Hysteresis and remanence in magnetoelectric ... - APS Link Manager

PHYSICAL REVIEW B 85, 104404 (2012)

Hysteresis and remanence in magnetoelectric effects in functionally graded magnetostrictive-piezoelectric layered composites U. Laletin,1,2 G. Sreenivasulu,1 V. M. Petrov,1,3 T. Garg,1,4 A. R. Kulkarni,4 N. Venkataramani,4 and G. Srinivasan1,* 1 Physics Department, Oakland University, Rochester, Michigan 48309, USA Institute of Technical Acoustics, National Academy of Sciences of Belarus, 13 Ludnikov Avenue, Vitebsk 210023, Belarus 3 Institute of Electronic and Information Systems, Novgorod State University, Veliky Novgorod 173003, Russia 4 Metallurgical Engineering and Materials Science Department, Indian Institute of Technology Bombay, Mumbai 400076, India (Received 31 December 2011; published 9 March 2012) 2

The observation and theory of a large remanent magnetoelectric (ME) coefficient and coercivity in the static field H dependence of the low-frequency ME effects are reported for bilayers of lead zirconate titanate (PZT) and a functionally graded ferromagnetic layer. The grading involves magnetization with the use of nickel zinc ferrite of composition Ni0.7 Zn0.3 Fe2 O4 (NZFO) and pure Ni. In homogeneous bilayers of PZT-Ni or PZT-NZFO, the ME voltage coefficient (MEVC) vs H data do not show any hysteresis or remanence. Upon grading the ferromagnetic layer, significant changes including hysteresis and remanece are observed. In PZT-Ni-NZFO, MEVC vs H data show a positive remnant MEVC and a negative coercive field. When the grading is reversed, in samples of PZT-NZFO-Ni, the remnant MEVC is negative and the coercive field is positive. A theory is proposed for the low-frequency ME effects in the graded composites. According to the model, the grading in the magnetization leads to a built-in magnetic field in the ferromagnetic layer, and this field depends on the sequence of grading and the thickness of the NZFO and Ni layers. As a result, the total torque moment and flexural deformations in the composite and the bias field dependence of ME voltage coefficient becomes strongly hysteretic. Calculated MEVC vs H , remnant MEVC, and coercive field are in good agreement with the data. DOI: 10.1103/PhysRevB.85.104404

PACS number(s): 75.85.+t, 75.50.Gg, 77.84.−s, 75.50.Cc

I. INTRODUCTION

Multiferroic composites of ferromagnetic and ferroelectric phases are of interest for studies on the nature of magnetoelectric (ME) interactions and for useful technologies.1–9 The coupling between the ferroic phases is facilitated by mechanical strain related to piezomagnetic and piezoelectric effects in the individual phases. Since ferromagnets in general are not piezomagnetic, a combination of dc and ac magnetic fields is necessary to achieve a pseudopiezomagnetic effect. In the direct-ME effect, an applied ac magnetic field dH manifests as an electric field dE in the composite, and the strength of ME interaction is defined in terms of the ME voltage coefficient αE = dE/dH = dV /(tdH), where dV is the induced voltage and t is the composite thickness. In the converseME effect, one studies the magnetic response of the sample to an applied electric field. Systems studied so far include ferrites, manganites, transition metals/alloys, or terfenol-D for the ferromagnetic phase and lead zirconate titanate (PZT), lead magnesium niobate-lead titanate (PMN-PT), lead zinc niobatelead titanate (PZN-PT), or Polyvinylidene fluoride (PVDF) for the ferroelectric phase.3–9 Several of these composites show a giant direct- or converse-ME coupling when subjected to excitation fields at low frequencies. When the frequency of the ac field is varied, one observes resonance enhancement of the ME coupling at bending modes or electromechanical resonance (EMR) corresponding to longitudinal or thickness acoustic modes.4 The multiferroic composites are of interest for applications in magnetic field sensors, transducers, and high-frequency devices.3–7 But ferroelectrics-based composites have several disadvantages, such as crystallographic phase transitions, hysteresis losses, and pyroelectric effects. Ferromagnetic-piezoelectric composites have attracted some attention in this regard.10 1098-0121/2012/85(10)/104404(8)

