A Sandwich Metal-Insulation-Metal Composite for Magnetoelectric Memory: Experiment and Modeling.

Driven by the development of internet technology, higher requirements on information materials and data storage devices were demanded. To improve the work efficiency and performance of the new generation of information materials and data storage devices, the magnetoelectric (ME) coupling and storage mechanism of magnetoelectric composites deserve more attention. Here, we explored the influence of applied magnetic fields on the output voltage on a metal-insulation-metal (MIM) sandwich composite for realizing the magnetoelectric memory by experiments and modeling. It is found that the DC magnetic field (H dc) and the output voltage of the polyvinylidene fluoride film are linearly correlated. At a frequency of 1 kHz, the magnetoelectric voltage coefficient is 60.71 mV cm-1 Oe-1, which is evidently larger than that of other film materials. From this work, we can conclude that the MIM sandwich composite could generate higher magnetoelectric voltage under the AC magnetic field (H ac) with higher frequency, which could be used as the magnetoelectric memory device, and provides significant support for improving the performance of magnetoelectric memory devices and the whole internet system.

Introduction

The digital era urges for data memory devices with excellent performance,[1−3] which are widely used in internet communication, wearable biomedical devices, artificial intelligence, and so on.[4−9] Magnetoelectric memory controlled by the electric field has recently developed a lot of interest because of the low cost and high efficiency.[9−11] In order to develop new generation magnetoelectric memory, it is essential to further explore the simpler structures and magnetoelectric material with higher performance of magnetoelectric energy conversion.[10,12] At present, there are a lot of magnetoelectric experiments for exploring the magnetoelectric coupling and storage mechanism of magnetoelectric composites.

In 2017, Zong et al.[13] developed a novel cellulose-based magnetoelectric laminate structure. The maximum magnetoelectric coefficient of the novel structure was 1.41 V cm–1 Oe–1 under the applied Hac and Hdc. However, the cellulose structure consisting of metglas–epoxy–gold electrode–cellulose film–gold electrode was relatively complicated. In 2020, Hyeon et al.[4] explored the performance of poly(vinylidene fluoride-co-trifluoroethylene) laminated onto a magnetostrictive multilayer metglas under the applied Hac with constant frequency by experiments and finite element method (FEM). However, the relationship between Hdc and magnetoelectric performance of this structure was not explored. In 2021, Wu et al.[6] investigated the magnetoelectric effect of the mica substrate attached on both sides of flexible piezoelectric PZT films under the applied Hac and Hdc. A more significant magnetoelectric coefficient could be observed. However, the modeling ignored in their work could help to evaluate the experimental results more intuitively and accurately.

Based on the above-mentioned investigations, this paper proposed the MIM structure, which comprised two sliver electrodes laminated on both sides of the polyvinylidene fluoride (PVDF) film. Its ME effect was explored in a different way from the coupling of magnetostrictive/piezoelectric phases. Compared to traditional ME composites with complex structures, the sandwich metal–insulation–metal (MIM) composite in this work presented a better trade-off between the conversion response and the flexibility. The MIM composite proposed in this work only consisted of two sliver electrodes sputtered on both sides of piezoelectric material, which was prone to achieve the ME coupling without requiring the magnetostrictive phase. Additionally, with low cost and high flexibility, the MIM composite was prone to be manufactured in various sizes or shapes. To verify the experiment’s accuracy, the model was established to analyze the magnetoelectric property of the MIM composite. Moreover, the MIM composite was placed in the Hdc and Hac with variable frequency to simulate the actual operating conditions. When the applied Hac generated by the electric conducting coil penetrated the metal electrodes, eddy currents were generated on the metal electrodes by the Faraday effect. Ampere forces generated by the applied Hdc acted on the sandwich MIM composites, leading to the generation of ME voltage. The modeling and experimental data on the sandwich MIM composites with simple structure exhibited excellent magnetoelectric properties when exposed to the eddy current, Hdc and Hac. The ME response and vibration in the PVDF film can be controlled by changing the magnetic field (AC and DC) and the eddy current, respectively. This experiment and modeling were divided into two sections. The first section explored the influence of the applied Hdc and Hac on the output voltage of the sandwich MIM composite. Specifically, the Hac (0 to 20 Oe) with a frequency of 1 kHz and the Hdc (−2500 to 2500 Oe) were applied on the sandwich MIM composite, respectively. The second section of this experiment was to investigate the influence of the frequency of the applied Hac on the output voltage of the MIM composite. When the Hdc and Hac were set to 1000 and 5 Oe, respectively, and the frequency of Hac changed from 10 to 1000 Hz, the output voltage of the sandwich MIM composite was measured and investigated. The investigation on ME effect of the sandwich MIM composite provided significant support and reference for developing excellent magnetoelectric memory devices.

