# Recent Progress in the Voltage-Controlled Magnetic Anisotropy Effect and the Challenges Faced in Developing Voltage-Torque MRAM

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## Abstract

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## 1. Introduction

^{7}k

_{B}T (k

_{B}is the Boltzmann constant and T is the temperature, assumed to be 300 K). On the other hand, the energy that is required to maintain magnetic information, i.e. the thermal stability, is about 60 k

_{B}T (green line in Figure 1), which means that we have a large energy gap between data writing and retention, in the order of 10

^{5}. This difference mainly comes from unwanted energy consumption due to ohmic dissipation of the electric-current flow. Overcoming this fundamental issue using a novel way of electric-field based spin manipulation is strongly desired. Not only for MRAMs, but all of the nonvolatile memories that have been proposed so far have a dilemma of choosing between stable nonvolatility and high operating energy. Therefore, the development of a novel type of memory having low operating energy as well as low stand-by energy can have great impact on the design of future memory hierarchy.

## 2. Overview of the VCMA Effect and Voltage-Induced Dynamic Switching

_{80}Co

_{20}layer is fixed at 0.58 nm. The bias direction is defined with respect to the top ITO electrode. A clear change in the saturation field in the out-of-plane direction can be seen, which suggests a modification in the PMA. Under the application of a positive bias, the PMA is suppressed and the in-plane anisotropy becomes more stable. On the other hand, the application of a negative voltage enhances the PMA and even the transition of the magnetic easy axis can be realized from the in-plane to the out-of-plane direction.

_{80}Co

_{20}(0.5 nm)/MgO(t

_{MgO})/Fe grown on a MgO(001) substrate [48]. Here, we made electrical ferromagnetic resonance (FMR) measurements through the TMR effect. The PMA energy, K

_{PMA}, was evaluated from the resonant frequency of the free layer at each applied voltage. In addition to FMR measurements, the effect of a bias voltage on normalized TMR curves has also often been used for the quantitative evaluation of the VCMA effect, as discussed later [49]. Generally, the PMA energy linearly changes as a function of the applied electric field, E, which is defined as the applied bias voltage, V

_{bias}, divided by the MgO thickness, t

_{MgO}. The slope of the linear relationship represents the VCMA coefficient in units of J/Vm, e.g. −37 fJ/Vm for the case in Figure 3. The VCMA coefficient is one of the most important parameters for demonstrating scalability and also in the reliable switching of the magnetization and thus the development of voltage-torque MRAM.

_{bias}. When a short pulse voltage is applied to eliminate the PMA completely, the magnetization starts to precess around the H

_{bias}(Figure 4b). If the voltage pulse is turned off at the timing of half turn precession, then the magnetization can be stabilized in the opposite “down” direction (Figure 4c). H

_{bias}is required to determine the axis of magnetization precession. The effective field, such as crystalline anisotropy field and the exchange bias field, is also applicable.

_{SW}) as a function of pulse width, as shown in Figure 5b. A high P

_{SW}is obtained at the timing of half turn precession; however, when the pulse width is twice this, one turn precession results in low P

_{SW}. From a practical point of view, the first half turn precession is effective in obtaining a low WER with fast switching speed. Under the condition that the PMA is completely eliminated, the amplitude of H

_{bias}determines the precession frequency, and then the switching time, t

_{SW}for the half turn precession is expressed as

_{0}are the magnetic damping constant, the gyromagnetic ratio, and the permeability of vacuum, respectively.

## 3. Physical Origin of the VCMA Effect

_{z}term (m

_{T}), respectively, the aforementioned two mechanisms can be validated by X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) spectroscopy.

_{S}, m

_{L}, and m

_{T}) can be determined from the measured XAS/XMCD spectra. Here, the measured orbital magnetic moments and magnetic dipole T

_{z}term have the following relationships;

_{z}term.

