ISSN 1063�7850, Technical Physics Letters, 2011, Vol. 37, No. 3, pp. 244–246. © Pleiades Publishing, Ltd., 2011.Original Russian Text © N.S. Perov, L.Yu. Fetisov, Yu.K. Fetisov, 2011, published in Pis’ma v Zhurnal Tekhnicheskoі Fiziki, 2011, Vol. 37, No. 6, pp. 1–7.

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The phenomenon of magnetoelectric (ME) inter�action in planar ferromagnetic–ferroelectric (FM–FE) structures has been extensively studied in recentyears in view of its potential applications in magneticfield sensors and electric voltage converters and gener�ators [1]. The ME interaction leads to the generationof electric voltage u( f ) between edges of the structureunder the action of magnetic field h( f ).This phenom�enon takes place due to a combination of the magne�tostriction in the FM layer and piezoeffect in the FElayer, which is mediated by the mechanical interactionbetween layers. The efficiency of the ME interaction ischaracterized by the coefficient αE = (u/b)/h. whereb is the thickness of the FM–FE structure. The voltageamplitude u exhibits resonant growth when the fieldfrequency coincides with the frequencies of acousticoscillations on the structure, which gives rise to defor�mations in the FE layer [2]. The resonance can takeplace at the frequencies of bending and planar oscilla�tions of the structure. Using the former oscillations, itis possible either to decrease the resonance frequencyby one or two orders of magnitude for the same struc�ture dimensions or to reduce dimensions of the struc�ture at a constant resonance frequency.

Previously, a value of αE = 14.6 V/(Oe cm) wasachieved at a bending frequency of 12.5 kHz in a two�layer structure with a Terfenol type alloy plate possess�ing high magnetostriction and a lead zirconate titanate(PZT) plate [3], ~1 V/(Oe cm) was obtained at 3–7 kHz in a Ni–PZT structure [4], and ~8.7 V/(Oe cm)at about 33.4 kHz in a GaFe–PZT structure [5]. Itshould be noted that, for the bending oscillations instructures with a single FE layer, a change in the signof deformations across the layer thickness limits thepossible voltage [6]. The voltage amplitude u wasincreased using a symmetric bimorphous structure

with two PZT layers sandwiched between identicalFM (Terfenol) layers [7], in which the ME voltagecoefficient reached up to ~80 V/(Oe cm) at 34 kHz.However, the excitation of bending oscillations in asymmetric structure required magnetizing the FM lay�ers in the opposite directions, which was achievedusing a complicated non�adjustable magnetic system.

In the present study, a resonant ME interaction wasdeveloped in a planar asymmetric bimorphous struc�ture comprising two oppositely polarized PZT layerssandwiched between two ferromagnetic layers madeof materials with the opposite signs of magnetostric�tion. In this structure, the bending oscillations areexcited in a homogeneous magnetic field thataccounts for a high efficiency of the ME interaction.

Figure 1 shows a schematic diagram of the asym�metric FM–FE structure under consideration, whichcomprises two oppositely polarized FE layers withelectrodes, which are sandwiched between two FMlayers made of materials with the opposite signs ofmagnetostriction. The external magnetic field H is ori�ented parallel to the plane of the structure. The FEplates were made of PZT ceramics (Pb0.52Zr0.48TiO3)with a piezoelectric modulus of d13 = 175 pC/N, lat�eral dimensions of 8 × 14 mm, and a thickness of100 μm, which were provided with ~3�μm�thick silverelectrodes. One magnetic plate was made of an amor�phous ferromagnetic (AF) alloy Fe90.3Ni1.5Si5.2B3 witha positive longitudinal saturated magnetostriction of

= 33 × 10–6. This plate had lateral dimensions of5 × 10 mm, and a thickness of 3 μm. The second mag�netic plate was made of nickel and had a negative lon�

gitudinal saturated magnetostriction of = –30 ×

10–6, lateral dimensions of 5 × 10 mm, and a thickness

λ1AF

λ11Ni

Resonant Magnetoelectric Interaction in Asymmetric Bimorphous Ferromagnetic–Ferroelectric Structure