Results and Discussion

Magnetoelectric Responses of the Sandwich MIM Composite

The vibration/deformation in the PVDF material results from the eddy current induced by the increase of Hac. When the vibration intensifies, the output voltage generated in the sandwich MIM composite also increases. Three cases are studied to analyze the corresponding vibration and output voltage generated in the sandwich MIM composite. Figure shows the increase in voltage on the sandwich ME composite, attributed to the vibration caused by applying AC magnetic field (from 0 to +20 Oe) and without Hdc. The measurement indicates that the silver layer on the sample generates an eddy current under the Hac and without Hdc, which could generate the thermoelectric effect. Since PVDF is a kind of piezoelectric and thermoelectric material, a thermoelectric effect generates voltage at a certain heat.[14] The Hac dependence of the ME voltage signal exhibits that ME voltage is only induced by the thermoelectric effect instead of ME effect. Under the applied Hdc, the induced magnetoelectric effect and the thermoelectric effect are distinguished by comparing the magnitude of the voltage generated by the thermoelectric effect. Compared with the magnetoelectric voltage under the condition of merging Hdc with Hac, the ME voltage without the applied Hac is so low that it may be negligible.

Figure 1

Linear relationship between ME voltage and AC magnetic field (@f = 1 kHz).

Figure shows the increase in ME voltage on the sandwich MIM composite due to the vibration generated by applying Hac from 0 to 20 Oe with a frequency of 1 kHz and Hdc from −1500 to 1500 Oe. As shown in Figure , a quadratic-type magnetoelectric response generates on the sandwich MIM composite under an Hac value of 2, 4 Oe with a frequency of 1 kHz when the Hdc is varied from −2500 Oe to 2500 Oe. In addition, when the Hac is zero, the ME voltage of the sandwich MIM composite remains at around zero, because the eddy current is not generated without Hac. Based on the above results, we can find the ME output voltage has a strong dependence of Hdc. Therefore, the amplitude of a DC magnetic field can be obtained by measuring the ME output voltage under a specific Hac.

Figure 2

Amplitude of ME voltage as a function of AC magnetic field amplitude for different DC magnetic fields (@f = 1 kHz).

Figure 3

Amplitude of ME voltage as a function of DC magnetic field.

Influence of DC Magnetic Field on PVDF Samples

Figure shows the simulation and experimental results of the magnetoelectric voltage under Hdc from −2500 to 2500 Oe. The results show that the magnetoelectric voltage is proportional to the applied Hdc, which could be attributed to the increase of the Lorenz force and bending degree on the sandwich MIM composite. When the Hdc is zero, the ME output voltage reaches the minimum value. The reason for the minimum ME output voltage is that there has not the Lorenz force when the Hdc is zero. In addition, there is a deviation of the minimum ME output voltage between the experimental measurement and simulation result, which can be attributed to the thermoelectric effect. As shown in Figure , the above mentioned results are consistent with the experimental result shown in Figure , which further confirms the thermoelectric effect. The thermoelectric effect is caused by the generation of eddy current in the metal layer on the sample under the Hac and without Hdc. Then, a deviation between the simulation and experimental results is obtained when moving the vortex center along the sample length direction.[15]

Figure 4

Comparison of ME effect between the simulation and experiment (@f= 1 kHz; Hac =5 Oe).

Influence of the Frequency of AC Magnetic Field on the Output Voltage of PVDF Samples

Figure shows experimental results of magnetoelectric voltage with the frequency of Hac from 10 to 1000 Hz. The results show that with the increase of the frequency of the Hac, the larger induced current and output voltage on the sandwich MIM composite can be observed, which results from the increase of magnetic field strength through the sandwich MIM composite. With the increase of AC magnetic field frequency, the stronger the magnetic field passing through the silver metal surface, the larger induced current and the larger the output voltage of the ME film can be generated. Due to the influence of frequency fluctuations, the output voltage fluctuates upward. The output voltage increases quickly with the increase of the frequency within 1 kHz. In addition, the behavior of applied Hac and Hdc and the influence of the frequency of the applied Hac on the output voltage are quite similar as they show linear responses to the output voltage. In this case, the ME effects are evidently related to the AC magnetic field frequency. The frequency of Hac dependence of direct ME coefficients is relevant to the relative dielectric constant and the variation in the piezoelectric phase coupled with a magnetic field. The experiment results in Figure show the linear response between the ME voltage and the frequency of between the ME voltage and the frequency of Hac, which prove that the ME output voltage can be controlled by AC magnetic field frequency.

Figure 5

Frequency dependence of the ME voltage signal (@Hac = 5 Oe, Hdc = 1000 Oe).