_{2}(5 nm)/Cr (2 nm)/Au (5 nm), was deposited on a MgO(001) substrate. Figure 8b shows the typical XAS/XMCD results around the L

_{3}and L

_{2}edges of Co with a magnetic field of 1.9 T (θ = 20°) to saturate the magnetization of the Fe/Co layer. The changes in the orbital magnetic moment and effective spin magnetic moment (m

_{S}− 7m

_{T}) of Co were determined while using sum-rule analysis, and they are summarized in Figure 8c,d. We can see that m

_{L}of Co with an electric-field of −0.2 V/nm is larger than that corresponding to +0.2 V/nm. Moreover, the induced change in m

_{L}with θ = 20° is larger than that with θ = 70°. The experiment demonstrates that an orbital magnetic moment anisotropy change of (0.013 ± 0.008)μ

_{B}between the magnetization angles of θ = 20° and 70° was generated in the presence of applied electric fields of ±0.2 V/nm. Figure 8d shows the electric-field-induced change in m

_{S}− 7m

_{T}of Co. As with m

_{L}, m

_{S}− 7m

_{T}is enhanced under the application of a negative electric-field. Moreover, the electric-field-induced change in the magnetic moment is anisotropic. In contrast to m

_{T}, it is known that m

_{S}is not sensitive to the magnetization direction. Hence, the anisotropic part of the induced change in the magnetic moment should be attributed to m

_{T}.

_{Co}= 5 meV, then the induced change in the PMA energy is estimated to be 0.039 ± 0.023 mJ/m

^{2}when the applied electric-field is switched from +0.2 V/nm to −0.2 V/nm. Here, the experimentally obtained Δm

_{L}= (0.017±0.010)μ

_{B}was used. From the VCMA coefficient in the Fe/Co/MgO system (−82 fJ/Vm), the PMA energy change at ±0.2 V/nm is 0.03 mJ/m

^{2}, which is in good agreement with the PMA energy change that was obtained using the first term of Equation (2). From the discussion above, the change in the orbital magnetic moment anisotropy in Co seems to explain the VCMA effect. However, the impact of the change in the magnetic dipole T

_{z}term (m

_{T}) that is shown in Figure 8d on the VCMA effect remains to be seen. In Ref. 113, a first principles study was employed to clarify this point. As a result, the VCMA effect from the spin-flip terms (ΔE

_{↓↑}+ ΔE

_{↑↓}) is found to be negligible and that from the spin-conserved terms (ΔE

_{↑↑}+ ΔE

_{↓↓}) appeared to be dominant. Therefore, the change in orbital magnetic moment is responsible for the VCMA effect. Due to the large exchange splitting for Co, the observed changes in m

_{T}do not contribute to the VCMA effect, as described by the second term in Equation (2).

_{3}and L

_{2}energy edges of Pt. A perpendicular magnetic field of ±60 mT was applied to saturate the magnetization of FePt. Figure 9c,d show electric-field-induced changes in the magnetic moments of Pt. The results confirm a clear bias voltage inductions of m

_{S}− 7m

_{T}, while there is no significant change to m

_{L}under voltage applications.

_{z}term (m

_{T}) [114,115,116,118]. In contrast to m

_{T}, m

_{S}is not sensitive to the magnetization direction. In Ref. 116, the voltage-induced change in m

_{S}− 7m

_{T}shows large magnetization direction dependence. Thus, the observations indicate the significant induction of m

_{T}in Pt by an external voltage. A first-principles study was also conducted for the FePt/MgO system, similar to the Fe/Co/MgO study. As a result, firstly, the monoatomic Pt layer at the interface with MgO makes the dominant contribution to the VCMA effect. Moreover, while the VCMA effect from the spin-conserved terms (ΔE

_{↑↑}+ ΔE

_{↓↓}) decreases the PMA energy, the VCMA effect that is induced by the applied voltage from the spin-flip terms of interfacial Pt increases the PMA energy (ΔE

_{↓↑}+ ΔE

_{↑↓}). The total PMA energy in the FePt/MgO system increases under the condition of electron depletion at the Pt/MgO interface, as the PMA energy increase by the spin-flip terms is greater than the PMA energy decrease by the spin-conserved terms.

_{0}-FePt, as shown in Ref. 116. As discussed in the recent review paper [111], it has been widely recognized that the XAS/XMCD spectroscopy is a powerful tool to investigate the voltage-induced effects in spintronic devices [28,113,116,119,120,121,122,123,124].

_{x}system. In Ref. 122, XAS/XMCD spectroscopy at the Co absorption edge was employed to a Ta (4 nm)/Pt (3 nm)/Co (0.9 nm)/GdO

_{x}(33 nm)/Ta (2 nm)/Au (12 nm) multilayer and found that an applied voltage changes the oxidation state and magnetization of the Co. Ref. 125 also reports real-time measurements of such an electrochemical VCMA effect. The operating speed strongly depends on the applied voltage and temperature, which strongly indicates that the electrochemical VCMA requires a thermal activation process. The reported maximum speed was in the sub-millisecond range. Therefore, such large values of the electrochemical VCMA seem attractive, but lie beyond the scope of VCMA studies for working memory applications. A similarly large VCMA effect with limited operating speed has been observed in many systems with electrochemical reactions [28,126,127] and/or charge traps [128,129].

