Enhancement of magnetoelectric coupling in a piezoelectric-magnetostrictive semiringstructureN. Zhang, V. M. Petrov, T. Johnson, S. K. Mandal, and G. Srinivasan Citation: Journal of Applied Physics 106, 126101 (2009); doi: 10.1063/1.3271140 View online: http://dx.doi.org/10.1063/1.3271140 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/106/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in DC magnetic field sensor based on electric driving and magnetic tuning in piezoelectric/magnetostrictive bilayer J. Appl. Phys. 115, 17E520 (2014); 10.1063/1.4866516 Effect of magnetic domain structure on longitudinal and transverse magnetoelectric response of particulatemagnetostrictive-piezoelectric composites Appl. Phys. Lett. 104, 112903 (2014); 10.1063/1.4869304 The effects of interface misfit strain and surface tension on magnetoelectric effects in layered magnetostrictive-piezoelectric composites J. Appl. Phys. 114, 044109 (2013); 10.1063/1.4816693 Dual-resonance converse magnetoelectric and voltage step-up effects in laminated composite of long-type0.71Pb(Mg1/3Nb2/3)O3–0.29PbTiO3 piezoelectric single-crystal transformer and Tb0.3Dy0.7Fe1.92magnetostrictive alloy bars J. Appl. Phys. 109, 104103 (2011); 10.1063/1.3587574 Magnetoelectric characteristics of a dual-mode magnetostrictive/piezoelectric bilayered composite Appl. Phys. Lett. 92, 072903 (2008); 10.1063/1.2840177

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Enhancement of magnetoelectric coupling in a piezoelectric-magnetostrictive semiring structure

N. Zhang,a� V. M. Petrov,b� T. Johnson, S. K. Mandal, and G. Srinivasanc�

Department of Physics, Oakland University, Rochester, Michigan 48309, USA

�Received 5 November 2009; accepted 8 November 2009; published online 17 December 2009�

Studies on magnetoelectric �ME� coupling in a semiring of lead zirconate titanate �PZT� with aTerfenol-D insert reveal strong ME coupling at low frequencies and two orders of magnitudeenhancement in the strength at resonance associated with a unique bending mode in PZT. A modelis discussed for the resonance ME coupling that arises from radial and shearing displacements andtheoretical estimates are in excellent agreement with the data. The model also predicts weak MEcoupling in a full ring of PZT with Terfenol-D insert in agreement with the experiment. The resultsare of importance for ME composite based magnetic field sensors. © 2009 American Institute ofPhysics. �doi:10.1063/1.3271140�

Magnetoelectric �ME� composites consisting of magne-tostrictive and piezoelectric phases have attracted consider-able attention in recent years for studies on the nature ofmechanical force mediated ME coupling and for use as mag-netic field sensors and tunable radio frequency devices.1–5

Composites of lead zirconate titanate �PZT� and Terfenol-D,in particular, have been studied extensively due to strongpiezoelectric coupling and high magnetostriction for the twophases.1,6–10 Efforts to date for enhancing the ME coupling inPZT-Terfenol-D include an ultrasonic horn to amplify ampli-tude of vibrations in PZT,6 use of a flextensional cymbal,7

driving the laminate at the bending resonance,8,9 and a highpermeability layer for magnetic flux concentration.10 Thebending resonance in which both piezoelectric and piezo-magnetic components undergo a collective deformation at10–100 kHz for nominal sample dimensions, in particular, isan attractive option for the enhancement of MEcoupling.11–13

This report is on experiment and theory of a new type ofbending mode associated with a specific composite geom-etry, i.e., a semiring of PZT and Terfenol-D insert. The modeis confined to PZT, occurs due to piezomagnetism ofTerfenol-D, and involves radial and shearing deformations.The measured resonance ME coefficient is 75 V /cm Oe,one of the largest reported for the system. Theoretical MEcoefficient versus frequency profiles is in very good agree-ment with the data. The theory also predicts vanishinglysmall ME coupling in a full ring of PZT and Terfenol-Dinsert in agreement with the data. Based on the model oneanticipates several avenues for enhancing the ME response inthe semiring composite, such as location of electrodes or aseries of strategically placed electrodes, results that are ofimportance for ME magnetic field sensors.

