Using Dipole Interaction to Achieve Nonvolatile Voltage Control of Magnetism in Multiferroic Heterostructures

Abstract

Nonvolatile electrical control of magnetism is crucial for developing energy‐efficient magnetic memory. Based on strain‐mediated magnetoelectric coupling, a multiferroic heterostructure containing an isolated magnet requires nonvolatile strain to achieve this control. However, the magnetization response of an interacting magnet to strain remains elusive. Herein, Co/MgO/CoFeB magnetic tunnel junctions (MTJs) exhibiting dipole interaction on ferroelectric substrates are fabricated. Remarkably, nonvolatile voltage control of the resistance in the MTJs is demonstrated, which originates from the nonvolatile magnetization rotation of an interacting CoFeB magnet driven by volatile voltage‐generated strain. Conversely, for an isolated CoFeB magnet, this volatile strain induces volatile control of magnetism. These results reveal that the magnetization response to volatile strain among interacting magnets is different from that among isolated magnets. The findings highlight the role of dipole interaction in multiferroic heterostructures and can stimulate future research on nonvolatile electrical control of magnetism with additional interactions.

A new strategy using the dipole interaction to achieve nonvolatile electrical control of magnetism is demonstrated in an interacting magnet using a volatile strain. This work reveals the important role of the dipole interaction in multiferroic heterostructures and can stimulate future research on the electrical control of magnetism by introducing additional interactions to multiferroic heterostructures.

1. Introduction

Multiferroics have aroused considerable interest in the electrical control of magnetism^{[ 1} , ^{2 ]} owing to the potential to develop energy‐efficient multifunctional devices, such as electrically controlled magnetic tunnel junctions (MTJs). However, most single‐phase multiferroic materials suffer from a low operating temperature and weak magnetoelectric effect.^{[ 2} , ^{3 ]} Alternatively, magnetic/ferroelectric multiferroic heterostructures^{[ 4} , ⁵ , ⁶ , ^{7 ]} provide an effective route to achieve a significant magnetoelectric effect at room temperature, which is promising for practical applications of magnetoelectric devices.^{[ 7} , ⁸ , ^{9 ]} In multiferroic heterostructures, the nonvolatile electrical control of magnetism has received increasing interest owing to its importance in information storage. To achieve this control, one method utilizes the charge effect to modulate the magnetic properties of the magnetic layer via the interfacial charge of the ferroelectric layer.^{[ 10} , ¹¹ , ^{12 ]} This charge effect only affects magnetic layers with a thickness of less than several nanometers^{[ 13 ]} and is easily eliminated by inserting a thin metal layer between the magnetic and ferroelectric layers.^{[ 14 ]} Another more popular approach is strain‐mediated magnetoelectric coupling,^{[ 6} , ^{15 ]} which utilizes the piezostrain of a ferroelectric material to modulate the magnetization of a magnetic layer via the converse magnetostriction effect. This approach has been widely investigated because of its simple structure and significant magnetoelectric effect.^{[ 4} , ⁵ , ⁶ , ^{15 ]}

To achieve nonvolatile electrical control of magnetism, strain‐mediated magnetoelectric coupling generally requires nonvolatile piezostrain. Applying bipolar asymmetric electric fields to a (011)‐oriented Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ (PMN–PT) ferroelectric single crystal, Wu et al.^{[ 16 ]} obtained a nonvolatile piezostrain originating from a non‐180° ferroelectric domain switching and observed nonvolatile electric‐field‐reoriented magnetization of a Ni film. In addition, Zhang et al.^{[ 17 ]} reported nonvolatile electric‐field control of magnetism in CoFeB/PMN–PT (001) multiferroic heterostructures, which was ascribed to the nonvolatile strain^{[ 18 ]} caused by 109° ferroelectric domain switching. Thus far, nonvolatile electrical control of magnetism in multiferroic heterostructures via strain‐mediated magnetoelectric coupling^{[ 16} , ¹⁷ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ , ²⁴ , ^{25 ]} has primarily employed nonvolatile strain based on the abovementioned two mechanisms. To obtain this nonvolatile strain, ferroelectric materials with a specific crystal orientation are required.^{[ 16} , ^{18 ]} However, the piezostrain of a ferroelectric material is usually volatile,^{[ 26 ]} which induces volatile electrical control of magnetism as expected.^{[ 27} , ²⁸ , ²⁹ , ^{30 ]} Therefore, it remains unclear whether volatile strain can enable nonvolatile electrical control of magnetism.

