# Low-Frequency Resonant Magnetoelectric Effects in Layered Heterostructures Antiferromagnet-Piezoelectric

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}O

_{3}crystal with easy-plane anisotropy and a piezoelectric layer are studied. The effects arise due to a combination of magnetostriction and piezoelectricity because of mechanical coupling of the layers. The field dependences of magnetization and magnetostriction of the hematite crystal are measured. The resonant ME effects in the hematite-piezopolymer and hematite-piezoceramic structures are studied. The strong coupling between magnetic and acoustic subsystems of hematite results in a tuning of the acoustic resonance frequency by the magnetic field. For the hematite layer, the frequency tuning was found to be ~37% with an increase in the bias field up to 600 Oe. For the hematite-PVDF heterostructure, the frequency tuning reached ~24% and the ME coefficient was 58 mV/(Oe∙cm). For the hematite-piezoceramic heterostructure, the frequency tuning was ~4.4% and the ME coefficient 4.8 V/(Oe∙cm). Efficient generation of the second voltage harmonic in the hematite-piezoceramic heterostructure was observed.

## 1. Introduction

_{2}O

_{4}, CoFe

_{2}O

_{4}), which have a high magnetostriction λ in low magnetic fields [5,6,7]. It has been shown that the magnitude of the ME effect depends on the permanent bias magnetic field H applied to the structure [8]. The efficiency of the ME conversion increases by 1–2 orders of magnitude when the excitation field frequency coincides with the frequency of natural acoustic oscillations of the heterostructure due to the resonant increase in deformations [9]. Nonlinear ME effects of generation of harmonics, subharmonics and combination frequencies, the bistability was found with an increasing excitation field [10,11].

_{2}O

_{3}with the Neel temperature T

_{N}= 960 K and iron borate FeBO

_{3}with T

_{N}= 348 K. The technologies for growing high-quality crystals of hematite and iron borate are well developed, their magnetic properties have been studied, these crystals are good dielectrics and possess high acoustic quality factors [12,13,14,15,16]. A feature of the AFM crystals with easy-plane anisotropy is a strong coupling of the magnetic and acoustic subsystems, which leads to a tuning of the frequency of acoustic oscillations of crystals by the magnetic field and a nonlinearity of their acoustic characteristics [15,16,17,18].

## 2. Materials and Methods

_{2}O

_{3}grown using the method of spontaneous solution-melt crystallization at MIREA by V.A. Murashev [16]. The single crystal was oriented using the X-ray method, cut and polished to optical quality. In measurements, a rectangular plate of hematite with a length of L = 17 mm, width of W = 5 mm and thickness of a

_{m}= 0.33 mm was tested. Hematite is a two-sublattice antiferromagnet with easy-plane anisotropy in the temperature range from the Morin temperature T

_{M}= 260 K to the Neel temperature T

_{N}= 960 K. Magnetic structure of hematite is schematically shown in Figure 1a. The magnetizations of the sublattices M

_{1}and M

_{2}lie in the easy “x-y” plane, the C

_{3}axis is parallel to the “z” axis, and the binary axis U

_{2}is also in the “x-y” plane and directed at the angle β with respect to the field H. The sublattices magnetizations are equal to M

_{1}= M

_{2}= 870 emu/cm

^{3}and canted in a weak external field H at an angle φ ≈ 1

^{0}with respect to the “y” axis, so that the resulting low magnetization M ≈ 2 emu/cm

^{3}is directed along the field H [20]. The anisotropy in the “x-y” plane is small and ferromagnetic vector M can freely rotate in the plane, following the direction of H.