This paper constitutes the observation of unique hysteresis and remanence in the static magnetic field H dependence of ME coefficient in composites with functionally graded ferroic phases. Past studies on graded ferroics have been primarily on order parameters; polarization-graded ferroelectrics show a built-in polarization, spontaneous strain, and enhanced dielectric tunability,11,12 and magnetization-graded ferromagnets show an induced anisotropy or an internal magnetic field.13 The use of graded ferroics in ME composites have been explored in some recent theoretical and experimental works.14–19 Theories predict an enhancement in the strength of ME coupling in a sample with piezomagnetic coefficient q-graded ferromagnetic layer or piezoelectric coefficient dgraded ferroelectric layer.14,15 Several recent studies have reported such an enhancement in the low-frequency and resonance-ME effects in functionally graded composites.16–19 This paper is concerned with the observation and theory of large remanent ME coefficient and coercivity in the static field H dependence of the low-frequency ME effects for bilayers of PZT and a graded ferromagnetic layer. The grading involves magnetization and piezomagnetic coefficient q and is achieved with the use of nickel zinc ferrite of composition Ni0.7 Zn0.3 Fe2 O4 (NZFO) and pure Ni. In homogeneous bilayers of PZT-Ni or PZT-NZFO, the ME voltage coefficient (MEVC) αE vs H data show typical characteristics attributable to variation of q with H and do not show any hysteresis or remanence. Upon grading the ferromagnetic layer by adding a layer of NZFO to PZT-Ni (or Ni to PZT-NZFO), significant changes including a pronounced hysteresis and a remanent MEVC (αE,r ) are observed. In samples of PZT-Ni-NZFO, measured MEVC vs H show a positive αE,r that increases with increase in the ferrite-to-Ni thickness ratio R to a maximum for R = 1 and then decreases at higher R. The coercive field Hc

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corresponding to MEVC = 0 is negative, and it increases with increasing R. When the grading is reversed, i.e. in samples of PZT-NZFO-Ni, both αE,r and Hc show a sign reversal: the remanent MEVC αE,r is negative and Hc is positive. A theory is proposed to account for these observations. The model is based on the assumption that the sample undergoes superposition of axial and bending strain. The ME voltage coefficient is determined by piezoelectric coefficient of PZT and combination of piezomagnetic coefficients of the magnetic phases. According to the model, a hysteresis for MEVC vs H is expected only for graded samples due to a built-in magnetic field. The ME voltage coefficient is estimated using the observed dependence of piezomagnetic coupling coefficients on bias field. Calculated αE,r and Hc are in good agreement with the data. II. EXPERIMENT

Polycrystalline nickel zinc ferrite Ni0.7 Zn0.3 Fe2 O4 (NZFO) and Ni foil (Goodfellow, UK) were used in this study for functional grading of the ferromagnetic layer. Ferrite discs of 10-mm diameter and 5-mm thickness were made by ceramic techniques and sliced into slabs of required thickness for use in the composite. The measured room temperature saturation magnetization are 4π Ms = 5.3 and 6 kG, respectively, for NZFO and Ni. The magnetostriction λ vs H for Ni and NZFO were measured with a strain gauge and a strain indicator on 20 × 10 × 0.25-mm platelets. With the sample plane defined by (1,2) and H parallel to the sample plane and along the sample length (direction 1), the in-plane magnetostriction λ11 and λ12 , parallel and perpendicular to H , respectively, were measured as a function of H . Figure 1 shows data on λ vs H for Ni and NZFO. For Ni, λ11 is negative and its magnitude increases with H over 0–200 Oe and then levels off at 35 ppm for higher H . Magnetostriction λ12 is positive and |λ12 | ≈ 0.5|λ11 |. The in-plane piezomagnetic coefficient q = q11 +q12 = dλ11 /dH + dλ12 /dH for Ni estimated from the data is also shown in Fig. 1(a). The coefficient q is negative for Ni and its magnitude increases initially with increasing H and reaches a maximum for H = 45 Oe. Further increase in H leads to a decrease in the magnitude of q and it becomes zero when λ attains saturation. Similar λ vs H data were obtained for NZFO and the estimated in-plane q( = q11 + q12 ) vs H is shown in Fig. 1(b). For NZFO λ is relatively small, and saturation occurs at a much higher H than for Ni. The maximum q value for NZFO occurs at H = 140 Oe and is a factor of 4 smaller than for Ni. Thus, NZFO [with Ms ∼ 0.88Ms (Ni) and q ∼ 0.25q (Ni)] and Ni layers were used to achieve the desired grading in the order parameters for the magnetic phase of the composites. Samples of PZT (APC-854 obtained from American Piezo Ceramics, PA) were used in our studies. All the layers, PZT, Ni, and NZFO, were discs of 10-mm diameter and thickness of 0.2 mm for PZT, 0.25 mm for Ni, and 0.125–0.625 mm for NZFO. The PZT disc with silver electrodes was initially poled in an electric field by heating to 100 ◦ C and cooled down to room temperature in an electric field of 25 kV/cm. It was then bonded to ferromagnetic layers with 2-μm-thick epoxy. For ME characterization, a 3-terminal sample holder was used. Measurements were made by applying a bias magnetic field