To date, multiferroic heterostructures are primarily intended to modulate magnetism in single magnetic layers^{[ 16} , ¹⁷ , ²⁰ , ²⁷ , ²⁸ , ³¹ , ^{32 ]} or isolated magnets^{[ 19} , ²¹ , ³³ , ^{34 ]} with negligible interactions. To develop high‐density magnetic memory, high‐density nanomagnets are indispensable. With a decreasing size and distance between the magnets, dipole interaction between two adjacent magnets cannot be neglected, such as in nanosized MTJ devices comprising two ferromagnetic layers separated by an extremely thin (≈nm) nonmagnetic tunnel barrier. The emerging dipole interaction introduces an additional degree of freedom and can lead to more interesting phenomena in multiferroic heterostructures. For instance, dipole interaction indeed played a role in strain‐induced magnetization switching in discrete dipole‐coupled nanomagnet pair on the ferroelectric.^{[ 35} , ³⁶ , ^{37 ]} Once the magnetization of the nanomagnet pair was switched, however, a magnetic field is required to initialize magnetization of the nanomagnet pair to be parallel. Apparently, this is not a purely electrical control. So the effect of piezostrain on the magnetism of an interacting magnet has rarely been investigated^{[ 35} , ³⁶ , ^{37 ]} and remains an open question.

Herein, by introducing dipole interaction to multiferroic heterostructures, we demonstrate nonvolatile voltage control of magnetization rotation in an interacting magnet driven by volatile strain without the assistance of a magnetic field. We generated a linear volatile localized strain by applying voltages to one pair of electrodes fabricated on a PMN–PT ferroelectric substrate. As expected, this volatile strain led to volatile voltage‐controlled magnetic anisotropy of both Co and CoFeB isolated magnetic layers without interaction via strain‐mediated magnetoelectric coupling. We then coupled the Co and CoFeB magnets in an MTJ with a core structure of Co/MgO/CoFeB exhibiting dipole interaction. Remarkably, the volatile strain induced a nonvolatile voltage‐controlled resistance of the MTJ at zero magnetic field resulting from the nonvolatile magnetization rotation of the interacting CoFeB in the MTJ. These results reveal that the magnetization response to volatile strain in an interacting magnet is different from that in an isolated magnet as confirmed by micromagnetic simulations and that the volatile strain can enable nonvolatile voltage control of magnetization rotation with the assistance of the dipole interaction. Our findings offer a new strategy to achieve nonvolatile electrical control of magnetism employing the dipole interaction, which is important for facilitating the electrical control of magnetism by introducing other interactions to multiferroic heterostructures.

2. Results and Discussion

2.1. Voltage‐Generated Volatile Localized Strain

As illustrated in Figure  1a, we fabricated one pair of electrodes on a PMN–PT ferroelectric substrate to generate strain^{[ 34} , ³⁸ , ³⁹ , ^{40 ]} by applying voltages to the top electrode pair and bottom grounded substrate. A rectangular isolated magnet or MTJ was placed at the central gap of the electrodes, whose joint line was perpendicular to the long edge of the rectangular magnet (Figure S1, Supporting Information). Figures 1b and 1c present the simulated strain distribution under an applied voltage of 150 and −150 V, respectively, by performing finite element analysis. It is evident that the voltage induced uniform localized strain at the central gap between the two electrodes. This localized strain along the long edge of the rectangular magnet (i.e., perpendicular to the joint line of the electrode pair) was compressive when applying a voltage of 150 V (Figure 1b) and tensile when applying a voltage of −150 V (Figure 1c). Figure 1d displays the simulated voltage‐induced strain at the location of the rectangular magnet, which exhibits linear and volatile behavior. Thus, a rectangular magnet or MTJ would experience tensile strain when applying a negative voltage and compressive strain when applying a positive voltage.

Figure 1.