Mechanical Analysis of the ME Film under Lorentz Force

The equation of the electromagnetic properties of two-way combined matter is the basis for solving the problem of the magnetic field. Static magnetic field refers to the constant magnetic field generated by direct current. According to the theory of vector analysis, magnetic induction intensity is expressed as the spin of another vector. Under the applied AC and DC magnetic fields, the coupling between the Lorentz force produced by the metal electrode and the piezoelectric effect of the sample is used to achieve magnetoelectric conversion. When the applied Hdc penetrates the surface of the metal electrodes, a magnetic flux ϕac is expressed aswhere S represents the surface area of the silver electrode; μ0 is the magnetic permeability. According to Faraday’s law of electromagnetic induction, induced currents are generated by AC magnetic field. The AC magnetic field hac is expressed aswhere ω= 2πf is the angular frequency, f = 1 kHz magnetic field frequency, and Hac is the amplitude of the AC magnetic field. The electromotive force (Ef) in the metal electrode is expressed as[16]where ϕloop is the magnetic flux in the metal electrode.

Determining the current density of the eddy current is the key problem to explore the magnetoelectric coupling further. The eddy current is calculated using the current density J form of Ohm’s law,where σ is the conductivity of silver and E is the electric field induced by the alternating magnetic field. However, the relationship between Ef and E is expressed aswhere L is the circumference of the eddy current loop. Then, substituting eq into eq , the eddy currents of the silver electrode can be expressed aswhen DC bias magnetic field acts on metal electrodes, a differential equation of Ampere force (dF) expressed as eq (17) is generated in each current loop.

where B is the magnetic induction vector, dL is a vector element of the loop’s closed contour, and Hdc is the uniform applied magnetic field. Then, a moment subjected to each loop is expressed aswhere z is the molecular magnetic moment of the eddy current loop and m is the area of the loop.

Finally, electrodes on both sides of the PVDF film are subjected to torques M1 and M2 because the sample is isotropic in the plane. Therefore, the torque of the PVDF film can be expressed asHowever, the electromechanical modeling of the unimorph bender could be calculated based on eq .where s3, E3, T3, and D3 are the strain, the electric field, the stress, and the electric displacement; g33 represents the piezoelectric constant; β33 and S33 express absolute permittivity and suppleness of the material, respectively.

Substituting the short circuit condition T3= 0 in eq yieldsThus, the theoretical expression of the ME current IME induced by the Lorenz force is given by[18]

In previous studies, only the free end of the bimorph is subjected to an external moment. The change of the generated electric charge can be expressed as[19]where d31, t, and l are the transverse piezoelectric coefficient, the sample’s thickness, and length, respectively. The magnetoelectric voltage generated by Ampere forces can be expressed aswhere C is the capacitance of the PVDF film.

Finally, the ME voltage coefficient α is calculated by solving eq .

As can be seen from Figure , when the applied Hdc is ±2500 Oe, the ME voltage coefficient reaches α = 60.71 mV cm–1 Oe–1 @1 kHz. As shown in Table , the optimal values of the ME voltage coefficient α are listed.

Figure 6

Simulation of the displacement diagram of ME beam.

Table 1

Comparison between ME Voltage Coefficients of Different Materials

types	materials	α (mV cm–1 Oe–1)
single-phase samples	Cr2O3 crystal @1 kHz[20]	20
particulate composite samples	P(VDF-TrFE) +0.3wt %Fe3O4 @5 kHz[21]	2.23
	P(VDF-TrFE) +72wt %CoFe2O4 @ 5 kHz[22]	40
multilayer samples	PZT/Alumina @ 4.9kHz[15]	79
	silver/PVDF/silver @1 kHz [this work]	60.71

The model is built by the FEM. When the body load of the Lorenz force is loaded into the sandwich MIM composite, the total displacement of the ME film along the direction of thickness is shown in Figure . From this figure, when the Lorenz force is applied to the sandwich MIM composite, the sample is subjected to different torsional moments, which induces strain on the piezoelectric phase causing asymmetrical stress. The ME composite moves along the direction of thickness (Y) under the Lorenz force generated by the vortex current, which is consistent with the theoretical analysis. At the same time, as the DC magnetic field increases, the Lorentz force is also increased. The increase of Lorentz force leads to the increase of strain of the film, which further leads to the increase of the magnetoelectric voltage.

When the Lorentz force acts on the piezoelectric phase, the force and deformation are induced in the sample. As shown in Figure , its vibration direction is along the thickness direction (Y) of the sample. Due to the piezoelectric effect, the surface charges of the sandwich ME composite migrate, and surface charges with opposite polarity are induced on two opposite surfaces. In this case, the PVDF layer of the tested material exhibits the magnetoelectric effect as piezoelectric ceramics.

Figure 7

Schematic of the vibration mode of the ME film under AC and DC magnetic fields.

From the previous analysis, it can be seen that under the Lorentz force generated by the eddy current, the sandwich MIM composite bends along the thickness direction. The surface of the sandwich MIM composite charges under the piezoelectric effect. A terminal into the electrostatic node is added to obtain the output potential on the sandwich MIM composite surface. Figure reflects that a uniform surface potential distribution of the sandwich MIM composite under the condition of an AC magnetic field strength of 15 Oe with a frequency of 1 kHz.