^{0}to the direction of the permanent field H, at which the magnetization oscillations were most effectively excited. A current with an amplitude up to I = 200 mA and a frequency of f = 0–500 kHz was passed through the internal coil from an Agilent 33210A generator (Agilent Technologies, Santa Clara, CA, USA), which created an excitation magnetic field with an amplitude h up to 2 Oe. Oscillations of the sample magnetization were recorded with an external measuring coil. The dependences of the voltage V induced in the measuring coil on the amplitude h and frequency f of the excitation field h and field H were measured using an SR844 lock-in amplifier (SRS, Sunnyvale, CA, USA). The permanent magnetic field H was measured using a LakeShore 421 Gaussmeter (Lake Shore Cryotronics, Westerville, OH, USA) with an accuracy of 0.1 Oe. The ac excitation field h was measured using the current through the coil calibrated at a frequency of 100 Hz. The measuring setup operated in automatic mode under the control of a specialized program.

_{p}= 50 μm, piezoelectric modulus of d

_{31}≈ 10 pC/N and relative permittivity of ε ≈ 10.4. Ag-electrodes with a thickness of ~1 μm were preliminarily deposited on the film surface using the thermal method. The ME effect was excited by an alternating magnetic field h(f) produced by the excitation coil. The voltage u(f) generated by the structure was taken across the electrodes of the PVDF-layer. The amplitude of the ME voltage was recorded at different values of f, h, and H.

_{0.52}Ti

_{0.48})O

_{3}ceramic (PZT). The PZT plate had in-plane dimensions of 17 mm × 6 mm, thickness of a

_{p}= 250 μm, piezoelectric modulus of d

_{31}= −175 pC/N and relative permittivity of ε ≈ 1750. The Ag-electrodes with a thickness of ~3 μm were preliminarily deposited on the wafer surface using the firing method. The hematite and PZT layers were bonded with a ~4 μm thick cyanoacrylate adhesive, which provided a strain transfer between the layers. The same setup was used to record the ME voltage u(f) generated by the PZT layer at different values of f, h and H.

^{−6}. All measurements were carried out at room temperature without electromagnetic shielding of the structures.

## 3. Results

#### 3.1. Magnetization and Magnetostriction of Hematite

_{2}O

_{3}plate when magnetized by field H along the long axis. It can be seen from Figure 2a that the magnetization M is equal to zero in the region of fields close to zero H ≈ 0, then increases abruptly to the value M ≈ 2 emu/cm

^{3}and grows linearly with a further increase in the field H up to 18 kOe. Features of magnetization reversal in the region of low fields with a cyclic change in the field are shown in an expanded scale in Figure 2b. It can be seen that the magnetization M begins to grow from zero in the field H

_{c}≈ 2 Oe and then smoothly increases with increasing H. As the field H falls from maximum to zero and its direction changes, a hysteresis occurs. The magnetization drops abruptly in the field H

_{c}≈ −2 Oe and the process is repeated. The value of the coercive force was H

_{c}≈ 2 Oe.

_{S}≈ 2.5 × 10

^{−6}with an increase in H up to ~300 Oe, and then increases approximately linearly with an increase in the field. Solid and dashed lines in Figure 3a show the calculated field dependences of the magnetostriction λ(H) and the piezomagnetic coefficient ${\lambda}^{(1)}(H)={\left.\partial \lambda /\partial H\right|}_{H}$, which is equal to the derivative of the magnetostriction with respect to the field. Saturation of the hematite magnetostriction in the range of fields up to 1.5 kOe was not observed.

_{c}≈ 2 Oe.

#### 3.2. Frequency Tuning of Acoustic Resonance of Hematite

_{1}≈ 165 kHz with an amplitude of ~4.3 mV and a quality factor Q

_{1}≈ 110, near the frequency f

_{2}≈ 314 kHz with an amplitude of ~2.7 mV and a quality factor Q

_{2}≈ 150, and a peak near the frequency ~394 kHz. The quality factor of the peaks was estimated using the formula Q = f/Δf, where f is the center frequency of the peak, and Δf is the peak width at a level of 0.71 from the maximum. As will be shown later, the peak with frequency f

_{1}corresponds to the excitation of the fundamental mode of planar vibrations along the length of the plate and the peak with frequency f

_{2}corresponds to the excitation of the main contour-shear mode of the plate. Other low-amplitude peaks, corresponding to the excitation of higher modes of planar, bending or shear vibrations of the plate will not be considered further.