FIG. 1. (Color online) In-plane parallel (λ11 ) and perpendicular (λ12 ) magnetostriction for Ni and nickel zinc ferrite Ni0.7 Zn0.3 Fe2 O4 . The static magnetic field H is applied parallel to the sample plane and along direction 1. The inset shows the H dependence of the in-plane piezomagnetic coefficient q.

H generated by an electromagnet and ac magnetic field dH = 1 Oe at 20 Hz produced by a pair of Helmholtz coils. The magnetic fields were applied parallel to the sample plane, along direction 1. The induced ac electric field dE was determined by measuring the voltage dV across the thickness of PZT. The ME voltage coefficient (MEVC) αE = dE/dH = dV /(tdH) where t is the thickness of PZT, was measured as a function of H . III. RESULTS

First, we measured the ME response in bilayers without grading, PZT-Ni and PZT-NZFO. Measured αE vs H for the frequency of the ac field f = 20 Hz are shown in Fig. 2. For PZT-Ni, αE increases with H to a maximum of 0.31 V/cm Oe at 150 Oe and is followed by a decrease to zero for H > 500 Oe. The variation in αE with H essentially tracks q vs H for Ni. Upon reversal of H direction, αE becomes

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HYSTERESIS AND REMANENCE IN MAGNETOELECTRIC . . .


hysteresis with a remanent MEVC αE,r = 0.22 V/cm Oe and a coercive field Hc = −70 Oe. (iv) The loop is counterclockwise (as is the case for traditional M vs H loops) and it tilts toward the H axis as the thickness of the ferrite layer is increased. (v) Figure 3 indicates an increase in Hc and a decrease in αE,r as R is increased. Similar data for samples with reverse grading, PZT-NZFONi, are shown in Fig. 4. Hysteresis and remanence are present for the graded samples, but with the following departures in the characteristics compared to the data in Fig. 3. (i) The αE vs H loop is clockwise with negative remanent MEVC and a positive Hc . (ii) The peak value of MEVC and the bias field for the peak value are both smaller than for PZT-Ni-NZFO. Figure 5 shows the variation in Hc and αEr with R for both types of grading. Data on Hc in Fig. 5(a) shows a somewhat constant Hc for PZT-NZFO-Ni for all R values, whereas Hc increases with increasing R for PZT-Ni-NZFO. The variation of αEr with R in Fig. 5(b) is essentially identical for both systems except for the difference that αEr is positive for PZTNi-NZFO and is negative when grading is reversed. We discuss next a theory for estimates of remanence MEVC and Hc for comparison with the data in Fig. 5. IV. THEORY

FIG. 2. Magnetoelectric voltage coefficient (MEVC) vs bias field H measured at 20 Hz for bilayers of PZT-Ni and PZT-NZFO for H and ac magnetic field dH parallel to each other and to the sample plane.