N. S. Perov, L. Yu. Fetisov*, and Yu. K. FetisovDepartment of Physics, Moscow State University, Moscow, 119992 Russia

Moscow Institute of Radio Engineering, Electronics, and Automation (Technical University), Moscow, 117454 Russia*e�mail: fetisov1@yandex.ru

Received July 6, 2010

Abstract—The magnetoelectric (ME) interaction in a planar asymmetric structure comprising a bimorphouspiezoelectric plate of lead zirconate titanate sandwiched between ferromagnetic layers of an amorphous mag�net and nickel with the opposite signs of magnetostriction has been studied. Owing to the effective excitationof bending oscillations at a resonance frequency of ~5 kHz, a ME voltage coefficient of about 18 V/(Oe cm)has been obtained.

DOI: 10.1134/S1063785011030291

TECHNICAL PHYSICS LETTERS Vol. 37 No. 3 2011

RESONANT MAGNETOELECTRIC INTERACTION 245

of 35 μm. The plates were glued together with a con�ducting epoxy glue, the thickness of which did notexceed 3 μm. After assembling the structure, the PZTlayers were polarized in the opposite directions byheating to 100°C and applying a dc voltage of 500 Vbetween the electrodes. Then the structure was placedbetween poles of an electromagnet, in a constant tan�gent bias field of H = 0–2 kOe. The modulating fieldhcos(2πft) with an amplitude of up to h = 7 Oe and afrequency of f = 10 Hz to 200 kHz was generated bycoils and oriented parallel to H. The response signalwas measured as the amplitude u of the alternatingvoltage between output electrodes and studied as afunction of H, h, and f.

Figure 2 shows a plot of the amplitude u of the gen�erated voltage versus frequency f of the alternatingfield at H = 120 Oe and h = 7 Oe. The region between0 and 30 kHz contains resonance peaks, the mostintense being observed at f1 = 5.12 kHz and f2 =12.9 kHz with Q1 = 61, Q2 = 30 and amplitudes u1 =2.54 V and u2 = 0.78 V, respectively. No such reso�nances are found at higher frequencies (up to200 kHz).

The resonant growth in the ME voltage at separatefrequencies is related to the excitation of bendingoscillations in the FM–FE structure. The MEinteraction efficiency was characterized by αE0 ≈0.7 V/(Oe cm) under nonresonant conditions (at10 kHz) and increased to αE1 ≈ 18 V/(Oe cm) at themain mode of bending oscillations. The latter value isgreater by an order of magnitude than the ME voltagecoefficient in Ni–PZT two�layer structures with anal�ogous material parameters and comparable dimen�sions [4].

Figure 3a shows plots of the response voltageamplitude u versus constant field H for the resonancefrequencies f1 and f2. For both resonances, the signalamplitude in small fields increases almost linearly withH and reaches a maximum at Hm = 120 Oe. Then, theamplitude decreases and, as the magnetic layers aresaturated (at H > 800 Oe), the resonant signal ampli�tudes vanish.

AF

PZT

Ni

H, h(f) u(f)

Fig. 1. Asymmetric bimorphous FM–FE structure. Thickarrows indicate the directions of magnetic field H and FEpolarization in the PZT layers (see text for explanations).

2

1

04.5 5.0 5.5

f1, kHz

3

2

1

00 50 100 150

f, kHz

u, Vu, V

f1 f2

Fig. 2. Dependence of the response voltage u generated inthe FM–FE structure on the frequency f of the alternatingmagnetic field at H = 120 Oe and h = 7 Oe. The inset showsthe main resonance line shape on a greater scale.

2000 400 600 800H, Oe

(a)

(b)

1

2

2000 400 600 800

−20

−40

0

20

40

1

2

Hm

u, V

λ11 ×106

H, Oe

Fig. 3. Effect of bias magnetic field H on (a) voltage u gen�erated in the FM–FE structure at frequencies (1) f1 and(2) f2 at h = 7 Oe and (b) longitudinal magnetostriction λ11in (1) AF alloy and (2) nickel film.