_{1}, the frequency tuning was γ

_{1}≈ 23.4%, and for the second mode with frequency f

_{2}, γ

_{2}≈ 37.1%. When evaluating the frequency tuning, ${f}_{1}(\infty )$ = 197 kHz was taken for the first mode, and ${f}_{2}(\infty )$ = 425 kHz for the second mode. Quality factors for both resonances increased from Q ≈ 60 in low fields to Q ≈ 4 × 10

^{3}in the saturation field. The dependences obtained are consistent with the data of [13,22]. Solid lines in Figure 5 show calculated dependences of the peak frequencies on the bias field (see below).

#### 3.3. ME Effect in Hematite-PVDF Heterostructure

_{3}is tuned within ~162–200 kHz with increasing H. The peak amplitude u

_{3}first increases with increasing H, reaches a maximum value u

_{3}≈ 0.058 mV at magnetic fields H = 50–300 Oe, and then decreases gradually as the field increases. The quality factor of the peak in this case increased from Q ≈ 50 to ~150. The dependence of the frequency f

_{3}on the magnetic field H plotted using data of Figure 6 is shown in Figure 5. It can be seen that the relative frequency tuning of the acoustic resonance in the hematite-PVDF structure by magnetic field was ~24%. No peaks were observed on the u(f) characteristic in the high-frequency region of 260–400 kHz.

#### 3.4. ME Effect in Hematite-PZT Heterostructure

_{4}≈ 142.5 kHz with an amplitude u

_{4}= 156 mV and a quality factor Q ≈ 180, and a weaker resonance near the frequency f

_{5}≈ 8.8 kHz with an amplitude u

_{5}≈ 18 mV and a quality factor Q ≈ 50. The peak with frequency f

_{4}corresponds to the excitation of the lowest mode of planar vibrations along the length of the heterostructure, and the low-frequency peak with frequency f

_{5}corresponds to the excitation of bending vibrations of the heterostructure. With an increase in the field H, an increase in the frequencies of both peaks was observed. The frequency f

_{4}increased from 141.5 kHz at H = 0 to ~147.8 kHz at H = 600 Oe, which corresponds to the frequency tuning by γ ≈ 4.4%. The dependences of the frequencies f

_{4}and f

_{5}on the magnetic field H for the hematite-PZT heterostructure are shown in Figure 5.

_{4}of the peak with frequency f

_{4}on the bias field H. It can be seen that u

_{4}first decreases monotonically from the maximum value of ~156 mV at H ≈ 0 to ~70 mV at H ≈ 0.3 kOe, and then remains approximately constant as the field increases up to 1.5 kOe. One can see a pronounced dip in the region of fields near zero H ≈ 0. The fine structure of the dependence u

_{4}(H) in the low field region is shown in Figure 8b. The peak amplitude hysteretically depends on the field H, reaching a minimum in the fields H

_{min}≈ ±2 Oe. In the absence of a field, H = 0, the ME voltage u

_{4}was ~70% of the maximum value at H ≈ 2.5 Oe. For a low-frequency resonance with a frequency f

_{5}, the dependences of the voltage u

_{5}on the magnetic field H had the form similar to the dependences shown in Figure 8.

#### 3.5. Second Harmonic Generation

_{1}/2 = 70.8 kHz and an amplitude h ≈ 1.3 Oe. One can see a voltage peak with an amplitude of ~170 mV and a width at the base δH ≈ 2 Oe. The peak amplitude and peak width increased approximately linearly with increasing excitation field h. Note that the amplitude of the peak is comparable to the amplitude of the voltage generated at linear ME effect (see Figure 7). When generating the second harmonic, there was also a hysteresis on the magnetic field.