Volatile voltage‐generated strain using one pair of electrodes. a) Schematic of the sample layout. One pair of electrodes was deposited on the PMN–PT substrate to generate piezostrain by applying a voltage between the top electrodes and bottom grounded substrate. A rectangular magnet or MTJ pillar, whose long edge was perpendicular to the joint line of the electrodes, was placed at the central gap so that the voltage‐generated strain could modulate its magnetic properties. x and y represent the short and long edges of the rectangular magnet or MTJ device, respectively. b,c) Distribution of the simulated strain ε _yy  − ε _xx along the long edge of the rectangular magnet with an applied voltage of 150 V (b) and −150 V (c). The dashed boxes indicate the locations of the electrodes. Localized uniform strain was generated at the central gap of the electrodes, which could control the magnetization of the isolated magnet and the resistance of the MTJ. d) Voltage dependence of the strain ε _yy  − ε _xx at the location of the rectangular magnet, which is linear and volatile. Applying a positive voltage induced compressive strain along the y direction, whereas applying a negative voltage induced tensile strain, as illustrated in the insets.

2.2. Volatile Voltage‐Modulated Magnetic Anisotropy in an Isolated Magnet without Interaction

We separately placed CoFeB and Co isolated rectangular magnets at the central gap of the electrodes (Figure  2a,b) and investigated the effect of the aforementioned volatile voltage‐generated strain on their magnetic anisotropy using the magneto‐optical Kerr effect (MOKE) at room temperature. As illustrated in Figure 2a, the magnetic hysteresis (M–H) loops of the CoFeB magnet for the applied magnetic field (H) parallel to the y‐axis became less square with increasing voltages. Conversely, the M–H loops became more square with increasing voltages when H was along the x‐axis. The evolution of the shape of the M–H loops under the applied voltages indicates that the application of a voltage of 150 V rotated the magnetic easy axis (MEA) from the y‐axis to the x‐axis for the single CoFeB magnet. For the Co magnet illustrated in Figure 2b, in contrast, increasing the voltage from −150 to 150 V caused the M–H loops to be more square for H applied along the y‐axis and less square for H along the x‐axis. It is notable that the M–H loops measured at 0 V after removal of the applied voltage of 150 V (referred to as +0 V) and −150 V (referred to as −0 V) in Figure 2a,b were almost identical, which strongly suggests the volatile control of magnetic anisotropy, and is consistent with the volatile strain illustrated in Figure 1d.

Figure 2.

Volatile voltage control of magnetic anisotropy in a single isolated magnet induced by volatile strain. a,b) In situ M–H loops with varying voltages for a CoFeB (a) and Co (b) single isolated magnet without interaction placed at the central gap of the electrodes. The M–H loops in the top and bottom panels were measured by sweeping H along the long and short edges of the rectangular magnet, respectively, as illustrated in the insets. The arrows indicate the trend of the M–H loops in conjunction with increasing voltages. +0 and −0 V denote 0 V after applying +150 and −150 V, respectively. Note that the M–H loops at ±0 V were almost identical with volatile behavior. c) Voltage‐dependent magnetic anisotropy of the CoFeB and Co isolated magnets deduced from (a) and (b), which indicates volatile and approximately linear behavior. The open symbols indicate the data measured by increasing the voltage from −150 to 150 V, whereas the open symbols with a cross indicate the data measured by reducing the voltage from 150 to −150 V.

We further extracted the magnetic anisotropy constants (K) from the M–H loops in Figures 2a and 2b for CoFeB and Co, respectively, at various voltages using the area method,^{[ 41 ]} as plotted in Figure 2c. K exhibits an approximately linear dependence on the applied voltage for both CoFeB and Co, which indicates volatile control of magnetic anisotropy. Clearly, the voltage‐dependent K for the CoFeB magnet exhibits the opposite trend from that for the Co magnet. This difference originates from different magnetostriction coefficients, which are positive and negative for CoFeB and Co,^{[ 42} , ^{43 ]} respectively. The solid lines in Figure 2c are plotted using K = K ₀ + K _strain, where K ₀ is the magnetic anisotropy constant without voltage originating from the shape magnetic anisotropy and applied magnetic field during film growth. In addition, K _strain is the voltage‐induced magnetoelastic anisotropy owing to the strain‐mediated magnetoelectric coupling and can be expressed as follows:^{[ 6} , ^{43 ]} $K_{\text{strain}}=\frac{3}{2}\lambda Y\epsilon$, where λ, Y, and ε are the magnetostriction coefficient, Young's modulus, and strain, respectively. The solid lines in Figure 2c agree well with the experimental data, suggesting that the volatile strain generated using one pair of electrodes efficiently transferred to the magnets and consequently modulated their magnetic anisotropy. Note that K of the Co magnet is always positive regardless of whether a positive or negative voltage was applied, indicating that the applied voltages could not change the MEA of the Co magnet owing to the relatively large K ₀ ^Co. For the CoFeB magnet, however, K _strain dominated the total magnetic anisotropy because of its small K ₀ ^CoFeB; thus, applying a positive voltage led to a negative K and applying a negative voltage led to a positive K.