1

2

246

TECHNICAL PHYSICS LETTERS Vol. 37 No. 3 2011

PEROV et al.

In order to explain the obtained results, let us con�sider specific features of the ME interaction in theasymmetric bimorphous structure. Figure 3b showsthe dependences of the longitudinal magnetostric�tion λ11 of the tangentially magnetized AF alloy andNi layers, which were measured using a stress sensor[8]. The transverse magnetostriction λ12 is significantlysmaller and can be ignored. Upon application of the

tangential field H, the AF layer is stretched ( > 0)

while the Ni layer is compressed ( < 0) in the fielddirection. These magnetic materials were speciallyselected so as to possess approximately equal absolutevalues of the magnetostriction (|λ11| ≈ 30 × 10–6) andpiezomagnetic coefficients (q11 = ∂λ11/∂H), which areattained at approximately the same magnetic fields ofHm ~ 102 Oe (indicated by the dashed vertical line inFig. 3b). This implies that, under the action of field H,the structure depicted in Fig. 1 exhibits bending withthe AF layer convex upward. The application of a vari�able field of small amplitude h( f ) will effectively excitebending oscillations in the structure with a maximumamplitude at a bias field of Hm ~ 102 Oe. The bendingresults in the compression of one PZT layer and theextension of another. Since the two layers are polarizedin the opposite directions, the voltages generatedacross these layers during bending oscillations willadd. In the case of planar oscillations, deformations inthe two PZT layers are of the same sign and, hence, thegenerated voltages have opposite signs. This must leadto vanishing of the ME voltage at the frequencies ofplanar oscillations, which is confirmed by Fig. 2. Theproposed structure (like that described in [7]) alsoensures suppression of the voltage oscillations causedby thermal noise.

Let us evaluate the frequency of the resonant MEinteraction using a formula for the lowest mode ofbending oscillations in a free square plate with edgelength a and thickness b [9]:

where β1 = 14.1 is a coefficient, Y is the Young’s mod�ulus, ρ is the material density, and γ is the Poisson’sratio. For inhomogeneous plates, Y and ρ imply effec�tive values that are calculated with allowance for thelateral dimensions and thicknesses of layers [4, 8]. Inthe case under consideration, the parameters of layersare as follows:

(PZT) YPZT = 7 × 1010 N/m2, ρPZT = 7.7 × 103 kg/m3;

(AF) YAF = 18.6 × 1010 N/m2, ρAF = 8.2 × 103 kg/m3;

(Ni) YNi = 21.5 × 1010 N/m2, ρNi = 8.9 × 103 kg/m3.Using these values and the known thicknesses of

layers, adopting γ ≈ 0.35, and considering square plates

with a = ≈ 10.6 mm, we obtain for the lowestmode of bending oscillations f1 = 5.9 kHz. By the sametoken, the lowest mode of planar oscillations can beestimated at ~120 kHz. The obtained f1 estimate wellagrees with the measured value, which confirms theproposed model of ME interaction in the bimorphousFM–FE structure featuring bending oscillations.

Thus, we considered the ME effect in a planarasymmetric bimorphous FM–FE structure. The useof FM layers with the opposite signs of magnetostric�tion provides effective excitation of bending oscilla�tions in this structure, while the use of a bimorphousFE plate ensures an increase in the amplitude of gen�erated voltage and the suppression of signals at the fre�quencies of planar oscillations. The efficiency of theME interaction in the proposed structure correspondsto αE ~ 18 V/(Oe cm), which is greater by an order ofmagnitude than the ME voltage coefficient in two�layer structures with analogous material parametersand comparable dimensions.

Acknowledgments. This study was supported in partby the Ministry of Education and Science of the Rus�sian Federation (project no. 2.11.6650) and the Rus�sian Foundation for Basic Research (project no. 09�02�12439�ofi_m).

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Translated by P. Pozdeev

λ11AF

λ11Ni

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