## 4. Discussion of Results

^{3}in weak magnetic fields. Using the magneto-optical method, it was shown [23] that in this field region, as H increases, the domain structure of the sample is rearranged, leading to the formation of a single-domain state. With a further increase in H up to 20 kOe, the magnetization grows linearly with the field due to the canting of the sublattices magnetizations in the field direction. In the fields ranging up to several kOe, the resulting magnetization of hematite M is small. Therefore, the demagnetization effects are also small and should not affect the characteristics of ME effects. Consequently, the field characteristics of ME effects in heterostructures with hematite layers will not depend on the layers size, in contrast to heterostructures with FM layers, where demagnetization effects play a significant role [24,25].

_{S}= 2.31 × 10

^{−6}, α = 0.012 Oe

^{−1}and τ = 1.1 × 10

^{−3}Oe

^{−1}are taken. The calculated curve is shown with a solid line in Figure 3a. The dashed line in Figure 3a shows the field dependence of the piezomagnetic coefficient ${\lambda}^{(1)}(H)$, found by differentiating the function (2). The maximum coefficient was ~2.8 × 10

^{−8}Oe

^{−1}, i.e., an order of magnitude smaller than for Metglas [10].

_{D}= 22 kOe is the Dzyaloshinski field, H

_{E}= 9.2 × 10

^{3}kOe is the effective exchange field [15], and H

_{ms}is the magnetostriction field. Here, ${H}_{ms}(\beta )={H}_{ms}{\mathrm{cos}}^{2}(2\beta )$ is for the contour-shear mode and ${H}_{ms}(\beta )={H}_{ms}{\mathrm{sin}}^{2}(2\beta )$ is for the longitudinal mode, where β is the angle between magnetic field H and the binary axis U

_{2}.

_{1}and f

_{2}on the field H calculated using Equation (3) are shown with solid lines in Figure 5. The parameters of the hematite plate found from experiment 2H

_{E}H

_{ms}≈ 2.2 kOe

^{2}, ${f}_{1}(\infty )$ = 197 kHz, ${f}_{2}(\infty )$ = 425 kHz, and angle β = 19

^{0}were used in calculations. The limiting frequencies can be estimated by the formulas: ${f}_{1}(H=\infty )=(1/2L)\sqrt{Y/\rho}$ for planar vibrations along the plate length L and ${f}_{2}(H=\infty )=(1/2W)\sqrt{{C}_{66}/\rho}$ for contour-shear vibrations along the plate width W. Calculation for a hematite plate of length L = 17 mm, width W = 5 mm, Young’s modulus Y = 23 × 10

^{10}N/m

^{2}, and shear modulus C

_{66}= 9.3 × 10

^{10}N/m

^{2}[13], gives the frequencies ${f}_{1cal}(\infty )=$ 193 kHz and ${f}_{2\mathit{cal}}(\infty )=$ 419 kHz, respectively. Thus, the theory explains the field dependences of the resonance frequencies of hematite plate well.

_{3}(H), as can be seen from Figure 3, completely coincided with the dependence f

_{1}(H) for a free hematite plate. This indicates that a thin PVDF film deposited on the hematite surface did not affect its magnetoacoustic characteristics. The frequency tuning of the resonant ME effect under magnetic field in the structure under study was ~24%, i.e., an order of magnitude greater than the frequency tuning due to the delta-E effect in structures with various FM materials: 1% in the structure with permendure (FeCoV) [5], 1.4% in the structure with amorphous FeGaB alloy [28], and 3.9% in the structure with Terfenol-D [29]. The maximum value of ME voltage coefficient for the hematite-PVDF heterostructure, as follows from data in Figure 6 was ${\alpha}_{E}={u}_{3}/({a}_{p}h)\approx $ 58 mV/(Oe∙cm) at a bias field of H ≈ 75–100 Oe. It is seen from Figure 6 that the resonant peak splits in magnetic fields of H ~ 100–150 Oe. This may be due to the intersection at a given field of the dispersion curves of vibration modes with close frequencies, which was recently observed in hematite disk resonators [22]. A lack of ME effect in the hematite-PVDF heterostructure at the frequency of contour-shear vibrations f

_{2}is explained by the non-responsivity of the PVDF film to shear deformations.