negative (an additional phase difference of 180◦ in ME voltage measured with the lock-in amplifier), but its magnitude and H dependence remain the same as for positive H . A similar αE vs H characteristics are evident in Fig. 2 for PZT-NZFO, but the maximum MEVC ∼ 0.24 V/cm Oe for H = 220 Oe. We then added a layer of 0.125–0.625-mm-thick NZFO to PZT-Ni to form the graded samples PZT-Ni-NZFO. The H dependence of αE is shown in Fig. 3 for samples with ferrite-to-Ni thickness ratio R = 0.5–2.5. In Fig. 3(a), for the sample with R = 0.5, significant changes are evident in αE vs H when 0.125-mm-thick NZFO is added to the PZT-Ni bilayer. (i) As H is increased from zero, αE increases to a peak value of 0.42 V/cm Oe for H = 220 Oe and then decreases down to zero for H > 500 Oe. Thus, the maximum in MEVC occurs at progressively increasing H as R is increased. (ii) As H is decreased from 500 Oe, αE remains the same as for increasing H until 100 Oe. (iii) For −100 < H < 100 Oe, the data show

We provide here a model for low-frequency ME coupling in the graded composites. Theoretical model rests on the assumption that the sample undergoes superposition of axial and bending strains under the dc and ac magnetic fields. These strains can be calculated by using the elastostatic equations for axial and flexural deformations and then they can be expressed in terms of stress components with the aid of laws of elasticity. Expressions for magnetic field dependence of ME coefficients are obtained using the solutions of electrostatic, magnetostatic, and elastostatic equations taking into account the flexural deformations in terms of material parameters for components (piezoelectric and piezomagnetic coupling coefficients, elastic constants, etc.). To obtain the expression for the ME voltage coefficient, we substitute the stress components into the open circuit condition. The magnitude of the ME voltage coefficient is determined by piezoelectric coefficient of PZT and combination of piezomagnetic coefficients of magnetic phases and taking into account the built-in magnetic field due to compositional grading of magnetic component. Further improvement of the theoretical model is achieved with due regard for internal magnetic field dependence of piezomagnetic coupling coefficients. A hysteresis for MEVC vs H is obtained since grading gives rise to a built-in magnetic that results nonzero piezomagnetic coefficients of magnetic layers for H = 0 and thus nonzero αE . The coercive force Hc is estimated here and is based on thermodynamic calculation of nucleation field for decreasing branch of the loop. A sample in the (x,y) [or (1,2)] plane with the thickness along the z axis (direction 3) and the bias field H and ac field H1 ( = dH ) along the x direction is assumed. The PZT is assumed to be poled along the z axis and E3 (= dE) is the measured ac electric field across the PZT. The analysis described here is based on the following equations for the strain, electric displacement, and magnetic induction

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FIG. 3. Similar data as in Fig. 2 when a single layer of NZFO is added to the PZT-Ni bilayer to form a graded composite. Results are for samples with ferrite-to-Ni thickness ratio R in the range 0.5–2.5. The arrows indicate the direction of H variation.

of piezoelectric and ferromagnetic phases:

layer to be linear functions of the vertical coordinate zi to take into account the cylindrical bending of the three layers:

Si = psij pTj + p dki pEk ; p Dk = p dki pTi + p εkn pEn ; p

Si =

m1

sij m1Tj +

m1

qki mHk ;

Bk =

m1

qki m1Ti +

m1

μkn mHn ;

Si =

m2

sij m2Tj +

m2

qki mHk ;

Bk =

m2

qki m2Ti +

m2

μkn mHn ,

m1 m1

m2 m2

S1 = pS10 + zp /R1 ;

p

S1 =

m2

(1)

S1 =

m1

S10 + zm1 /R1 ;

m1

S10 + zm2 /R1 ;

m2

(2)

where iS10 are the centroidal strains along the x axis at zi = 0, R1 is the radius of curvature and zi is measured relative to centroidal plane of the i layer. It can be shown that centroidal strains obey the following conditions:

where Si and Tj are strain and stress tensor components, Ek and Dk are the vector components of electric field and electric displacement, Hk and Bk are the vector components of magnetic field and magnetic induction, sij , qki , and dki are compliance, piezomagnetic, and piezoelectric coefficients, εkn is the permittivity matrix and μkn is the permeability matrix. The superscripts p, m1, and m2 correspond to piezoelectric and two piezomagnetic layers, respectively. We assume the symmetry of piezoelectric to be ∞m and the magnetic to be cubic. For finding the low-frequency MEVC, we solve magnetostatic and elastostatic equations in piezomagnetic layers, and elastostatic and electrostatic equations in PZT, taking into account boundary conditions. In this case, the theoretical modeling is similar to our recent treatment for a compositionally graded composite on a substrate.15 To adapt that model to the present case, we assume the longitudinal axial strains of each