## 4. Materials Research for a Large VCMA Effect

_{free}and M

_{S}are the thickness and saturation magnetization of the free layer. K

_{i}(E) is the PMA under application of the electric-field (E), and it is given by

_{0}are the area of the free layer and the thermal stability under zero electric-field, respectively.

_{0}can be expressed as,

_{SW}is the amplitude of the switching electric-field.

_{free}= 1 nm and E

_{SW}= 1 V/nm for each value of Δ

_{0}. If we take cache memory applications as an example, the required K

_{PMA}t

_{free}values range from 0.2 mJ/m

^{2}to 0.5 mJ/m

^{2}, depending on the target Δ

_{0}values; consequently, the required VCMA coefficient is estimated to be from 200 fJ/Vm to 500 fJ/Vm. The main memory applications need higher K

_{PMA}t

_{free}values in the range from 0.6 mJ/m

^{2}to 1.5 mJ/m

^{2}. As a result, the required VCMA coefficient is in the range from 600 fJ/Vm to 1500 fJ/Vm. However, in experiments that have only focused on the purely-electronic VCMA effect, the achieved VCMA coefficient that is demonstrated in practical materials, such as CoFeB, has been limited to about 100 fJ/Vm [71,78,81,98].

_{Fe})/MgO (t

_{MgO}= 2.3 nm)/Fe(10 nm) on MgO(001) substrates. Here, the bottom ultrathin Fe layer is the voltage-controlled free layer with perpendicular magnetic easy axis and the top 10 nm-thick Fe is the in-plane magnetized reference layer. Figure 11a shows an example of the applied bias voltage, V

_{bias}, and dependence of the half-MR loop measured under an in-plane magnetic field, H

_{ex}. The vertical axis is normalized using the maximum (H

_{ex}= 0 Oe) and minimum (H

_{ex}= −20 kOe) resistances. The Fe thickness is fixed at t

_{Fe}= 0.44 nm.

_{90}+ (G

_{P}−G

_{90})cosθ. Here, G

_{90}and G

_{P}are the conductance under the orthogonal and parallel magnetization configurations. Therefore, the ratio of the in-plane component of the magnetization of the free layer, M

_{in-plane}, to its saturation magnetization, M

_{S}, is expressed as

_{P}is the MTJ resistance in the parallel magnetization configuration, R

_{90}is the MTJ resistance in the orthogonal magnetization configuration, and R(θ) is the MTJ resistance when the magnetization of the ultrathin Fe layer is tilted towards the in-plane direction at angle θ under the application of an in-plane magnetic field. Using Equation (8), we can evaluate the normalized in-plane magnetization versus the applied magnetic field. The inset in Figure 11b shows an example of a normalized M-H curve measured under V

_{bias}= 10 mV. The PMA energy, K

_{PMA}can be calculated from M

_{in-plane}(H) with the saturation magnetization value evaluated by SQUID measurements (yellow area in the inset of Figure 11b). Figure 11b summarizes the applied electric-field, V

_{bias}/t

_{MgO}, dependence of K

_{PMA}t

_{Fe}. With ultrathin layers of Fe, an unexpected nonlinear VCMA effect was observed. Under the application of negative voltages, the PMA monotonically increases with a large VCMA coefficient of −290 fJ/Vm. On the other hand, the PMA deviates from a linear relationship under the application of positive voltages. Figure 12 summarizes the Fe thickness dependence of the VCMA coefficient. This nonlinear VCMA effect was only observed with ultrathin layers of Fe, t

_{Fe}< 0.6 nm (blue dots), and the usual linear VCMA effect appears for thicker layers (red dots). Xiang et al. systematically investigated the tunneling conductance, the PMA, and the VCMA effect in a similar system to determine the origin of the nonlinear VCMA effect, but the MgO was replaced by a MgAl

_{2}O

_{4}barrier, which has smaller lattice mismatch with Fe. Interestingly, they found strong correlation between the VCMA effect and the quantum well states of Δ

_{1}band formed in an ultrathin Fe layer that is sandwiched between the Cr and MgO layers [138]. These results may indicate that artificial control of the electronic states in an ultrathin ferromagnetic layer may provide a new approach for designing the VCMA properties. In addition to the influence of quantum well states, we found that intentional Cr doping at the Fe/MgO interface can enhance the PMA and the VCMA effect [62]. Therefore, intermixing with the bottom Cr buffer may also have an influence on the observed large VCMA effect. A theoretical investigation to understand the role of the inter-diffused Cr atoms has been proceeded [139,140].