Thus, the MEA of a single CoFeB magnet can be toggled along the y‐ and x‐axes by applying negative and positive voltages. Therefore, for CoFeB and Co isolated magnets, volatile voltage‐generated strain induces a volatile control of magnetic anisotropy with opposite trends due to the difference in λ. Moreover, applying a voltage can rotate the MEA of the CoFeB magnet and can change the strength of K for the Co magnet without changing the direction of its MEA (more details shown in Figures S2 and S3, Supporting Information).

2.3. Nonvolatile Voltage Modulation of the Resistance of the Co/MgO/CoFeB Magnetic Tunnel Junctions Containing Dipole Interaction

We coupled CoFeB and Co isolated magnets with in‐plane magnetic anisotropy (Figure 2) by fabricating an MTJ with a core structure of Co/MgO/CoFeB, as presented in Figure  3a. Note that the voltage is applied to the electrode pair on the PMN–PT (Figure 1a) rather than to the MTJ, being different from that in some studies in which the voltage was directly applied the MTJs to manipulate magnetoresistance (MR) though voltage‐controlled magnetic anisotropy.^{[ 44} , ⁴⁵ , ^{46 ]} This Co/MgO/CoFeB MTJ did not comprise an antiferromagnetic layer or artificial antiferromagnetic structure, and the Co and CoFeB layers exhibited dipole interaction mediated by the stray field, as illustrated in Figure 3b. Moreover, compared with a previous PMN–PT/MTJ system with both CoFeB ferromagnetic layers,^{[ 38} , ⁴⁰ , ⁴³ , ^{47 ]} this Co/MgO/CoFeB MTJ system had two different ferromagnetic layers (Co and CoFeB) with different λ and K such that their magnetizations exhibited different responses to a given piezostrain, as demonstrated in Figure 2. As a long‐range order parameter, the strain can transfer more than 1 µm,^{[ 4 ]} so that the voltage‐generated strain can effectively affect both the Co and CoFeB layers in the MTJ, because they are from the PMN–PT less than 20 nm (see the Experimental Section).

Figure 3.

Nonvolatile voltage modulation of the resistance of the Co/MgO/CoFeB MTJ exhibiting dipole interaction. a) A Co/MgO/CoFeB MTJ with interacting Co and CoFeB magnets placed at the central gap of the electrode pair on the PMN–PT ferroelectric substrate. b) Schematic of the interacting CoFeB in the Co/MgO/CoFeB MTJ deposited on the PMN–PT ferroelectric substrate. The fixed Co magnetization supplied a dipolar field as denoted by the dashed arrows, which caused the CoFeB magnetization to rotate away from the Co magnetization. c) MR curves measured at ±0 V after applying ±150 V to the electrode pair. The different resistances at zero magnetic field for ±0 V indicate nonvolatile voltage control. d) Voltage‐dependent resistance of the Co/MgO/CoFeB MTJ at zero magnetic field with six switching cycles, which exhibits a loop‐like behavior with high and low resistance at ±0 V. The arrows indicate the voltage sweeping directions. e) Retention of high/low resistance at ±0 V and zero magnetic field. The slight increase in the resistance at −0 V may be caused by the dipole interaction.

We placed the Co/MgO/CoFeB MTJ at the central gap of the electrode pair (Figure 1a) to explore how volatile piezostrain affects its magnetotransport properties. Remarkably, the MR curves at ±0 V after applying ±150 V in Figure 3c are distinct from each other. More importantly, the different resistances at H = 0 Oe for the ±0 V states suggest nonvolatile voltage‐modulated resistance. This nonvolatile resistance modulation can be easily observed from the dependence of the resistance on the voltage at H = 0 Oe, as illustrated in Figure 3d, which exhibits a loop‐like behavior. Apparently, applying a voltage of 150 V induced a high‐resistance state, whereas applying a voltage of −150 V induced a low‐resistance state. These high/low resistances were stable, as presented in Figure 3e.