S10 −

m2

S10 = h2 /R1 ,

m1

S10 − pS10 = h1 /R1 ,

m1

(3)

where h1 = (m1 t +p t)/2 and h2 = (m1 t+m2 t)/2 are distances between the centroidal planes of piezoelectric and first magnetic layer and between the two magnetic layers, respectively, and p t, m1 t, and m1 t are thicknesses of the three layers. The axial forces in the three layers must add up to zero, and the rotating moments of axial forces in the three layers must be counteracted by resultant bending moments p M 1 , m1M1 , and m2M1 , induced in the piezoelectric and two piezomagnetic layers to preserve force and moment equilibrium, F1 +m2 F1 +p F1 = 0, m1 F1 h1 +m2 F1 (h1 + h2 ) = pM1 + m1M1 + m2M1 , t/2 t/2 where i F1 = −t/2 i T1 dz1 ,iM1 = −t/2 zi i T1 dzi .

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m1

(4) (5)



FIG. 4. MEVC vs H for PZT-NZFO-Ni bilayers for samples with ferrite-to-Ni thickness ratio R in the range 0.5–2.5. The arrows indicate the direction of H variation.

To obtain the expression for ME voltage coefficient, we use the open-circuit condition p t /2 p p d31 T1 E3 =− p p dz; (6) αE31 = − t /2 tH1 p ε33 H1 where E3 (=dE) and H1 (=dH ) are the average electric field induced across the piezoelectric layer and applied ac magnetic

field. Solving Eqs. (4) and (5) for R1 and p S 10 enables one to find the axial stress p T 1 from Eq. (1). Substituting the obtained value of stress into Eq. (6) yields: αE =

p

where c1 = m1 Y

d31 p Y1 (r1 m1 t m1 q11 + r2 m2 t m2 q11 ) ; 2 c1 p K31 + c2 p ε33 m1

t(h2 b3 − b1 ) + m2 Y

m2

(7)

t(b3 h − b1 );

c2 = b1 Y ∗ t; r1 = r2 = b1 = Y∗ = t=

th1 − p Y p th2 ) + m2 Y m2 t(h1 m2 t m2 Y − p Y p th2 )h − b1 Y ∗ t ; Y ∗t m2 m2 Y th(m1 Y m1 th1 + p Y p th) + m1 Y m1 t(h1 h2 m1 t m1 Y + p Y p th2 h) + b1 Y ∗ t −m2 Y Y ∗t m2 m1 m1 p p m1 m1 p D − th( Y th1 + Y th) + Y th2 (h1 m2 t pm2 Y − p Y p th2 ) m1 m2 − ; D − D − ∗ Y t (1 − p K 2 ) m1 m1 Y t + m2 Y m2 t + p Y p t ; t m1 t + m2 t + p t; h = h1 + h2 ; m1

m1

Y

Y

m1

th2 (m2 Y

m2

where m1D, m2D, and pD are the cylindrical stiffnesses and m1 Y , m2Y , and p Y are Youngs modules of layers.

It is clear from Eq. (7) that MEVC is substantially determined by the piezoelectric coefficient of the piezoelectric

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coupling FME , magnetostatic interaction FM , and elastic FE energy of magnetic sublayers: F = FH + FA + FME + FE + FM ,

(8)

where

FH = −μ0 v1 1Ms cos β1 + v2 2Ms cos β2 H0 ,

FA = v1 1K1 (sin2 β1 − sin4 β1 ) + v2 2K1 (sin2 β2 − sin4 β2 ), FME = −v1 1λ11 1Ms2 cos2 β1 m1T10 + sin2 β1 m1T20 − v2 2λ11 2Ms2 cos2 β2 m2T10 + sin2 β2 m2T20 , m1 FE = v1 T10 m1S10 + m1T20 m1S20 m2 + v2 T10 m2S10 + m2T20 m2S20 , FM = −μ0 v1 v2 1Ms 2Ms cos β1 cos β2 + sin β1 sin β2 , where μ0 is the permeability, β1 and β2 are angles between Ms and the x axis and 2Ms and the x axis, v1 and v2 are the volume fractions of magnetic layers, 1K1 and 2K1 are the magnetic crystalline anisotropy constants of layers, 1λ11 and 2 λ11 are the magnetostriction constants of layers. The magnetic field is supposed to be applied along the x axis. Here, m1Ti0 , m2 Ti0 , m1Si 0 , and m2Si 0 are the stress and strain components induced by applied dc magnetic field H0 . Equation (8) implies first finding the equilibrium strain components from boundary mechanical conditions and then substituting them into Eq. (8). However, we neglect magnetoelastic energy in what follows since it is small compared to other terms. Equilibrium magnetization direction can be found by minimizing the free energy. Thus, we have 1