_{Fe})/Ir(t

_{Ir})/MgO (2.5 nm) with indium-tin oxide (ITO) or Fe (10 nm) top electrodes to investigate the impact of the introduction of Ir on the interfacial PMA and the VCMA effect [35]. The ultrathin Ir layer was inserted between the Fe and MgO layers; however, we found that the Ir atoms were dispersed inside the Fe layer during the post-annealing process, as seen in the HAADF-STEM images in Figure 13a. Atomic-scale Z-contrast HAADF-STEM imaging enabled the identification of inter-diffused Ir atoms as bright spots that are indicated by yellow arrows. The first-principles calculation predicts strong in-plane anisotropy at the Ir/MgO interface [141]; however, we observed an unexpected enhancement in the PMA. Figure 13b shows a comparison between the polar MOKE hysteresis curves of a single Fe layer (t

_{Fe}= 1.0 nm) and an Ir-doped Fe layer formed the bilayer structure consisting of Fe (1.0 nm)/Ir (0.1 nm)). The pure Fe layer exhibits large saturation fields of about 7 kOe, which indicated an in-plane magnetic easy axis. On the other hand, the introduction of the quite thin Ir doping layer resulted in transition of the magnetic easy axis from the in-plane to the out-of-plane direction. Figure 13c summarizes the dependence of the intrinsic interfacial magnetic anisotropy, K

_{i,0}, on the thickness of the Ir layer. With appropriate Ir doping, K

_{i,0}reaches 3.7 mJ/m

^{2}, which is about 1.8 times that observed at the Fe/MgO interface (2.0 mJ/m

^{2}) [35,134].

_{FeIr}= 0.82 nm; formed from Fe (0.77 nm)/Ir (0.05 nm)). The saturation field shifts with changes in the applied voltage, as is the case in a pure Fe/MgO structure. However, the applied electric-field dependence of K

_{PMA}t

_{FeIr}exhibits a completely different trend when compared with that observed in the Fe/MgO structure. We observed a large reduction in PMA with a VCMA coefficient of −320 fJ/Vm under positive voltages (see Figure 14b). It is interesting that such a low doping concentration of Ir, which is even thinner than one monolayer, can have a drastic effect on the VCMA properties. In addition, voltage-induced FMR measurements confirmed the high speed response of the VCMA effect, as shown in the inset in Figure 14b. Thus, the observed large VCMA comes from purely-electronic origin.

_{94}Ir

_{6}(5ML)/MgO(5ML) structures to discuss the physical origin of the large VCMA effect in Ir-doped Fe. The Ir-doped bcc Fe was modeled by a supercell consisting of 4×4 unit cells as shown in Figure 15a. Figure 15b depicts the atomic-resolved electric-field induced magnetic anisotropy energies (MAE) for the Fe and Ir atoms. The variation in the MAE for the Ir atoms is more than five times greater than that for the Fe atoms. Interestingly, MAE change in the second layer (layer 2 in Figure 15b) from the interface with the MgO layer is larger than that of the layer 1, contrary to expectations.

_{↑↑}is larger than that for the minority spin states δE

_{↓↓}. On the other hand, the spin-flip terms that are by the electric-field, δE

_{↑↓}and δE

_{↓↑}have almost the same absolute value, but with opposite sign, so the VCMA effect that arises from the spin-flip term is small. Therefore, the large VCMA effect in Ir-doped Fe is mainly caused by the electric-field effect on the majority spin Ir-5d states and it can be interpreted by the modulation in the first term of Equation (2), i.e. the orbital magnetic moment mechanism.

