## 1 Introduction  
The magnetoelectric (ME) effect is a polarization response \(P\) to an external magnetic field \(H\)[1]. In recent years, the magnetostrictive/piezoelectric ME laminates have attracted considerable attention because the composites have better ME properties than single-phase materials owing to their high product effect of the piezoelectric and magnetostrictive effects [2; 3; 4; 5; 6]. Most previous investigations have focused on the Tb\({}_{0.3}\)Dy\({}_{0.7}\)Fei\({}_{1.92}\)/Pb(Zr\({}_{0.52}\)Ti\({}_{0.48}\))O\({}_{3}\) (Terfenol-D/PZT) composites due to their high magnetostriction (\(\lambda_{{}_{\chi}}=2000\) ppm) in Terfenol-D [7; 8; 9]. The selection of appropriate magnetostrictiveand piezoelectric materials is the primary step toward the goal of high ME coupling. On the basis of the expression of the upper bound (\(\sqrt{\mu_{r}\cdot\epsilon_{r}}\), where \(\mu_{r}\) is the relative magnetic permeability and \(\epsilon_{r}\) is the relative dielectric permittivity) given by [PERSON] _et al._ to estimate the ME coupling of a magnetostrictive-piezoelectric composite [10], the low permeability (\(\mu_{r}=10\)) of Terfenol-D may result in few magnetic flux lines concentrated on the Terfenol-D surface, which is unfavorable to the ME effect [11; 12; 13]. Recently, Metglas/PZT composites, with high relative permeability (\(\mu_{r}=5000\)) and the piezomagnetic coefficient (\(d_{33}^{m}=4.71\times 10^{-7}\) Wb/N), have attracted considerable attention and have been reported to possess the most excellent ME properties [14]. The ME electric field coefficient of Metglas/PZT composites (\(\alpha_{{}_{E}}=\partial V\) / (\(t_{p}\cdot\partial H\)), where \(V\), \(t_{P}\), and \(H\) are the induced ME voltage output, the thickness of the piezoelectric layer, and the applied external magnetic field, respectively) reaches \(\sim\)220 V/Oe.cm [14; 15; 16; 17], which agrees well with the theoretical prediction in Ref. [10]. It should be noted that, in practical application, the ME voltage coefficient (\(\alpha_{{}_{V}}=\partial V\) / \(\partial H\) ) is more important in the estimate for the properties of ME materials than \(\alpha_{{}_{E}}\) because the ME output voltage can be easily and directly measured. The production of Metglas materials usually uses melt spinning to give the high cooling rates required to avoid crystallization during quenching (\(10^{5}\)-\(10^{6}\) K/s), and the alloy takes the form of a ribbon that is typically 10\(\sim\)100 \(\upmu\)m thick [18], which makes it difficult to fabricate Metglas with thicker sizes. The optimized thickness ratio for fabricating high performance piezoelectric/magnetostrictive ME composites is approximately 1:1. Thus, the thickness of the piezoelectric layer in the Metglas/PZT composites is generally limited to decades of micrometer, leading to a low \(\alpha_{{}_{V}}\). Despite possessing high \(\alpha_{{}_{E}}\), the Metglas/PZT composites are difficult to use in practical devices due to their low \(\alpha_{{}_{V}}\). Furthermore, the saturation magnetostriction of Metglas is so low (\(\lambda_{{}_{s}}=20\) ppm) that it limits the strain of the piezoelectric layer to 0.002%, which is also unfavorable to the \(\alpha_{{}_{V}}\). On the other hand, the optimal dc bias magnetic field (\(H_{\mathrm{dc}}\)) for Metglas is only about 6\(\sim\)10 Oe (about 10 times of the Earth's magnetic field), which leads to a low signal/noise ratio (SNR) and a narrow ac magnetic field (\(H_{\mathrm{ac}}\) ) detective range with a maximum detectable magnetic field \(H_{\mathrm{ac}}\) of \(\sim\)0.1 Oe (the maximum detectable \(H_{\mathrm{ac}}\) should be lower than the percentage of \(H_{\mathrm{dc}}\)) [14; 15; 16; 17; 18; 19]. Thus, it is crucial to define a figure of merit to characterize the magnetic performance of a piezoelectric-magnetostrictive composite with high ME coupling. Here, a figure of merit (\(FM=\lambda_{{}_{s}}\cdot\mu_{r}\), dimensionless) for the selection of magnetostrictive materials for a large ME coefficient was suggested.