The ME composite was fabricated using Terfenol-D ofthe composition Tb0.30Dy0.70Fe1.92 �TDF� and PZT as the

magnetostrictive and piezoelectric materials, respectively.The PZT was in the shape of a semiring of 2.2 mm in thick-ness and 6.2 and 10.2 mm in inner and outer diameters,respectively, and was poled in an electric field in the radialdirection. A slab of TDF of 6.20 mm in length, 5 mm inwidth, and 1 mm in thickness was fitted across the innerdiameter of the semiring and cemented with epoxy. Bothends of the TDF insert closest to the ring were machined tofit the semiring, as shown in Fig. 1. The axis of maximummagnetostriction coefficient of the TDF was along its length.A dc bias magnetic field and an ac magnetic field were ap-plied along the length of TDF and the ME voltage was mea-sured across the electrodes between the inner and outer sur-faces of PZT.

Measurements of ME voltage coefficients �MEVCs� �E

were performed as a function of bias magnetic field H andfrequency f of ac magnetic field. With H along the length ofTDF, we get minimum demagnetizing field and maximumpiezomagnetic and ME coupling. Representative data on �E

versus H are shown in Fig. 1 for f =800 Hz and 2 kHz. One

a�Present address: Department of Physics, Nanjing Normal University, Nan-jing 210097, China.

b�Present address: Institute of Electronic and Information Systems,Novgorod State University, Veliky Novgorod 173003, Russia.

c�Electronic mail: srinivas@oakland.edu.

FIG. 1. �Color online� The bias magnetic field H dependence of the MEVC�E in a semiring of PZT and a Terfenol-D �TDF� insert as shown in thefigure. An ac magnetic field �H �frequency f =800 Hz and 2 kHz� and thebias field H were applied parallel to the length of TDF �direction-1�. The acvoltage was measured across the electrodes on the inner and outer surfacesof the semiring.

JOURNAL OF APPLIED PHYSICS 106, 126101 �2009�

0021-8979/2009/106�12�/126101/3/$25.00 © 2009 American Institute of Physics106, 126101-1

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observes a rapid increase in �E with increasing H, reaches amaximum of 250 mV /cm Oe at about 850 Oe, and then de-creases gradually to near zero. Figure 2 shows the frequencyspectrum for �E under a magnetic bias field of 850 Oe. Withincreasing frequency f , �E remains unchanged except for asharp peak at about f =72.8 kHz. The value of �E at reso-nance is 75 V /cm Oe and is a factor of 280 higher than thelow-frequency maximum in Fig. 1. The quality factor Q forthe resonance is 40.

Next we discuss a model for the resonance enhancementin Fig. 2 due to bending in PZT that arises due to deforma-tion in the piezomagnetic phase. The mode in this case isdifferent from the bending resonance in ME bilayers inwhich both piezoelectric and piezomagnetic components un-dergo a collective deformation.11–13 A piezoelectric semiringin Fig. 1 can also execute an out-of-plane motion, but suchvibrations are not considered in this work. We assume thatthe width of TDF is much smaller than the diameter of thering. The PZT semiring with radius R is in the �1,2� planeand assumed to be poled along the radial direction and thebias field is assumed to be parallel to direction-1 along thelength of TDF. Thus we get minimum demagnetizing fieldand maximum piezomagnetic coupling. The equations ofmotion in the radial and tangent directions for harmonic vi-brations of PZT semiring are14

−1

R

�2M

��2 − N = − �RA�2ur,

�N

��−

1

R

�M

��= − �RA�2u�, �1�

where ur and u� are the radial and tangent displacements, � isthe PZT density, A is the cross-section area, N=�A

pT�dA andM =−�A

pT�rdA are the axial force and bending moment act-ing in a cross section of PZT semiring, respectively, pT� isthe stress component, and r is the distance of a semiringpoint from the mean radius.

The constitutive relations for piezoelectric and piezo-magnetic phases are as follows:

pS� = ps11pT� + pd31

pEr,

mS1 = ms11mT1 + mq31

mH1,

pDr = pd31pT� + p�33

pEr, �2�

where mS1 and

pS� =1

R� �u�

��+ ur� +

r

R2� �u�

��−

�2ur

��2�are the strain components, Ek and Dk are the components ofelectric field and electric displacement, Hk is the magneticfield, sij, qki, and dki are compliance, piezomagnetic, and pi-ezoelectric coefficients, and �kn is the permittivity matrix.The superscripts p and m correspond to piezoelectric andpiezomagnetic phases, respectively.