## 5. Towards Reliable Voltage-Induced Dynamic Switching

_{sw}is the switching probability, t

_{pulse}is the pulse width; and, V

_{pulse}is the voltage amplitude. When V

_{pulse}is small, the VCMA effect cannot completely eliminate the magnetic energy barrier; therefore, the magnetization switching in this region is dominated by thermal activation. As V

_{pulse}is increased, well-defined oscillation of P

_{sw}appears, which is a signature of precession-mediated switching induced by the VCMA effect. As discussed in Section 2, the highest P

_{sw}is obtained at t

_{pulse}that corresponds to one-half the magnetization precession cycle, and then P

_{sw}gradually moves toward 0.5 while undergoing damped oscillations. This behavior can be understood as the combined action of magnetization damping and thermal fluctuations.

_{80}B

_{20}/W cap and experimentally demonstrated a WER of 4 × 10

^{−3}. They also demonstrated in numerical simulations that the WER could be reduced by improving the thermal stability factor, Δ and by reducing the magnetic damping, α of the free layer, as shown in Figure 17c. An improved Δ effectively reduces the thermal fluctuations in the initial state and in the relaxation process after switching. Moreover, a lower α can reduce the influence of thermal fluctuations during the switching process, which leads to more accurate writing. However, it should be noted that, the larger the value of Δ, the larger the VCMA efficiency required, otherwise the magnetization switching is dominated by thermal activation, and well-controlled magnetization switching cannot be obtained. By using CoFeB/MgO/CoFeB p-MTJs, Grezes et al. experimentally investigated the WER and the read disturbance rate as a function of read/write pulse width and amplitude, and examined the compatibility of the bit-level device performance for integration with CMOS processes [110]. They also simulated the performance of a 256 kbit voltage-torque MRAM block in a 28 nm CMOS process, and showed the capability of the MTJs for delivering WERs below 10

^{−9}for 10 ns total write time by introducing the read verify processes. The introduction of read verify processes makes it possible to reduce the effective WER, however it causes an increase in the total writing time. Therefore, we need further effort to reduce the essential WER that is induced by single pulse switching. Recently, Shiota et al. showed that improvement in the PMA and VCMA properties can be achieved in the MTJ consisting of Ta/(Co

_{30}Fe

_{70})

_{80}B

_{20}/MgO/reference layer, and demonstrated a WER of 2 × 10

^{−5}without the read verify process [106]. Further optimization of the composition of the CoFeB alloy and the device structure allowed for a WER lower than 10

^{−6}to be achieved, as shown in Figure 18 [109]. In this case, the introduction of a once read verify process enables a practical WER of the order of 10

^{−12}.

**M**, and its time evolution can be obtained by numerically solving the Landau-Lifshitz-Gilbert equation:

_{s}is the saturation magnetization, t is the time, α is the damping constant, and

**H**

_{eff}is the effective field given by

**m**= (m

_{x}, m

_{y}, m

_{z}) is the magnetization unit vector and H

_{x}is an in-plane bias magnetic field. As displayed in Figure 19a, without the VCMA effect, the magnetization has two energy equilibrium at ${\tilde{\mathit{m}}}_{\pm}=\left({\tilde{m}}_{x},\text{}0,\text{}\pm \sqrt{1-{\tilde{m}}_{x}^{2}}\right)$, where ${\tilde{m}}_{x}={M}_{\mathrm{s}}{H}_{x}/\left(2{K}_{\mathrm{PMA}}\right)$, one maximum at m

_{x}= −1, and one saddle point at m

_{x}= 1. By letting K

_{PMA}fall to zero, the magnetization precesses around H

_{x}associated with damping, and the appropriate duration can switch the magnetization direction.

_{pulse}that was observed in an MTJ consisting of a Ta/(Co

_{30}Fe

_{70})

_{80}B

_{20}(1.1 nm)/MgO/reference layer. The amplitude of the in-plane component of the bias magnetic field is 890 Oe. The filled circles and the line denote data were obtained from experiments and numerical simulations, respectively [107]. Good agreement with the experimental data suggests the validity of the model used for the numerical simulations. It is noteworthy that the WER exhibits a local maximum at a certain t

_{pulse}, which cannot be explained just by considering the VCMA effect. A detailed analysis of the magnetization trajectory revealed that thermal agitation during the relaxation process (i.e., after the pulse application) induces the transition of the magnetization between the precession orbits surrounding the energy minima and that the precession-orbit transition enhances the WER. The numerical simulations also revealed that the probability of the precession-orbit transition depends on t

_{pulse}(see Ref. 107 for more details). In the present case, the probability is maximized at around t

_{pulse}= 0.12 ns. This results in the appearance of a local maximum in the WER, and it narrows the operating t

_{pulse}range for which reliable magnetization switching is assured. As the appearance of the WER local maximum is related to magnetization fluctuations during the relaxation process, we need to reduce its influence by improving the PMA and VCMA properties in order to achieve a wide operating t

_{pulse}range.