_{4}of the hematite-PZT heterostructure increased by 4.5% with increasing H, i.e., the frequency tuning decreased by a factor of ~6 compared to the frequency tuning for a free hematite plate. The mechanism of magnetoelastic excitation in the geometry of Figure 1d is modulation of the non-saturated magnetostriction by the longitudinal alternating magnetic field. Longitudinal susceptibility in the fields up to 1.5 kOe is mainly determined by the residual growth stresses and weakly dependents on magnetizing field. As a result, the sensitivity of the magnetoelastic coupling to the magnetic field variations also deceases.

_{4}and bending f

_{5}resonances for the hematite-PZT structure were estimated using the formulas for the natural vibration frequencies of a free rod [30]. Taking into account dimensions of the structure, effective values of Young’s modulus Y

_{ef}= 16.1 × 10

^{10}N/m

^{2}and density ${\rho}_{ef}=$ 6.2 × 10

^{3}kg/m

^{3}, the frequencies f

_{4cal}≈ 149.2 kHz and f

_{5cal}≈ 8.02 kHz were obtained, which are in good agreement with the measured ones. The maximum value of the ME voltage coefficient for the hematite-PZT heterostructure, as follows from the data in Figure 8, was ${\alpha}_{E}={u}_{4}/({a}_{p}h)\approx $4.8 V/(Oe∙cm) at a bias field of H ≈ 2.5 Oe.

_{4}(H) for the hematite-PZT heterostructure qualitatively differs from similar dependence for the structures with FM layers. This is due to the unusual field dependence of the magnetostriction λ(H) and piezomagnetic coefficient ${\lambda}^{(1)}(H)$ of hematite, which are shown in Figure 3a. It is known that in composite heterostructures with a stress-mediated ME effect, the dependence u(H) qualitatively repeats field dependence of the piezomagnetic modulus of magnetic layer [4]. Comparison of the curves ${\lambda}^{(1)}(H)$ in Figure 3a and u

_{4}(H) in Figure 8a confirms this connection. The quantitative difference between the experiment and theory can be due to a change in the shape of the dependence λ(H) for a hematite plate loaded with a PZT layer.

^{2}), which is comparable to the coefficient for the Metglas-PZT structure ~4.5 V/(cm∙Oe

^{2}) and exceeds by an order of magnitude the coefficients for structures with Ni or FeCo layers [31]. The high nonlinearity of ME effect is due to peculiarities of the hematite magnetostriction: the linear field dependence of the magnetostriction in low fields H ≈ 0 and symmetry of the magnetostriction with respect to the field direction λ(H) = λ(−H) (see Figure 3b). Therefore, the amplitude of the second harmonic at H ≈ 0 is proportional to the magnetostriction u

^{(2)}~λ, and not to its second derivative ${u}^{(2)}~{\lambda}^{(2)}$, as for the structures with ferromagnetic layers. The amplitude u

^{(2)}should be maximum at H = 0 and drop to zero with increasing magnetic field up to H ≈ h, which was observed experimentally. A decrease in the hysteresis of the nonlinear ME effect during second harmonic generation (see Figure 9) down to H

_{c}≈ 0.5 Oe compared to the hysteresis of linear ME effect (Figure 8b) may be due to suppression of ME effect hysteresis with an increase in the amplitude of the excitation magnetic field [32].

## 5. Conclusions

_{2}O

_{3}single crystal and piezoelectric layers of PVDF polymer or PZT piezoceramics. The dependences of the magnetization M and magnetostriction λ of a hematite plate on the permanent magnetic field are measured. It is shown that the strong coupling of magnetic and acoustic subsystems in the hematite crystal leads to a change in its rigidity (delta-E effect) and allows one magnetic tuning of the acoustic resonance frequency of crystals up to ~37%. In the hematite-PVDF heterostructure, the frequency tuning of planar acoustic resonance by magnetic field reached 24%, and the value of ME coefficient was 58 mV/(Oe∙cm). In the hematite-PZT heterostructure, the resonance frequency tuning by magnetic field reached ~4.4%. The ME coefficient in weak magnetic fields was ~4.8 V/(Oe∙cm) and monotonically decreased with increasing field. Efficient generation of the second voltage harmonic in the hematite-piezoceramic heterostructure in the absence of a bias field was found. The results show that by choosing the material and the size of the PE layer in bilayers with hematite, it is possible to realize both a wideband magnetic tuning of the resonance frequency and a high efficiency of ME conversion. The ME effects in heterostructures with layers of antiferromagnetic hematite single crystals open up new possibilities for creating magnetic field sensors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Schematic view of magnetic structure of hematite; (

