 0.4 V. A static magnetic field is applied along the y-axis ranging from − 120 to + 120 mT (see Methods). In this figure, each curve of V rec artificially shifts by 0.25 mV vertically.
The curves of V rec show two FMR peaks 35 . One of the FMR peaks shows a strong dependence of resonance frequency (f FMR ) on H y (indicated by red arrows), whereas the other peak shows a slight change in f FMR with H y (indicated by blue arrows). The former peak corresponds to the FMR of the top CoFeB layer, whereas the latter peak corresponds to that of the bottom CoFeB layer.
The difference between the dependencies of f FMR on H y in the two layers can be explained as follows. The f FMR of a ferromagnetic layer depends on the effective magnetic field of the layer. The effective field of the top CoFeB layer monotonically increases with |H y | due to the in-plane easy-axis of magnetization. On the other hand, the effective field of the bottom CoFeB layer does not vary significantly in the range of applied magnetic field due to the presence of strong PMA. In the case at μ 0 |H y | = 120 mT, the magnetization of the bottom CoFeB layer tilts only up to 13° from the z-axis (Fig. 3(c)).
The line shapes of resonance peaks ( Fig. 2(a)) in the bottom and top layers can be fitted by the sum of the symmetric and anti-symmetric Lorentzians given by 24,35,36 : where V s (V as ) is the symmetric (anti-symmetric) term of signal amplitude, and σ is the half width at half maximum. Here, V s originates from the STT-induced FMR, whereas V as comes from the FMR induced by modulation of the effective field through VCMA and field-like torque (FLT) 24,36,37 . Equation (1) fits the experimental resonance peaks quite well. Figure 2(a) shows an example of such fitting for V rec at μ 0 H y = − 120 mT for the bottom CoFeB layer (yellow line). According to the results of fitting, V as is around ten times larger than V s for both layers. Therefore, the contribution of VCMA torque is dominant over the STT because the contribution of the STT is too small to induce FMR due to the large resistance of the 2.0-nm-thick MgO barrier (current density is less than 1.0 × 10 6 A/m 2 ). Similarly, the FLT is also expected to be much smaller than VCMA torque 28 .   Fig. 2(b), the V as of the top layer is maximum at H y = 0 and decreases with |H y |. This is because the equilibrium direction of the magnetization slightly tilts from the x-y plane at H y = 0 due to the interlayer dipolar coupling and aligns toward the y-direction as H y increases (see Fig. 3(b)). The small angle tilted from the x-y plane contributes to the magnetization motion in this case. Therefore, V as strongly depends on the initial configuration of the magnetizations, i.e., having a finite angle between the magnetization direction and z-axis at H y = 0. In contrast, the V as of the bottom layer is almost zero at H y = 0 and increases monotonically with |H y |. The reason for the V as behaviour of the top and bottom layers is discussed in detail with the help of micromagnetic simulations in the last section of this report. Figure 2(c) plots the f FMR of the top and bottom layers obtained from the fitting as functions of H y . As shown in Fig. 2(c), the f FMR of the top layer increases with |H y |, reflecting the increase in the effective field, as mentioned above. The f FMR of the bottom layer slightly decreases as |H y | increases because of the weak dependence of the effective field on H y in the out-of-plane magnetization configuration.
From the experiments, we find that the dependence of the magnitude of the magnetization motion on H y is different between the top and bottom CoFeB layers. The results indicate that the amplitude of the magnetization motion in MTJs can be potentially controlled by the initial configuration of two magnetizations in the top and bottom magnetic layers.