_{pulse}, a recent study revealed that the WER depends in a unique manner on the rise time (t

_{rise}) and fall time (t

_{fall}) [108]. Figure 20 displays the magnetization trajectories that were obtained by using three different waveforms. When a pulsed voltage is applied, the magnetization rotates from m+ towards m− (red line) and, after the pulse, the magnetization relaxes to either ${\tilde{m}}_{+}$ or ${\tilde{m}}_{-}$, depending on t

_{pulse}(green line). An important thing is that, due to the nonzero magnetization damping, the magnetization direction at the end of the voltage pulse (m′) never reaches ${\tilde{m}}_{+}$ or ${\tilde{m}}_{-}$ whatever t

_{pulse}is chosen as long as one uses square pulses (Figure 20a). Therefore, it takes some time before the magnetization settles down to the energy minimum. During that time, the magnetization is subjected to thermal agitation, and a finite number of write errors will be counted. When a nonzero t

_{rise}and/or nonzero t

_{fall}is introduced, the magnetization is subjected not only to H

_{x}, but also to the anisotropy field due to the uncompensated PMA K

_{PMA}′(V,t), which is given by

_{ani}switches according to the polarity of m

_{z}, it applies additional torque to the magnetization that tilts the magnetization to H

_{x}during t

_{rise}(Figure 20b), and it pulls the magnetization away from H

_{x}during t

_{fall}(Figure 20c). As a result, for t

_{rise}= 0.085 ns, m′ comes closer to the saddle point, whereas, for t

_{fall}= 0.085 ns, m′ almost overlaps with ${\tilde{m}}_{-}$ and thereby one can minimize the time that is required for relaxation. This suggests that there is a certain t

_{fall}which can minimize the WER. Indeed, such WER reduction is experimentally obtained and the numerical simulations reproduce it, as shown in Figure 20d,e.

_{PMA}of the free layer, and thereby reduces the thermal fluctuations in the initial state and during the relaxation process. It should be noted that inverse biases can also be used for the pre-read and read verify processes, which thereby offers a read-disturbance-free operation as well as WER reduction. Noguchi et al. first proposed the inverse bias method [37] and the effectiveness was later studied using numerical simulations [144]. In Ref. 144, a substantial reduction in WER was confirmed by introducing inverse biases, whose absolute intensity was the same as that of the write pulse, but with opposite sign (see Figure 21b).

## 6. Conclusions

_{0}-FePt film, an electric quadrupole mechanism also has significant influence on the VCMA effect. To increase of the VCMA coefficient, the utilization of proximity-induced magnetism in a 5d transition metal, which has large spin-orbit coupling, is promising. A large VCMA coefficient of −320 fJ/Vm has been achieved in an Ir-doped ultrathin Fe layer with a demonstration of high-speed responsiveness. As for the reliability of writing while using voltage-induced dynamic switching, low write error rates of the order of 10

^{−6}have been realized by improving the thermal stability and the VCMA effect in practical perpendicularly-magnetized MTJs. Further enhancement in the VCMA coefficient is the key to demonstrating the potential for scalability and realizing more reliable switching for voltage-torque MRAM. A novel nonvolatile memory maintaining low operating power as well as zero stand-by power can provide a broader option for the design of memory hierarchy in future data-driven society. We expect that the voltage-torque MRAM has the potential to be applied in IoT edge devices and wearable/implantable computing systems, in which, ultimately, low power consumption is strongly demanded. Furthermore, the voltage-control of spin may also lead to the improvement in other spintronic devices, such as a voltage-tuned magnetic sensor, spin-torque oscillator, and spin-based neuromorphic devices.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Reported writing energy for toggle magnetoresistive random-access memory (MRAM) (red dots) and spin-transfer torque-based switching (STT-MRAM) (blue dots) as a function of magnetic tunnel junctions (MTJ) cell size and the target area for voltage-torque MRAM.

**Figure 2.**(

**a**) Schematic illustration of sample stack used for the first demonstration of the voltage-controlled magnetic anisotropy (VCMA) effect in an all-solid state structure, and (

**b**) applied bias voltage dependence of the polar-magneto-optical Kerr effect (MOKE) hysteresis curves for a 0.58 nm-thick Fe

_{80}Co

_{20}layer.