To solve Eq. �1� for ur and u�, we use Eq. �2� and theboundary conditions in the form ur= mS1L for �=0 and �=�, M =0 for �=0 and �=�, and N= mT1

mA for �=0 and�=�, where L and mA are the length and cross-sectional areaof Terfenol rod. Expressing the stress pT� from Eq. �2� withthe use of obtained expressions for ur and u� enables findingthe MEVC for open circuit condition

MEVC =1

AH1�

A

ErdA , �3�

where

Er = −pd31

�p�33�

0

�pT�d� .

Next we consider the nature of the mode and estimatesof frequency dependence of MEVC. We used the followingmaterial parameters:

PZT:� = 7.7 g/cm3, d31 = − 175 pm/V,

s11 = 15.6 10−12 m2/N, �33/�0 = 1750,

TDF:s33 = 33 10−12 m2/N, q33 = 13.8 10−9 m/A.

The radial displacement waveform in PZT obtained by nu-merical solution of Eq. �3� is shown in Fig. 3. The positionsof maximum in displacement amplitudes in PZT correspondto polar angles of 30°, 90°, and 150°, as shown in the figure.Figure 2 shows the calculated values of MEVC versus fre-quency for comparison to the data. As can be seen, the the-oretical values of resonance frequency and ME coefficientsagree well with the data.

It is also clear from Eq. �3� that the electric field gener-ated in PZT depends on electrode design. Figure 3 shows thepeak MEVC generated at resonance as a function of the �an-gular� length of the electrodes that are on the interior andexterior surfaces of PZT. One anticipates an increase inMEVC with decreasing length of the electrode. Of particularinterest is the fact that using narrow electrodes placed in themiddle of semiring ��→� /2� enables obtaining the highestpossible MEVC of 200 V / �cm Oe�. Alternately, a series ofelectrodes could be strategically placed and connected in se-ries to obtain maximum ME voltage. It should be noted thatthe internal resistance of the sample increases with decrease

FIG. 2. �Color online� Data on �E vs frequency for the semiring structure inFig. 1 for H=850 Oe. The peak value corresponds to frequency of in-planebending vibrations. The inset shows the data around resonance on an ex-panded frequency scale. Theoretical values are shown for comparison.

126101-2 Zhang et al. J. Appl. Phys. 106, 126101 �2009�

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in the electrode area and will make it difficult to satisfy theopen circuit condition, which is assumed to obtain Eq. �3�.

The model discussed here can be used to predict the MEresponse in a full ring of PZT with a TDF insert. Since theangular dependences of strain and stress should be periodicfunctions for a full ring, it is clear from Eq. �3� that theaverage ME voltage induced in the ring should be zero �in-tegral over 0 to 2��. Results of our ME measurements for afull ring of PZT and TDF insert �of identical dimensions asthe semiring� are shown in Fig. 4. The results are for a PZTpoled in the thickness direction and MEVC measured acrossthe thickness, as shown in Fig. 4. The figure shows MEVCversus H at the bending resonance frequency. The measuredME voltages are orders of magnitude smaller than for thesemiring structure. The nonzero ME voltage for the full ringcould be due to inhomogeneous strain-piezoelectric responsein PZT.

In conclusion, experiments on low frequency and reso-nance ME coupling in a semiring of PZT and a Terfenol-Dinsert show evidence for strong ME coupling. The enhancedME coupling is attributed to in-plane bending that occursonly in PZT due to the specific composite structure. Theoret-ical estimates of the mode frequency and MEVCs are in verygood agreement with the data.

This work was supported by grants from the DARPAHUMS program and the National Science Foundation.

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FIG. 3. �Color online� �a� Estimated radial displacement amplitude of bend-ing mode vs polar angle � for the semiring of PZT. �b� Calculated values ofpeak MEVC at resonance as a function of the angular length of the elec-trodes on the inner and outer surfaces of the semiring. The length of theelectrode decreases with increase in �.

FIG. 4. �Color online� Bias field dependence of MEVC at bending reso-nance frequency for a full ring of PZT and TDF inset.

126101-3 Zhang et al. J. Appl. Phys. 106, 126101 �2009�

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