The V rec can be expressed as a time-averaged value of the product of oscillating magneto-resistance due to the precession of magnetization via the VCMA and RF tunnel current as 24,36 where R is the static resistance of an MTJ, p is spin polarization, and ϕ(t) is the time-dependent relative angle between the magnetizations in the top and bottom CoFeB layers. The term R(t) = R/(1 + p 2 cosϕ(t)) represents the time-dependent resistance due to oscillation of ϕ, and I RF (t) = V RF sin(2πf RF t)/R represents the time-dependent tunnel current. As shown in Eq. (2), V rec is represented by the time variation of ϕ when V RF is applied. To obtain the magnetization motion of the top and bottom CoFeB layers through the time variation of ϕ, therefore, we conduct micromagnetic simulations based on the LLG equation of motion by taking into account the VCMA effect. The LLG equation of motion is given by where the STT term can be ignored because of its small contribution in the MTJ. In this equation, M is magnetization, γ = 1.7 × 10 −11 is the gyromagnetic ratio, α = 0.03 is the Gilbert damping constant 33 , and H eff is the effective magnetic field. The effective field in the perpendicular direction (H eff ) z = [H k + Δ H k sin(2πf RF t)]cosθ includes contributions from H k and the time-dependent modulation of the PMA field Δ H k sin(2πf RF t) by applying V RF . Equation (3) is numerically solved using the object-oriented micromagnetic framework (OOMMF) simulator 38 . The model samples for the simulations have top (with the in-plane magnetic easy axis) and bottom (with the perpendicular magnetic easy-axis) CoFeB layers separated by a distance of 2.0 nm (Fig. 3(a)) to mimic the experimentally measured MTJ with a 2.0-nm-thick insulating MgO layer (see Methods). The μ 0 Δ H k is taken as 30 mT, which corresponds to the experimentally applied V RF of 0.4 V. In all our simulations, a static magnetic field of 120 mT is applied along the y-axis.
The simulation results of the polar angles (angles with respect to the z-axis) of the magnetizations in the top and bottom CoFeB layers, θ top and θ bot , are plotted as functions of an elapsed time t when applying RF voltage with f RF = 15.0 GHz in Fig. 3(b) and (c), respectively. In this case, the VCMA field is applied only to the area of the bottom CoFeB layer just below the top CoFeB layer (blue area in Fig. 3(a)). The θ top is obtained from the averaged magnetization over the top CoFeB layer and θ bot from the averaged magnetization over the blue area in the bottom CoFeB layer.
As shown in Fig. 3(b), at t = 0, the magnetization in the top CoFeB layer makes a small angle (~1.8°) with respect to the x-y plane due to the interlayer dipolar coupling with the bottom CoFeB layer. The magnetization of the bottom CoFeB layer is also tilted from the perpendicular direction by around 11° (Fig. 3(c)), reflecting the effect of the sum of H y and interlayer dipolar coupling.
As t increases, the magnetization in the bottom CoFeB layer oscillates at a frequency of 15 GHz due to VCMA. The magnetization in the top CoFeB layer also oscillates despite the fact that VCMA is not taken into account in the simulation model and 15 GHz is not the resonance frequency of the top layer. These results indicate that a small amount of angular momentum of the bottom CoFeB layer is transferred to the top CoFeB layer due to the dynamic dipolar coupling between them while they are separated by a distance of 2.0 nm 39 .
As shown in Fig. 3(b) and (c), Δ θ top and Δ θ bot are defined as amplitudes of oscillation angles of magnetizations in the top and bottom CoFeB layers, respectively. At f RF = 15.0 GHz, Δ θ bot = 2.9° and Δ θ top = 0.1° are obtained. To confirm the magnitude of the transferred angular momentum, we also conduct a simulation by using a model sample with a bottom CoFeB layer only. Figure 3(d) plots θ bot as a function of t. In this case, we obtain Δ θ bot = 3.4°, which is larger than that in the sample with the top CoFeB layer. This result indicates that in our simulation model, the angular momentum is transferred from bottom to top CoFeB layers by more than 3% in angle equivalent. Similarly, the angular momentum induced in the excitation area (blue area in Fig. 3(a)) may also be transferred to the remaining area in the bottom CoFeB layer (red area in the bottom CoFeB layer in Fig. 3(a)).
We conduct the simulations at various f RF at μ 0 H y = 120 mT using a model sample with the top and bottom CoFeB layers and plotted V rec calculated from simulation results as a function of f RF (Fig. 4(a)). Note that the VCMA field is applied only to the bottom CoFeB layer in this simulation.
The simulated V rec reproduces the experimentally obtained FMR signal at 15.6 GHz from the bottom CoFeB layer, as shown in Fig. 2(a). However, the simulated resonance frequencies of the top and bottom CoFeB layers are larger than the experimental values due to the smaller dimensions of the model sample for simulation compared to the dimensions of the experimental sample 40 . The height of the resonance peak at around 10 GHz, which comes from the oscillation in the top CoFeB layer, is much smaller than that at 15.6 GHz, unlike the experimental results.