**Figure 3.**Example of applied electric-field dependence of K

_{PMA}t

_{free}observed in an MgO-based MTJ structure. Reprinted figure with permission from [48], Copyright 2010 by the AIP Publishing LLC.

**Figure 4.**Conceptual diagram of voltage-induced dynamic switching for a perpendicularly-magnetized film. The in-plane bias magnetic field, H

_{bias}, which determines the axis of the precessional dynamics, is applied in the +x direction. (

**a**) initial state (point S), (

**b**) precessional switching process induced by an application of pulse voltage (from point S to point M), and (

**c**) relaxation process (from point M to point E).

**Figure 5.**Experimental demonstration of voltage-induced dynamic switching. (

**a**) Schematic of the sample structure of a voltage-controlled perpendicularly-magnetized MTJ and observed bi-stable switching between parallel and antiparallel magnetization configurations induced by successive pulse voltage applications. (

**b**) Pulse width dependence of switching probability, P

_{SW}. Due to the precessional dynamics, P

_{SW}exhibits oscillatory behavior depending on the pulse width.

**Figure 6.**Microscopic origin of the VCMA effect. (

**a**) Orbital magnetic moment mechanism. (

**b**) Electric quadrupole mechanism. (

**c**) Schematic of the nonlinear electric field at the interface between the dielectrics and the ferromagnet, which induces a charge redistribution-induced VCMA effect.

**Figure 7.**Diagram of the electronic states related to X-ray absorption spectroscopy and X-ray magnetic circular dichroism (XAS/XMCD) measurements at the L-edges of transition metals.

**Figure 8.**Voltage-induced changes to the magnetic moment of Co in the Fe/Co/MgO system. (

**a**) Schematic of the sample structure. (

**b**) Typical XAS/XMCD results around the Co-absorption edges. (

**c**) Voltage-induced change to the orbital magnetic moment in Co. (

**d**) Voltage-induced changes to the effective spin magnetic moment (m

_{S}− 7m

_{T}) in Co. Reprinted figure with permission from [113], Copyright 2017 by the American Physical Society.

**Figure 9.**Voltage-induced changes to the magnetic moment of Pt in the Fe/Pt/MgO system. (

**a**) Schematic of the sample structure and its high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image. (

**b**) Typical XAS/XMCD results around the Pt-absorption edges. (

**c**) Voltage-induced change to the orbital magnetic moment in Pt. (

**d**) Voltage-induced changes to the effective spin magnetic moment (m

_{S}− 7m

_{T}) in Pt. Reproduced from [116]. CC BY 4.0.

**Figure 10.**Scalability issue for voltage-torque MRAMs. The dependence of the required K

_{PMA}t

_{free}and VCMA coefficient on the diameter of the MTJ was estimated for each thermal stability factor (Δ

_{0}).

**Figure 11.**(

**a**) Bias voltage dependence of normalized tunnel magnetoresistance (TMR) curves measured under in-plane magnetic fields for an orthogonally magnetized MTJ consisting of Cr/ultrathin Fe (0.44 nm)/MgO/Fe (10 nm). The inset shows a cross-sectional TEM image of the MTJ. (

**b**) Applied electric-field dependence of K

_{PMA}t

_{Fe}values. The inset displays an example of a normalized M-H curve. K

_{PMA}was evaluated from the yellow-colored area with the saturation magnetization value that was obtained by a SQUID measurement. Reprinted figure with permission from [133], Copyright 2017 by the American Physical Society.

**Figure 12.**Fe thickness dependence of the VCMA coefficient observed in a Cr/ultrathin Fe(t

_{Fe})/MgO/Fe structure. A large VCMA coefficient with nonlinear behavior was found in the thinner Fe thickness range, t

_{Fe}< 0.6 nm (blue dots). Reprinted figure with permission from [133], Copyright by the American Physical Society.

**Figure 13.**(

**a**) HAADF-STEM images of a multilayer structure of Cr/ultrathin Ir-doped Fe/MgO. Inter-diffused Ir atoms can be identified by atomic-scale Z-contrast HAADF-STEM imaging as indicated by the yellow arrows. (

**b**) Comparison of the polar MOKE hysteresis curves for pure Fe (1 nm)/MgO and Fe (1 nm)/Ir (0.1 nm)/MgO structures. (

**c**) Dependence of the intrinsic interface magnetic anisotropy energy, K

_{i,0}, on the thickness of the Ir layer. Reproduced from [35]. CC BY 4.0.