It is well known that the resistance of the MTJ is determined by the relative magnetization alignment of the two magnetic layers in the MTJ;^{[ 38} , ⁴³ , ^{47 ]} therefore, the nonvolatile high‐/low‐resistance states at H = 0 Oe after applying ±150 V represent different magnetization alignments and depend strongly on the magnetization responses to the voltage‐generated strain for the Co and CoFeB magnetic layers in the MTJ. Volatile voltage‐generated strain induced volatile control of the magnetic anisotropy for CoFeB and Co isolated magnets, as demonstrated in Figure 2; however, the results obtained for the MTJ with interacting CoFeB and Co magnets were notably different owing to the nonvolatile voltage‐modulated resistance of the Co/MgO/CoFeB MTJ. Therefore, the nonvolatile voltage control of resistance in the Co/MgO/CoFeB MTJ using volatile piezostrain cannot be understood by solely considering volatile‐strain‐controlled magnetic anisotropy. It should also be noticed that such a nonvolatile voltage‐controlled resistance of the Co/MgO/CoFeB MTJs via a volatile piezostrain is different from our previous work in which a nonvolatile strain was used to achieve nonvolatile electric‐field manipulation of the resistance in the MTJ.^{[ 47 ]}

To elucidate the mechanism and physics underlying the nonvolatile voltage control of resistance in the Co/MgO/CoFeB MTJ, we measured the angular dependence of the MR of the MTJ at ±0 V after applying ±150 V, as presented in Figure  4a,b. Because voltage cannot change the direction of the MEA for the Co magnet (Figure 2b), the orientation of the Co magnetization changed only slightly upon the application of voltages. Moreover, the coercive field of Co is larger than that of CoFeB (Figure 2); thus, the MR of the MTJ at a low magnetic field is determined by the magnetization vector of CoFeB and can reflect the magnetization of the CoFeB layer in the MTJ. For the case of −0 V in Figure 4a, when increasing the magnetic field from zero with a low resistance, the onset magnetic fields for increasing the resistance of the MTJ at 0°/180° (i.e., the long edge of the rectangular MTJ pillar or the y‐axis) were larger than those at 90°/270°, as illustrated by the dashed line, indicating that the magnetization of CoFeB was along the y‐axis and was difficult to reverse. Conversely, the MR increased quickly at 0°/180° for the +0 V case, as illustrated in Figure 4b, suggesting that the magnetization of CoFeB was along the x‐axis. This sharp contrast between the ±0 V cases reveals nonvolatile magnetization rotation of the interacting CoFeB magnet in the MTJ, which is remarkably different from the volatile voltage modulation of magnetization for the isolated CoFeB magnet in Figure 2a.

Figure 4.

Nonvolatile voltage control of magnetization rotation in the interacting CoFeB magnet. a,b) Color‐coded polar plots of MR measured at −0 V (a) and +0 V (b). The long edge of the rectangular MTJ pillar was defined as 0°. For each angle, a magnetic field of −2000 Oe was first applied to align the magnetizations in the MTJ and then reduced to zero. Subsequently, the resistance was measured upon increasing the magnetic field from zero. The measurements were performed at every 5° step of the angle. The black dashed lines indicate the onset magnetic fields when the resistance of the MTJ increased at each angle, which can reflect the magnetization of the interacting CoFeB magnet.

2.4. Different Magnetization Responses to the Volatile Strain in Isolated and Interacting CoFeB Magnets

To gain further insight into the mechanism of the volatile‐strain‐driven nonvolatile magnetization rotation of an interacting magnet, we performed micromagnetic simulations to investigate the evolution of the magnetization for the isolated and interacting CoFeB magnets (Figure S4, Supporting Information). Figure  5a presents the voltage‐dependent y component of the average magnetization (<m _y >) for a single isolated CoFeB magnet. Here, <m _y > decreased as the voltage increased because the MEA reoriented from the y‐axis to the x‐axis. The almost identical <m _y > at ±0 V unambiguously indicates volatile behavior, which can be further confirmed through the analogous magnetization distribution at ±0 V, as illustrated in Figure 5b. For the Co/MgO/CoFeB MTJ containing dipole interaction in Figure 5c, <m _y > of the Co layer did not exhibit a significant change because the voltage did not change the direction of its MEA. Conversely, cycling the voltage between ±150 V substantially changed <m _y > of the CoFeB layer. More importantly, <m _y > values at ±0 V were different, as highlighted by stars, indicating a nonvolatile behavior. The magnetization distributions under various voltages in Figure 5d indicate the different magnetization configuration of the MTJ at ±0 V owing to the nonvolatile magnetization rotation of the CoFeB magnet. These simulation results are consistent with the experimental results in Figures 2 and 3 and demonstrate that the magnetization responses to volatile strain are different in isolated and interacting magnets.