FIG. 5. (Color online) Variation of coercive field Hc and remanent MEVC αEr with R for samples of PZT-Ni-NZFO and PZT-NZFO-Ni. The solid lines are theoretical estimates.

phase and the combination of piezomagnetic coefficients of magnetic phases. The weight coefficients for m1 q11 and m2 q11 depend on sample geometry and elastic properties of composite components. It should be noted that the weight coefficient optimization and using the most suitable magnetic phases is a new path for increasing the ME coupling. Using the stepped magnetic layer leads to a dependence of total torque moment on the magnetic layer sequence. Beyond that point, the torque moment is a function of the bias magnetic field due to piezomagnetic coupling. The MEVC and its variation with H can be determined for q vs H for the magnetic layers. As a result, the bias field dependence of the ME voltage coefficient becomes strongly hysteretic, and it depends on magnetic layer sequence and composition. It should be emphasized that this hysteretic loop can have an unusual trend. Estimate of the coercive force for stepped magnetic layer is based on thermodynamic calculation of the nucleation field for the decreasing branch of the loop. Free energy density includes the Zeeman FH , crystalline anisotropy FA , magnetoelastic

∂F = 0; ∂β1

∂ 2F > 0; ∂β12

∂F = 0; ∂β2

∂ 2F > 0. ∂β22

The locus of critical points is determined by

(9)

∂F ∂β1

2

= 0; ∂∂βF2 = 0

2

1

∂F and ∂β = 0; ∂∂βF2 = 0. 2 2 Estimate of the coercive force for the stepped magnetic layer is based on calculation of the nucleation field Hn for the decreasing branch of the loop. So, we get

Hn = −1Ha − v2 2Ms ;

1

Hn = −2Ha − v1 1Ms ;

2

(10)

where 1Ha = 1K1 /(μ0 1Ms ) and 2Ha = 2K1 /(μ0 2Ms ). Although Eq. (10) is obtained in single domain approximation, it enables one to estimate the external magnetic fields on the assumption that magnetization curves of magnetic layers take the form of approximately rectangular hysteresis loop. Next, we apply the model to the composites considered here. The following material parameters and data on q vs H for the magnetic phases Fig. 1 were used:

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PZT : ε33 /ε0 = 3250; d31 = −270 pm/V; s33 = 17.3 10−12 m2 /N NZFO : s33 = 4.3 10−12 m2 /N; Ni : s33 = 4.9 10−12 m2 /N.



to grading and (ii) the coercive field Hc for M vs H from thermodynamic consideration. Then MEVC vs H profiles were estimated using data on magnetic field dependence of piezomagnetic coefficients in Fig. 1. The shapes of MEVC vs H are different for PZT-NZFO-Ni and PZT-Ni-NZFO due to redistribution of flexural and axial deformations. As a result, the H dependence of MEVC for PZT-NZFO-Ni appears to look like an inverted hysteresis loop.

V. DISCUSSION

FIG. 6. Theoretical MEVC vs H for PZT-Ni-NZFO and PZTNZFO-Ni for R = 1. Data from Figs. 3 and 4 are shown for comparison.

