## 3 Results and Discussion  
Table 1 lists the comparison in the parameters of permeability, saturation magnetostriction, piezomagnetic coefficient, and the optimal dc magnetic field between Permendur, Metglas, and Terfenol-D. Here, \(g_{33}^{m}\) is the piezomagnetic constant of the magnetostrictive phase. From Table 1, Permendur, commonly composed of 50% Fe, 49% Co, and 1% V, and Metglas are more suitable for the ME structure than Terfenol-D due to their high permeabilities. Furthermore, compared to Metglas (\(\lambda_{s}=20\) ppm; the optimal \(H_{\textrm{dc}}\) is 6\(\sim\)10 Oe; the maximum detectable \(H_{\textrm{ac}}\) is \(\sim\)0.1 Oe), Permendur alloy possesses a higher saturation magnetostriction (\(\lambda_{s}=100\) ppm), which contributes to a larger \(\alpha_{v}\), and a medium optimal bias magnetic field (\(\sim\)250 Oe), which is beneficial to obtaining a high SNR and a wide \(H_{\textrm{ac}}\) detective range (\(\sim\)2.5 Oe), and has potential for practical applications of ME magnetic sensitive devices [20,21]. Figure 1 shows the ME coefficient ( \(\alpha_{\textrm{E}}\) ) _versus_ the bias dc magnetic field ( \(H_{\textrm{dc}}\) ) for the Permendur/PZT, Metglas/PZT, and Terfenol-D/PZT laminated composites (with the same dimension and structure) at the frequency of \(\sim\)1 kHz, respectively. Here \(\alpha_{\textrm{E}}\) increases initially, reaching the maximum value, and then decreases with the increasing \(H_{\textrm{dc}}\). The \(H_{\textrm{dc}}\) dependence of \(\alpha_{\textrm{E}}\) essentially follows the trend of the \(H_{\textrm{dc}}\) dependence of \(d_{33}^{m}\) of magnetostrictive materials [22]. The maximum ME coefficients for Permendur/PZT, Metglas/PZT, and Terfenol-D/PZT composites are \(\sim\)23.1 V/Oe.cm, \(\sim\)20.2 V/Oe.cm, and \(\sim\)16.5 V/Oe.cm, respectively. The most excellent ME performance is observed in the Permendur/PZT laminates, which agrees well with the predicted results from the new figure of merit (\(FM=\lambda_{s}\cdot\mu_{r}\)). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Title** & \(\lambda_{s}\) **(ppm)** & \(\mu_{r}\) & \(H_{\textrm{dc}}\) **(Oe)** & \(g_{33}^{m}\) **(T\({}^{-1}\))** & \(\sqrt{\mu_{r}\cdot\epsilon_{r}}\) & \(FM=\lambda_{s}\cdot\mu_{r}\) \\ \hline Terfenol-D & 2000 (+) & 10 (-) & 400 (Medium) & \(9.5\times 10^{-4}\) & 110 & \(2\times 10^{4}\) \\ Metglas & 20 (-) & 5000 (+) & 10 (-) & \(7.5\times 10^{-5}\) & 2450 & \(1\times 10^{5}\) \\ Permendur & 100 (+) & 5000 (+) & 250 (Medium) & \(7.8\times 10^{-5}\) & 2450 & \(5\times 10^{5}\) \\ \hline \end{tabular}  
* Here “Medium”, “+” and “–” denote the moderate, favorable, and unfavorable terms for ME laminates, respectively.  
\end{table} 
Table 1: Magnetic and magnetostrictive parameters of Terfenol-D, Metglas, and Permendur alloy *. It should be noted that, unlike the single-phase magnetoelectric materials, the magnetoelectric performance of bi-phase magnetostrictive/piezoelectric laminated magnetoelectric composites is dependent on many factors, such as the interface of the adherence layer, the shape demagnetization, the thickness ratio, and so on. Therefore, it is not easy to prepare many more kinds of samples to test and verify the definition of the new figure of merit. It is necessary to optimize the current definition of the figure of merit in the future on theoretical/thermodynamic means, since only three kinds of samples were used to serve as a firm basis for the new definition of the figure of merit in this work. The dielectric constants, piezoelectric coefficients, and the ferroelectric polarization strength of the piezoelectric phase can greatly affect the ME coefficient. In this work, all of the selected piezoelectric phase materials for the three types of samples are PZT. Since 1950, the commercial piezoelectric market is mainly dominated by PZT ceramic, which has a market share of \(>\)90% today. Therefore, the new figure of merit in our work does not contain information about the piezoelectric material behavior.