## 3 Results and Discussion
The application of the new figure of merit is mainly used to select suitable magnetic-phase material to obtain high ME performance. Compared with Metglas (the optimal \(H_{\text{dc}}\) is 6\(\sim\)10 Oe; the maximum detectable \(H_{\text{ac}}\) is \(\sim\)0.1 Oe), Permendur alloy possesses a medium optimal bias magnetic field (\(\sim\)250 Oe), which is beneficial to obtaining a high SNR and a wide \(H_{\text{ac}}\)  detective range (the maximum detectable \(H_{\text{ac}}\) is \(\sim\)2.5 Oe). Figure 2 plots the induced voltage (\(V_{\text{out}}\) ) from the Permendur/PZT laminated composite as a function of the ac magnetic field (\(H_{\text{ac}}\)) under various frequencies at the dc bias magnetic field of \(\sim\)250 Oe. It is seen that \(V_{\text{out}}\)  has good linear responses to \(H_{\text{ac}}\)  in the entire \(H_{\text{ac}}\)  range of 0\(\sim\)0.2 Oe under measured frequencies. From the slope of the \(V_{\text{out}}\) - \(H_{\text{ac}}\) plot, the ME coefficient is determined to be \(\sim\)23.5 V/Oe.cm (the thickness of the PZT plate is \(\sim\)0.1 mm). Figure 3 shows the dependence of frequency (\(f\) ) on the ME coefficient for the Permendur/PZT composite at the dc bias magnetic field of \(\sim\)250 Oe. No remarkable frequency dispersion is observed except for the resonance ranges, indicating an excellent frequency stability of ME properties in the  
Figure 1: Magneto-electric (ME) coefficient _versus_ bias magnetic field for the Permendur/PZT, Metglas/PZT, and Terfenol-D/PZT laminated composites (with the same dimension and structure) at a frequency of \(\sim\)1 kHz, respectively. frequency range of 0-150 kHz. The remarkable resonance frequency is \(\sim\)208 kHz, while the largest \(\alpha_{\mbox{\tiny E}}\) peaks at \(\sim\)309 V/Oe.cm. Figure 4 plots the resonance ME coefficient (\(\alpha_{\mbox{\tiny E}}^{{}^{\prime}}\) ) and the corresponding frequency (\(f_{\mbox{\tiny r}}\) ) as functions of the dc bias magnetic field (\(H_{\mbox{\tiny dc}}\)) for Permendur/PZT laminates. Interestingly, \(\alpha_{\mbox{\tiny E}}^{{}^{\prime}}\)  is maximized up to \(\sim\)309 V/Oe.cm at \(H_{\mbox{\tiny dc}}\)  of \(\sim\)250 Oe, where the associated \(f_{\mbox{\tiny r}}\)  is minimized at \(\sim\)207.6 kHz. Physically, the change in both \(\alpha_{\mbox{\tiny E}}^{{}^{\prime}}\)  and \(f_{\mbox{\tiny r}}\) with increasing \(H_{\mbox{\tiny dc}}\) can be explained by the \(H_{\mbox{\tiny dc}}\) -induced motion of the available non-180\({}^{\circ}\) domain walls in the magnetostrictive layer of the laminated composite [23]. As \(H_{\mbox{\tiny dc}}\)  is increased near \(\sim\)250 Oe, the compliance associated with the increased deformation contribution from the non-180\({}^{\circ}\) domain wall motion is maximized, resulting in a maximum in strain (and, hence, \(\alpha_{\mbox{\tiny E}}\)  and \(\alpha_{\mbox{\tiny E}}^{{}^{\prime}}\) ) and a minimum in stiffness (and, hence, \(f_{\mbox{\tiny r}}\) ). Beyond the optimal \(H_{\mbox{\tiny dc}}\)  level, constraining of non-180\({}^{\circ}\) domain wall motion due to interaction with \(H_{\mbox{\tiny dc}}\)  gives rise to a decrease in strain (and, hence, \(\alpha_{\mbox{\tiny E}}\)  and \(\alpha_{\mbox{\tiny E}}^{{}^{\prime}}\) ) and an increase in stiffness (and, hence, \(f_{\mbox{\tiny r}}\) ). Figure 3: Dependence of frequency on the ME coefficient for the Permendur/PZT laminate at the dc bias magnetic field of \(\sim\)250 Oe. Figure 2: Induced voltage from the Permendur/PZT laminated composite as a function of ac magnetic field under various frequencies at the dc bias magnetic field of \(\sim\)250 Oe.