Figure 6 shows calculated MEVC vs H for two representative cases, PZT-Ni-NZFO and PZT-NZFO-Ni for R = 1, and compared with data. For theoretical values of remanent MEVC, we first calculated the built-in field at the sample interface due to grading. The magnitude and direction of this field depends on the thickness of the Ni and NZFO layers. Next, the coercive field Hc was determined. Following this, MEVC vs H was estimated. One notices good agreement between theory and data in Fig. 6. The bias field dependence of MEVC becomes strongly hysteretic due to the grading induced built-in field at the interface and its dependence on thickness of magnetic layers. The loop shapes are different for PZT-NZFO-Ni and PZT-Ni-NZFO due to redistribution of flexural and axial deformations. As a result the H dependence of MEVC for PZT-NZFO-Ni is an inverted hysteresis loop. Estimated remanence MEVC and Hc are shown in Fig. 5. There is good agreement between theory and data for both systems. To summarize, the theoretical estimates in Figs. 5 and 6 are based on first finding (i) the built-in magnetic field due

The low-frequency ME coupling and its bias field dependence for the graded composites discussed here show a zero-bias ME effect in the form of a remanence and a unique hysteresis that could only be attributed to the grading in the order parameter for the ferromagnetic layer. Very few such studies on ME effects in graded composites have been undertaken in the past.16–19 We reported on low-frequency ME effects in oppositely poled PZT (for grading of d) and compositionally graded nickel zinc ferrite (for grading of q). The grading resulted in an ME effect under zero-magnetic bias and an enhancement in ME coefficient under a magnetic bias field.16 A related study of significance is the ME interactions under zero-bias in a bilayer of PZT and a ferromagnetic layer in which the magnetization is graded with the use of Ni and Metglas. At low frequencies, the ME coefficient ranges from 0.3 to 1.6 V/cm Oe and depends on the thickness of Metglas. A similar dependence is also observed for the ME coupling at bending modes. The zero-bias ME coupling is attributed to strain mediated coupling between the transverse magnetization due to magnetization grading at the interface of Ni-Metglas and the in-plane ac magnetic field. Another study of interest for zero-bias ME effect is the work on laminates with a layer of nickel and a layer of Ni-Zn ferrite particles dispersed in a lead-free piezoelectric.17 A remanent MEVC, as in this paper, was observed for the composites. The detailed MEVC vs H data for a graded system is presented here on inversion of hysteresis, remanence, and coercivity in the static field dependence of magnetoelectric coupling in a multiferroic composite. Further studies of importance in the present system are (i) the effects of static electric field E on the nature of MEVC vs H since recent studies report on the control of Hc with E and (ii) the use of an antiferromagnetic layer for exchange biased induced shift in the hysteresis.8,20,21 The results presented here for functionally graded ME composites are of technological importance for room-temperature pico-Tesla magnetic sensors. Several recent studies have reported on ultrasensitive magnetic field sensors based on ME composites.22–24 The sensing is based on the ME response of the composite to an ac magnetic field. The√best sensitivity of 10 pT and magnetic floor noise of 5 pT/ Hz, both at 1 Hz, were reported for a Metglas/PMN-PT fibers/Metglas sensor operating under a dc bias field.24 But a functionally graded ME composite discussed here can operate under zero-bias and eliminate the need for permanent magnets required for dc bias. It is, however, necessary to optimize the remanence MEVC and decrease the noise with proper selection of the ferromagnetic phases for grading.

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PHYSICAL REVIEW B 85, 104404 (2012) VI. CONCLUSIONS

measured when the grading scheme is reversed in samples of PZT-NZFO-Ni. The observed hysteresis and remnant MEVC are attributed to a grading-related magnetization at the NiNZFO interface the results in the ME coupling for zero external dc magnetic bias. Theoretical estimates of the remnant MEVC and Hc and their dependence on R are in good agreement with the data.

Studies on low-frequency magnetoelectric effects have been performed on magnetization-graded ferromagneticpiezoelectric composites. The grading is accomplished with the use of nickel zinc ferrite and pure Ni. Data on the static field H dependence of the low-frequency ME effects in homogeneous bilayers of PZT-Ni or PZT-NZFO show typical characteristics attributable to variation of piezomagnetic coefficient q with H and do not show any hysteresis or remanence. Upon grading the ferromagnetic layer, hysteresis and remanence are observed. For samples of PZT-Ni-NZFO, a positive remnance MEVC and a negative coercive field Hc are measured. Reversal in the signs of remnance MEVC and Hc are

The work at Oakland University was supported by grants from the National Science Foundation, the Defense Advanced Research Project Agency (DARPA) HUMS program, the Office of Naval Research, and the Army Research Office.

*

13

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