**b**) the scheme for excitation and registration of magnetization oscillations in hematite plate; (

**c**) the scheme for observation of ME effect in the hematite-PVDF heterostructure; (

**d**) schematic view of the hematite-PZT heterostructure.

**Figure 2.**Magnetization curves for the hematite plate: (

**a**) in the high field region; (

**b**) in the low field region. The arrows show directions of the field change.

**Figure 3.**Dependences of hematite magnetostriction λ vs. magnetic field H: (

**a**) points are the data, solid line is the calculation, dashed line is the piezomagnetic modulus vs. field; (

**b**) magnetostriction λ vs. field H in the low field region. The arrows show directions of the field change.

**Figure 4.**Frequency response of the hematite plate under excitation and registration of acoustic vibrations by coils at excitation field h = 0.3 Oe and bias field H = 50 Oe.

**Figure 5.**Magnetic field dependences of resonance frequencies f

_{1}and f

_{2}for the hematite plate (blue dots), resonance frequency f

_{3}for the hematite-PVDF heterostructure (red dots), and resonance frequencies f

_{4}and f

_{5}for the hematite-PZT heterostructure (purple dots and lines). Points are the data and black solid lines are the calculation using Equation (3).

**Figure 6.**Dependences of the ME voltage u on the excitation field frequency f for the hematite-PVDF heterostructure at different magnetic fields H.

**Figure 7.**Dependence of the ME voltage u on the excitation field frequency f for the hematite-PZT heterostructure at excitation field h = 1.3 Oe and bias field H = 10 Oe. The blue and red peaks correspond to acoustic resonance in the plane of the structure and bending resonance of the structure, respectively.

**Figure 8.**Dependence of the ME voltage u

_{4}on the magnetic field H for the hematite-PZT heterostructure at excitation field h = 1.3 Oe and frequency 142 kHz: (

**a**) in the wide field region; (

**b**) in the low field region. The arrows show directions of the field change.

**Figure 9.**Dependence of the second voltage harmonic ${u}^{(2)}$ on permanent field H for the hematite-PZT heterostructure at excitation field h = 1.3 Oe and frequency 70.85 kHz. The arrows show directions of the field change.

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## Share and Cite

**MDPI and ACS Style**

Burdin, D.A.; Chashin, D.V.; Ekonomov, N.A.; Fetisov, L.Y.; Preobrazhensky, V.L.; Fetisov, Y.K.
Low-Frequency Resonant Magnetoelectric Effects in Layered Heterostructures Antiferromagnet-Piezoelectric. *Sensors* **2023**, *23*, 5901.
https://doi.org/10.3390/s23135901

**AMA Style**

Burdin DA, Chashin DV, Ekonomov NA, Fetisov LY, Preobrazhensky VL, Fetisov YK.
Low-Frequency Resonant Magnetoelectric Effects in Layered Heterostructures Antiferromagnet-Piezoelectric. *Sensors*. 2023; 23(13):5901.
https://doi.org/10.3390/s23135901

**Chicago/Turabian Style**

Burdin, Dmitri A., Dmitri V. Chashin, Nikolai A. Ekonomov, Leonid Y. Fetisov, Vladimir L. Preobrazhensky, and Yuri K. Fetisov.
2023. "Low-Frequency Resonant Magnetoelectric Effects in Layered Heterostructures Antiferromagnet-Piezoelectric" *Sensors* 23, no. 13: 5901.
https://doi.org/10.3390/s23135901