Figure 5.

Different magnetization evolutions for isolated and interacting CoFeB magnets under volatile voltage‐generated strain. a) Simulated voltage‐dependent <m _y > of a single isolated CoFeB magnet without interaction. b) Evolution of the magnetic domain images of a single isolated CoFeB magnet when sweeping voltages within ±150 V. The almost identical domain images at ±0 V indicate volatile voltage control of magnetism. c) Simulated voltage dependence of <m _y > in the Co/MgO/CoFeB MTJ exhibiting dipole interaction. d) Magnetization configurations of the Co/MgO/CoFeB MTJ under different voltages. The magnetic domain of the Co magnet did not exhibit a significant change, whereas that of the CoFeB magnet changed significantly, which suggests nonvolatile voltage‐driven magnetization rotation of the interacting CoFeB magnet. In (a) and (c), the stars indicate <m _y > at ±0 V and the arrows indicate the voltage sweeping directions. The dashed boxes in (b) and (d) highlight the magnetic domain image at ±0 V.

In contrast to the single isolated CoFeB magnet, the CoFeB magnet in the MTJ interacted with the Co magnet via dipole interaction as illustrated in Figure 3b; thus, the dipole interaction is vital for the nonvolatile magnetization rotation driven by volatile strain. Here, we attempt to understand the nonvolatile voltage control of the resistance in the Co/MgO/CoFeB MTJ, taking into account the dipolar field and voltage‐modulated magnetic anisotropy. The in‐plane magnetized Co layer in the MTJ generated a local dipolar field or stray field, which did not significantly change because the applied voltages slightly changed the orientation of the Co magnetization. Interestingly, when the magnetizations of the Co and CoFeB layers in the MTJ were parallel, this dipolar field tended to drag the magnetization of CoFeB away from the orientation of the Co magnetization, resulting in a noncollinear structure. Note that this dipolar field of ≈5.5 Oe is comparable with the effective anisotropy field of the CoFeB magnet without an applied voltage (Figure S5, Supporting Information). We assumed that the magnetization of the Co layer was fixed and focused only on the magnetization rotation of the CoFeB layer. As illustrated in Figure  6 , applying a voltage of −150 V enhanced the magnetic anisotropy of CoFeB along the long edge of the MTJ pillar so that the magnetizations of both magnetic layers in the MTJ were almost parallel, leading to a low‐resistance state, as presented in Figure 5d. At −0 V, after removing the voltage of −150 V, the CoFeB layer exhibited a small positive K ₀ ^CoFeB. The dipolar field was not sufficiently strong to overcome K ₀ ^CoFeB; thus, the low‐resistance state remained unchanged owing to the unchanged CoFeB magnetization. Owing to the MEA rotation of the CoFeB layer, applying a voltage of 150 V rotated the CoFeB magnetization away from the parallel state of the MTJ, resulting in a high‐resistance state of the MTJ. When reducing the voltage to +0 V, the dipolar field prevented the magnetization vector of CoFeB from rotating back to the y‐axis despite the small K ₀ ^CoFeB; thus, the high‐resistance state remained unchanged until a sufficiently large negative voltage was applied. Thus, nonvolatile control of the resistance in the Co/MgO/CoFeB MTJ was achieved by cycling voltages within ±150 V owing to the nonvolatile magnetization rotation of the interacting CoFeB magnet, which results from the competing dipole interaction and K ₀ ^CoFeB. This nonvolatile control of magnetization rotation was achieved by a volatile voltage‐induced piezostrain, in which the dipole interaction being comparable to K ₀ ^CoFeB is crucial.

Figure 6.

Interconversion of the magnetization configuration of the MTJ between −0 and +0 V driven by the applied voltages of −150 and 150 V. The applied voltages enable rotating the MEA of the CoFeB magnet and do not change the direction of the Co magnet's MEA. The arrows indicate the directions of the magnetizations and the double‐headed arrows indicate the MEA of the interacting CoFeB layer, which can be rotated by the applied voltages, in the Co/MgO/CoFeB MTJ.