The possible reason for the small amplitude of the resonance peak at around 10 GHz is explained as follows. The simulated Δ ϕ (blue line), which is the oscillation amplitude of the relative angle between magnetizations of the top and bottom layers, is plotted as a function of f RF together with Δ θ top (red line) and Δ θ bot (green line) in Fig. 4(b). Both Δ ϕ and Δ θ bot increase as f RF increases and reach a maximum of around 4° when f RF approaches f FMR of 15.6 GHz. In the case of the top CoFeB layer, Δ θ top shows a maximum value of 0.2° at 10.2 GHz. This peak corresponds to the f FMR of the top CoFeB layer, as shown in Fig. 2(a), which is generated by the transfer of angular momentum from the bottom CoFeB layer, although the Δ θ top is not large enough to reproduce the experimentally obtained peak.
The Δ θ top shows another peak (0.1°) at 15.6 GHz, which corresponds to the f FMR of the bottom CoFeB layer. This peak is considered to be induced by the FMR mode of the bottom CoFeB layer. Therefore, we conclude that the top CoFeB layer with the in-plane magnetic easy axis can be excited by the transfer of angular momentum from the bottom CoFeB layer. However, the signal is much smaller than that of the experiment.
We also conduct a simulation by taking into account the VCMA in the top CoFeB layer. It is also possible to excite the top layer by VCMA, like the bottom layer 25 , since the top CoFeB layer has an interfacial PMA of about 0.8 T (< M s ), and the magnetization of the top CoFeB layer makes a small angle with in-plane direction under the equilibrium (static) condition ( Fig. 3(b)). To reproduce the V rec signal from the top CoFeB layer at around 10.0 GHz, the VCMA in the top CoFeB layer is included in the simulations in addition to that in the bottom CoFeB layer. The magnetization of the top CoFeB layer makes a small angle with the x-y plane. Because the VCMA field decreases in proportional to cosθ 25,41 , the VCMA field applied to the top CoFeB layer must be smaller than that in the bottom CoFeB layer. In this model, the magnitude of the VCMA field applied to the top CoFeB layer is selected to be Δ H k = − 1.5 mT, which is comparable to the estimated VCMA field considering factor cosθ. The Δ H k in the z-direction is applied to the lower 1.0-nm region of the top CoFeB layer since VCMA is effective only at the interface area.
The simulation results of V rec are plotted as a function of f RF at μ 0 H y = 120 mT in Fig. 4(c). The simulated V rec agrees well with the line shape of the experimentally obtained V rec plotted in Fig. 2(a), showing two FMR peaks. Figure 4(d) illustrates the dependencies of Δ ϕ (blue line), Δ θ top (red line), and Δ θ bot (green line) on f RF . In this figure, Δ ϕ shows two peaks, at 10.2 and 15.6 GHz, reflecting the FMR signals from the top and bottom CoFeB layers. In this simulation, therefore, the top layer is predominantly excited by VCMA, like the bottom layer.
Finally, we discuss the magnetization motion of the top and bottom CoFeB layers generated by RF voltage in detail. The V as in the top CoFeB layer is maximum at H y = 0 and decreases as |H y | increases. In the case of the top CoFeB layer, it is important to have a small angle between the magnetization direction and x-y plane for the magnetization motion, as mentioned above.
The V as in the bottom CoFeB layer increases as |H y | increases in the magnetic-field range from − 120 to +120 mT, while the V as is almost zero at H y = 0, as shown in Fig. 2(c). The dependence of V as on H y is consistent with the results presented in a previous study 25 . The possible reason for this behavior of V as is explained as follows.
In the absence of H y , the equilibrium direction of magnetization of the bottom CoFeB layer is in the z-axis. In this situation, the magnetization does not show apparent motion because VCMA corresponds to a modulation along the z-direction. As a result, the magnetization (red arrow) remains in the z-direction even under applied RF voltage, as shown in Fig. 4(e). In contrast, the equilibrium direction of the magnetization tilts toward the y-direction if H y is applied. When RF voltage is applied, the VCMA field modulates the magnetization toward the z-direction. Therefore, the magnetization in this situation shows reciprocal motion in the y-z plane in addition to precessional motion, as shown in Fig. 4(f). We have also confirmed that the precessional amplitude (cone angle of precession) increases with the increase in |H y | in the range of our measurement (not shown), which is consistent with our experimental results.

