Theory of low-frequency magnetoelectric coupling in magnetostrictive-piezoelectric bilayers

Abstract

A theoretical model is presented for low-frequency magnetoelectric (ME) effects in bilayers of magnetostrictive and piezoelectric phases. A novel approach, the introduction of an interface coupling parameter k, is proposed for the consideration of actual boundary conditions at the interface. An averaging method is used to estimate effective material parameters. Expressions for ME voltage coefficients α′ E = δE/δH, where δE is the induced electric field for an applied ac magnetic field δH, are obtained by solving elastostatic and electrostatic equations. We consider both unclamped and rigidly clamped bilayers and three different field orientations of importance: (i) longitudinal fields (α′ E,L ) in which the poling field E, bias field H and ac fields δE and δH are all parallel to each other and perpendicular to the sample plane; (ii) transverse fields (α′ E,T ) for in-plane H and δH parallel to each other and perpendicular to out-of-plane E and δE, and (iii) in-plane longitudinal fields (α′ E,IL ) for all the fields parallel to each other and to the sample plane. The theory predicts a giant ME coupling for bilayers with cobalt ferrite (CFO), nickel ferrite (NFO), or lanthanum strontium manganite (LSMO) for the magnetostrictive phase and barium titanate (BTO) or lead zirconate titanate (PZT) for the piezoelectric phase. Estimates of α′ E are carried out as a function of the interface coupling k and volume fraction v for the piezoelectric phase. In unclamped samples, α′ E increases with increasing k. The strongest coupling occurs for equal volume of the two phases for transverse and longitudinal cases , but a maximum occurs at v=0.1 for the in-plane longitudinal case. Upon clamping the bilayer, the ME effect is strengthened for the longitudinal case and is weakened for the transverse case. Other important results of the theory are as follows. (i) The strongest ME coupling is expected for the inplane longitudinal fields and the weakest coupling for the (out-of-plane) longitudinal case. (ii) In ferrite based composites, α′ E,T and α′ E,IL are a factor of 2-10 higher than α E,L . (iii) The highest ME voltage coefficients are expected for CFO-PZT and the lowest values are for LSMO-PZT. Results of the present model are compared with available data on volume and static magnetic field dependence of α′ E . We infer, from the comparison, ideal interface conditions in NFO-PZT and poor interface coupling for CFO-PZT and LSMO-PZT.

Giant magnetoelectric effect (under a dc magnetic bias of 2Oe) in laminate composites of FeBSiC alloy ribbons and Pb(Zn1∕3,Nb2∕3)O3–7%PbTiO3 fibers

“…10,11 Recently, 12 we reported that a three-layer laminate with a ͑2-1͒ phase connectivity consisting of high-permeability magnetostrictive FeBSiC alloy layers longitudinally ͑L͒ magnetized and piezoelectric Pb͑Ti, Ti͒O 3 ͑PZT͒ fibers longitudinally ͑L͒ poled had ME voltage coefficients of 22 V / cm Oe at low frequency and of 500 V / cm Oe at resonance. These values are nearly an order of magnitude higher than prior reports for ͑L-L͒ Terfenol-D/PZT laminates, [2][3][4][5][6][7][8][9] which up to that time had the highest known values. Here, we report a long-type ME laminate configuration consisting of Pb͑Zn 1/3 ,Nb 2/3 ͒O 3 -7 % PbTiO 3 ͑PZNPT͒ single crystal fibers laminated between two long FeBSiC alloy ribbon layers, operated in a longitudinally ͑L͒ magnetized and transversely ͑T͒ poled ͑or L-T͒ mode.…”

“…1 Orders of magnitude larger ME coefficients have been reported in two phase composites: in particular, the largest ME coefficients are found in laminated composites of magnetostrictive and piezoelectric layers. [2][3][4][5][6][7][8][9] Large magnetoelectric coefficients offer potential device applications as highly sensitive magnetic field sensors, microwave filters, transformers, and gyrators. 10,11 Recently, 12 we reported that a three-layer laminate with a ͑2-1͒ phase connectivity consisting of high-permeability magnetostrictive FeBSiC alloy layers longitudinally ͑L͒ magnetized and piezoelectric Pb͑Ti, Ti͒O 3 ͑PZT͒ fibers longitudinally ͑L͒ poled had ME voltage coefficients of 22 V / cm Oe at low frequency and of 500 V / cm Oe at resonance.…”

Magnetoelectric effect of mildly conducting magnetostrictive/piezoelectric particulate composites

“…[16][17][18][19] Bichurin and co-workers theoretically studied the frequency dependence of the ME voltage coefficient including the appearance of electromechanical resonances ͑EMRs͒ and its effects on the ME response. 20,21 However, most of the theoretical investigations of magnetoelectric effect are rather focused on layered structures than particulate composites. In addition, none of the suggested models have explicitly taken the effect of conductivity into account, and hence cannot discuss the influence of the constituent's electrical conductivity on the ME effect.…”

NiCo-lead zirconium titanate-NiCo trilayered magnetoelectric composites prepared by electroless deposition

“…Hence, the ME coefficients α E,31 are proportional to piezomagnetic coefficient q ∼ δλ/δH, where λ is the magnetostriction. 26 Therefore, the characteristics of ME voltage coefficient in Fig. 5 Figure 5(b) shows the dependence of ME voltage coefficient α E,31 on the magnetic field frequency f at H dc = 2000 Oe for NiCo/PZT/NiCo trilayers with various Ni/Co atomic ratio.…”