It is worth noting that two key points differentiate our work from previous studies on multiferroic heterostructures containing dipole interaction.^{[ 35} , ³⁶ , ^{37 ]} i) The interacting magnets in our work are integrated in an MTJ device, while the dipole‐coupled magnets are patterned on the surface of the ferroelectric substrate with a distance.^{[ 35} , ³⁶ , ^{37 ]} ii) Once the magnetization of the nanomagnet pair was switched, however, a magnetic field is required to initialize magnetization of the nanomagnet pair to be parallel.^{[ 35} , ³⁶ , ^{37 ]} In this work, the nonvolatile voltage control of magnetization rotation in interacting magnets is achieved without the assistance of a magnetic field as demonstrated by the nonvolatile voltage control of the resistance in the Co/MgO/CoFeB MTJ at zero magnetic field (Figure 3).

The realization of nonvolatile electrical control of magnetization rotation using volatile strain in this study has several advantages over previous studies using nonvolatile strain.^{[ 16} , ^{17 ]} Nonvolatile strain strongly depends on the orientation of a PMN–PT single crystal and the approach using which the electric field is applied. In a (001)‐oriented PMN–PT substrate, nonvolatile strain originates from 109° ferroelectric domain switching, which only occurs in less than 26% of the ferroelectric domain.^{[ 17} , ^{18 ]} To obtain the nonvolatile strain in a (011)‐oriented PMN–PT substrate, a critical reversed electric field should be applied to prevent the remnant strain from decreasing drastically.^{[ 16} , ^{48 ]} Thus, these two methods for achieving nonvolatile strain are inefficient and inconvenient. Contrastingly, volatile strain generated using one pair of electrodes is achievable for all ferroelectric materials regardless of whether they are single crystal^{[ 34} , ³⁸ , ^{40 ]} or polycrystalline.^{[ 39 ]} Furthermore, the nonvolatile strain in both (011)‐oriented and (001)‐oriented PMN–PT substrates is nonuniform at the microscale,^{[ 19} , ²⁰ , ²¹ , ^{33 ]} whereas the localized strain generated using an electrode pair is uniform at the central gap of the electrodes, as illustrated in Figure 1a,b. Thus, using one pair of electrodes to generate localized uniform strain is universal for ferroelectric materials, particularly for future applications using ferroelectric films.^{[ 49} , ^{50 ]}

3. Conclusion

We have proposed a new strategy using the dipole interaction to achieve nonvolatile electrical control of magnetism in an interacting magnet using a volatile strain. Applying voltages to one pair of electrodes on a PMN–PT ferroelectric substrate generated volatile localized strain that could volatilely modulate the magnetic properties of isolated CoFeB and Co magnets via strain‐mediated magnetoelectric coupling, as expected. When coupling the CoFeB and Co magnets in a Co/MgO/CoFeB MTJ exhibiting dipole interaction, this volatile strain surprisingly had the ability to nonvolatilely rotate the magnetization of the interacting CoFeB layer in the MTJ, as revealed by the nonvolatile voltage control of the resistance at zero magnetic field, which was significantly different from the volatile magnetization rotation in the single CoFeB magnet. Our results highlight the role of the dipole interaction in the electrical control of magnetism and offer a new approach to explore the nonvolatile electric control of magnetism in multiferroic heterostructures containing interacting magnets, instead of a single isolated magnet.