Conclusion
We have investigated the magnetization motion in the two magnetic layers in MTJs under applied RF voltage by using both experimental measurements and micromagnetic simulations by taking into account VCMA. From the experiments, the dependence of the magnitude of the magnetization motion on H y is different between the top and bottom CoFeB layers, and magnetization dynamics strongly depends on the initial angles of magnetizations with respect to the VCMA direction. From the simulation results, the magnetization motion in both the top and bottom CoFeB layers is induced by a combination of VCMA and transferred angular momentum, although the magnetization direction of the two layers is different. Our results will have a large impact on understanding the mechanism of magnetization dynamics in MTJs excited by VCMA and developing voltage-controlled MTJs having PMA by controlling the initial angle between magnetizations and VCMA directions.

Methods
Sample fabrication. The film-stacking structure used in this study is prepared on a thermally oxidized Si(001) substrate by RF sputtering at room temperature at a base pressure of 10 −9 Torr. The structure consists of the following layers (from the substrate side; nominal thicknesses in nanometres are stated in parentheses): Ta (5)/Ru (10)/Ta (5)/Co 20 Fe 60 B 20 (1.3)/MgO (2.0)/Co 20 Fe 60 B 20 (3.0)/Ta (5)/Ru (5). Rectangular shaped MTJs, as shown in Fig. 1(a), are fabricated by a combination of photolithography, Ar-ion milling, and RF sputtering in a multistep fabrication method. First, the top CoFeB layer of 2 × 6 μm 2 is prepared by photolithography followed by Ar + ion milling down to the top MgO layer and subsequent deposition of Al 2 O 3 . In the second step, the bottom CoFeB layer with larger dimensions 40 × 40 μm 2 is defined, keeping the former rectangular structure in the middle followed by Ar + ion milling down to the Si substrate. Third, 80-nm-thick insulator Al 2 O 3 was deposited by sputtering everywhere except at the extremities of the top and bottom CoFeB layers. Finally, contacts made of Au (100 nm) are prepared by electron beam evaporation. The fabricated MTJs are annealed at 300 °C in vacuum under a perpendicular magnetic field of 600 mT for one hour.
Experimental measurement. The magnetization dynamics in CoFeB layers are excited by sending RF voltage through the capacitor port of a bias tee. The RF voltage (V RF ) produces an RF electric field (E RF ) at the interfaces of the top and bottom CoFeB/MgO layers. The E RF modulates the interfacial PMA of both CoFeB layers. When the frequency of V RF matches the f FMR of any layer, the magnetization dynamics of that layer is excited. The magnetization dynamics produces an oscillatory TMR (depending upon the relative angle between the magnetizations of two layers) at the same frequency as that of the V RF . The mixing of an oscillatory TMR and small RF tunnel current generates finite DC voltage (rectified voltage), which is measured using a voltmeter connected to the DC port of the bias tee.
Micromagnetic simulations. Two types of model samples are considered for the simulations. One has top and bottom CoFeB layers with thicknesses of 3.0 and 1.0 nm, respectively, as shown in Fig. 3(a). The mesh size is set to 2 × 2 × 1 nm 3 . The two CoFeB layers are arranged 2.0 nm apart. The MTJs are downscaled to reduce the computation time. The lateral dimensions of the bottom CoFeB layer is 60 × 180 nm 2 , and those of the MgO and top CoFeB layers is 20 × 60 nm 2 . For the other model sample, we chose only a single CoFeB layer with a thickness of 1.0 nm and area 60 × 180 nm 2 . We adopt the anisotropy energy density of the bottom CoFeB layer in the perpendicular direction of 1.2 MJ/m 3 , and the saturation magnetization M s of 1.5 T, resulting in μ 0 H k of around 500 mT. The ground state of magnetization is first prepared by applying a bias magnetic field along the y-axis. The dynamics is then excited by applying a sinusoidal RF magnetic field (Δ H k ) equivalent to a PMA field modulated by applied V RF of 0.4 V. For the bottom layer, Δ H k is selected as 30 mT (calculated from the experimental results shown in Fig. 1(c)). As the PMA is only modulated in the area of the bottom CoFeB layer underneath the top layer (blue area in Fig. 3(a)), Δ H k is applied only to the blue area of the bottom CoFeB layer. In some simulations, the dynamics of the top CoFeB layer are also exited by a much smaller value of Δ H k = − 1.5 mT along the z-axis. The reason behind this small value is explained in the main text.