Figure 8

Simulation results of output voltage of the ME film.

As shown in Figure , with evident direct ME effect resembling the bulk ME composite, the flexible ME composite could be used in magnetoelectric memories, microdevice sensors, magnetic memories, oscillators, phase shifters, and the like. For the ME memories, the sensitivity is a significant issue. Specifically, when the ME sensitivity is around 1 μV Oe–1, the response signal on the ME films could reach 100 μV under the media field up to 100 Oe. Consequently, the ME memories with larger ME coefficients could reach higher output signal at a relatively weak magnetic field.[23] Based on the above description, the sandwich MIM composite has considerable potential in ME memory devices depending on the higher ME coefficient.

Figure 9

Schematic diagram of magnetoelectric memory.

Conclusions

In conclusion, we fabricated a sandwich MIM composite which could be used for magnetoelectric memory devices. The sandwich MIM composite has higher ME voltage coefficients of 60.71 mV cm–1 Oe–1, which is beneficial for the magnetoelectric conversion. Specifically, the ME output voltage increases with the increase of the applied DC magnetic field. In addition, when the Hac is constant, the ME output voltage increases with the increase of Hdc. Moreover, the relationship between the frequency of Hac and the ME output voltage exhibits a linear tendency. Finally, the simulation results are consistent with the experimental results, which reflects the model established in this paper could help to evaluate the experimental results more intuitively and accurately. It can be concluded that the sandwich MIM composite has considerable potential in magnetoelectric memory devices. This paper provides significant support for developing magnetoelectric memory devices, which is essential to develop the whole internet system and its subsystem in the future.

Experiment Section

Magnetoelectric Experiment

The sandwich MIM composite samples (40 × 10 × 0.028 mm) were subjected to the Hac and Hdc, which were generated by two DC sources and one AC coil source. Firstly, the top of the sandwich MIM composite was vertically fixed on a specimen holder. Then, the DC bias magnetic field driven by a DC programmable power current source (CH-Hall, F2030) was applied on both sides of the sample to ensure the sample’s plane and DC magnetic field in the same direction. Two Helmholtz coils were driven by a voltage amplifier (NJFNKJ, HEAS-50) regulated by a waveform generator (RIGOL, DG1022U), while the AC magnetic field superimposed on a constant DC magnetic field was applied perpendicularly to the plane of the films, as shown in Figures and 11. The magnitude of the magnetic field was measured with a tesla meter (CH-Hall, 1500). Finally, data acquisition equipment (CH-Hall, NET) was employed to store the measurement.

Figure 10

Schematic diagram of the experimental setup for the magnetoelectric measurement.

Figure 11

Enlarged image of the sample in the magnetic fields.

In this experiment, for the sandwich MIM composite, DC and AC magnetic fields were perpendicular to each other. The induced Lorentz force was perpendicular to the sandwich MIM composite. This force vibrated the sandwich MIM composite, which led to the generation of the voltage in the sandwich MIM composite. Moreover, the magnetic flux induced by the eddy current penetrated into the silver electrode can be observed in the sandwich MIM composite. Because of the influence of DC bias magnetic field, the magnetoelectric output voltage and the vibration amplitude can be accurately regulated by manipulating the applied Hac and Hdc.

Magnetoelectric Modeling

There were four interfaces considered in the simulation including magnetic fields interface, magnetic fields−solid interface, solid interface and electrostatic interface. The magnetic fields interface was mainly used to calculate the distribution of induced current and the surrounding magnetic field within the coil, conductor, and magnet. The magnetic fields−solid interface was defined by Ampere law. The solid interface was employed for calculating the displacements, stresses and strains of the ME film. The electrostatic interface was employed for calculating electric displacement field and potential distributions of ME film. The boundary condition, including the size of sample, magnetic flux vector and tangential components of the magnetic field etc., had been added.

The Helmholtz coils paralleled to each other can produce an alternating magnetic field, and the distance between the coils was equal to the radius of the coil, as shown in Figure . The simulated Helmholtz coil required adding coil nodes under the magnetic field interface and a current excitation of 0.5 kA in the coil.

Figure 12

FEM simulation of the Helmholtz coil.

According to the Figure , a magnetic field environment was simulated. The ME sample was placed in the alternating magnetic field space. The modeling space was cut into by the “finite element” area. The continuous solution domain was separated into a limited number of subregions to solve the physical variables of each subregion, and each subregion was continuous and coordinated, which was beneficial for improving the computational accuracy and computional sensitivity. Figure showed the mesh generation of the ME film.

Figure 13

Modeling process of the ME film.

Figure 14

The mesh generation of the ME film.