4. Experimental Section

Sample Fabrication

The MTJ multilayer films were deposited on (011)‐oriented PMN–PT single crystals with a typical size of 10 × 10 × 0.5 mm³ in the sequence of Ta (5 nm)/Ru (5 nm)/Pt (5 nm)/Co (2 nm)/MgO (2 nm)/CoFeB (2.8 nm)/Ta (8 nm)/Ru (7 nm). The CoFeB and Co isolated magnets, which were deposited on the (011)‐oriented PMN–PT substrate with a size of 5 × 6 × 0.5 mm³ to investigate the voltage‐modulated M–H loops in Figure 2, comprised Ta (5 nm)/Ru (5 nm)/Pt (5 nm)/Co (2 nm)/MgO (2 nm)/Ta (2 nm) and Ta (5 nm)/Ru (5 nm)/MgO (2 nm)/CoFeB (2.8 nm)/Ta (2 nm), respectively. The size of the magnet pattern was 30 × 100 µm² for measuring the M–H loops using MOKE. All samples were deposited using a Singulus ROTARIS magnetron sputtering system with a base pressure below 1 × 10⁻⁶ Pa. A magnetic field of ≈50 Oe was applied in situ along the [100] crystal direction of the PMN–PT substrate during the deposition of the Co and CoFeB layers. Electron beam lithography, photolithography, and ion milling were used to process the MTJ multilayer films into a rectangular shape of 2 × 6 µm², whose long edge was along the direction of the applied magnetic field during film growth. Subsequently, the MTJ devices were annealed in vacuum at 300 °C for 1 h with a magnetic field of 8000 Oe along the long edge of the rectangular MTJ pillar. CoFeB denoted the Co₄₀Fe₄₀B₂₀ alloy with the nominal target composition. The patterned electrodes, Ti (10 nm) and Au (50 nm), were fabricated using a lift‐off technique. The size of the electrodes was 300 × 300 µm², with a distance of 150 µm between the facing edges, and the joint line of the electrodes was perpendicular to the long edge of the rectangular MTJ pillar. The Ti (10 nm) and Au (150 nm) layers were sputtered on the bottom of the PMN–PT substrate as the bottom electrode.

Simulation of the Voltage‐Generated Localized Strain

The localized strain induced by voltage was simulated using finite element analysis (COMSOL Multiphysics package) with the piezoelectric coefficients of PMN–PT (011) obtained from a prior study.^{[ 51 ]}

Magnetic and Magnetoresistance Measurements

An electromagnet system was used to obtain the resistance of the MTJs using the four‐probe method with a Keithley 6221 current source and a Keithley 2182 nanovoltmeter. A Keithley 6517 electrometer was used to apply voltages to the PMN–PT substrate for the generation of localized piezostrain. The M–H loops of the CoFeB and Co magnets with in situ voltages were measured using Durham NanoMOKE 2. The solid lines in Figure 2c were plotted using K = K ₀ + K _strain, where K ₀ denoted the magnetic anisotropy constant with zero voltage deduced from the M–H loops in Figure 2a,b. K _strain was estimated using $K_{\text{strain}}=\frac{3}{2}\lambda Y\epsilon$, where λ, Y, and ε denote the magnetostriction coefficient, Young's modulus, and strain, respectively. ε can be found in Figure 1d. The parameters used for CoFeB were as follows:^{[ 43 ]} λ^CoFeB = 2 × 10⁻⁵, Y ^CoFeB = 160 GPa. The parameters used for Co were as follows:^{[ 42 ]} λ^Co = −2.9 × 10⁻⁵, Y ^Co = 200 GPa. All measurements were performed at room temperature.

Micromagnetic Simulations

Simulations using MuMax3^{[ 52 ]} were performed to explore the evolution of the magnetization states of the CoFeB/MgO/Co MTJ and single isolated CoFeB magnet under the voltage‐induced localized strain. In all simulations, a rectangular (2.0 × 6.0 µm²) Co (2 nm)/MgO (2 nm)/CoFeB (3 nm) sandwich structure was considered with the unit cell dimension set to 2.5 × 2.5 × 1.0 nm³. The magnetic anisotropy constant of the CoFeB and Co layers was set to change as the solid lines in Figure 2c (i.e., K ^CoFeB = 510 − 15.2 × U [J m⁻³] and K ^Co = 9500 + 28.5 × U [J m⁻³], respectively, where U was the applied voltage). The magnetic parameters were as follows: for the CoFeB layer,^{[ 20} , ^{38 ]} the exchange stiffness coefficient was A ^CoFeB = 28 × 10⁻¹² J m⁻¹ and the saturation magnetization was M _S ^CoFeB = 12 × 10⁵ A m⁻¹; for the Co layer,^{[ 53 ]} A ^Co = 30 × 10⁻¹² J m⁻¹ and M _S ^Co = 14 × 10⁵ A m⁻¹. The MgO layer was set to be a nonmagnetic material. The initial magnetized states of the CoFeB and Co layers with the easy axis along the x‐ and y‐axes were obtained from the random state via magnetization relaxation.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Chen A., Piao H.‐G., Ji M., Fang B., Wen Y., Ma Y., Li P., Zhang X.‐X., Using Dipole Interaction to Achieve Nonvolatile Voltage Control of Magnetism in Multiferroic Heterostructures. Adv. Mater. 2021, 33, 2105902. 10.1002/adma.202105902

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.