**Figure 14.**(

**a**) Bias voltage dependence of normalized TMR curves measured under in-plane magnetic fields for an orthogonally-magnetized MTJ consisting of Cr/Ir-doped Fe(0.82 nm)/MgO/Fe(10 nm). (

**b**) Applied electric-field dependence of K

_{PMA}t

_{FeIr}. The inset shows an example of voltage-induced FMR excitation measured by a homodyne detection technique, which proves the high speed responsiveness of the observed VCMA effect. Reproduced from [35]. CC BY 4.0.

**Figure 15.**First principles calculations of the electric-field induced magnetic anisotropy energy change in an Ir-doped Fe/MgO system. (

**a**) Supercell structure used for the calculation, consisting of MgO (5 ML)/FeIr (5 ML)/MgO (5 ML). (

**b**) Atomic-resolved magnetic anisotropy energies (MAE) change induced by an electric-field of 0.1 V/nm in MgO. The Ir concentration was maintained at about 6% in the FeIr layer. (

**c**) The electric-field induced MAE arising from second-order perturbation of the spin-orbit coupling for Ir atoms in layers 1 and 2. Reproduced from [35]. CC BY 4.0.

**Figure 16.**Spin polarized local density of states of Ir-5d orbitals and magnetic anisotropy energy as a function of the band energy in layer 2.

**Figure 17.**(

**a**) Experimental setup for evaluating the WER of an MTJ. (

**b**) Pulsed-voltage-driven magnetization switching in a p-MTJ. (

**c**) WER as a function of Δ obtained from numerical simulations.

**Figure 18.**Example of the optimized WER as a function of t

_{pulse}observed in a perpendicularly-magnetized MTJ consisting of Ta/(Co

_{50}Fe

_{50})

_{80}B

_{20}/MgO/reference layer. The blue and red symbols represent the WER of parallel (P) to antiparallel (AP) and AP to P switching, respectively. Reprinted figure with permission from [109], Copyright 2019 by the IOP Publishing Ltd.

**Figure 19.**(

**a**) Contour plot of energy density in the absence of a bias voltage. (

**b**) Appearance of a local peak in the WER observed in an MTJ consisting of Ta/(Co

_{30}Fe

_{70})

_{80}B

_{20}(1.1 nm)/MgO/reference layer. The filled circles and the lines represent experimental data and numerical simulations, respectively. Reprinted figure with permission from [107], Copyright 2018 by the American Physical Society.

**Figure 20.**(

**a**)–(

**c**) Effects of pulse shaping on magnetization trajectory. The red and green lines represent the magnetization trajectory during and after application of the pulse, t

_{pulse}, respectively. (

**d**), (

**e**) WER minimum as a function of rise time (blue symbols) and fall time (red symbols). (

**d**) experimental results; (

**e**) numerical simulation results. Reprinted figure with permission from [108], Copyright 2019 by the American Physical Society.

**Figure 21.**(

**a**) Comparison of write pulse sequence in conventional and inverse bias methods. (

**b**) Numerically obtained WER as a function of Δ using two different methods.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nozaki, T.; Yamamoto, T.; Miwa, S.; Tsujikawa, M.; Shirai, M.; Yuasa, S.; Suzuki, Y.
Recent Progress in the Voltage-Controlled Magnetic Anisotropy Effect and the Challenges Faced in Developing Voltage-Torque MRAM. *Micromachines* **2019**, *10*, 327.
https://doi.org/10.3390/mi10050327

**AMA Style**

Nozaki T, Yamamoto T, Miwa S, Tsujikawa M, Shirai M, Yuasa S, Suzuki Y.
Recent Progress in the Voltage-Controlled Magnetic Anisotropy Effect and the Challenges Faced in Developing Voltage-Torque MRAM. *Micromachines*. 2019; 10(5):327.
https://doi.org/10.3390/mi10050327

**Chicago/Turabian Style**

Nozaki, Takayuki, Tatsuya Yamamoto, Shinji Miwa, Masahito Tsujikawa, Masafumi Shirai, Shinji Yuasa, and Yoshishige Suzuki.
2019. "Recent Progress in the Voltage-Controlled Magnetic Anisotropy Effect and the Challenges Faced in Developing Voltage-Torque MRAM" *Micromachines* 10, no. 5: 327.
https://doi.org/10.3390/mi10050327