## 3 Results
Figure 4: Field dependences of the quality factor \(Q\) at resonance frequency \(f_{\rm r1}\) and \(f_{\rm r2}\) obtained for sample S1. Arrows denote the direction of field change. Figure 5: Dependences of the ME voltage \(u\) of sample S1 on the amplitude \(h\) of the AC magnetic field for different resonance frequencies. \(H=H_{\rm mr1}=55.7\) kA/m for \(f_{\rm r1}\) and \(H=H_{\rm mr2}=79.6\) kA/m for \(f_{\rm r2}\). \(R^{2}\) stands for the determination coefficient of the linear regression. Figure 3: Frequency dependences of the ME voltage coefficient \(\alpha\) for sample S1 at different bias magnetic fields for the following curves: 1—\(H\) = 18; 2—31.8; 3—55.7; 4—79.6; 5—175; 6—240 kA/m. The inset shows part of the frequency dependence of the ME voltage coefficient for sample S2 at bias magnetic field \(H=175\) kA/m. The amplitude of the AC magnetic field was \(h=0.22\) kA/m. The field dependence of \(\alpha\) at a resonance frequency, shown in Figures 6b and 7b, demonstrated the existence of the optimum magnetic field (\(H_{\mathrm{m}\mathrm{r}\mathrm{r}\mathrm{1}}\), \(H_{\mathrm{m}\mathrm{r}\mathrm{2}}\)), where the ME voltage coefficient had its maximum. Table 1 summarizes the results of measurements for all samples. Significantly higher ME voltage coefficients were observed for three samples with thinner MAE layers (1.93 mm, 1.05 mm, 0.85 mm). Therefore, composite multiferroic structures with thinner MAE layers seemed to be of primary interest, as was emphasized in the present work. For thicker MAE layers (samples S4, S5), nonlinear effects in higher magnetic fields may have come into play. We observed some specific features in the field behavior of the S4 and S5 samples, which distinguished them from samples with thinner MAE layers. For samples S4 and S5 the ME voltage coefficient at resonance frequency \(f_{\mathrm{r}\mathrm{2}}\) monotonically increased with increasing bias magnetic field \(H\) in the entire measurement range. For the sample S5 the ME voltage coefficient had two local maxima in the field dependence. In Table 1 the corresponding values of \(Q\) and \(\alpha\) are given for the first local maximum with the smaller value of \(H\). This unexpected behavior of samples with thicker MAE layers should be investigated in the future. Figure 6: Field dependences of **(a)** the fundamental bending resonance frequency \(f_{\mathrm{r}\mathrm{1}}\) and **(b)** the corresponding ME voltage coefficient \(\alpha\) at resonance for sample 1. \(h=0.22\) A/m. Arrows denote the direction of field change. Figure 7: Field dependences of the **(a)** second bending resonance frequency \(f_{\mathrm{r}\mathrm{2}}\) and **(b)** the corresponding ME voltage coefficient \(\alpha\) at resonance for sample S1. \(h=0.22\) A/m. Arrows denote the direction of field change. At a particular thickness of MAE layer, the maximum ME voltage coefficient at a fundamental bending resonance frequency was higher than the maximum \(\alpha\) at a second bending resonance frequency (except for a specific case of sample S5). This could be attributed to the more effective resonance enhancement because the typical quality factor of the fundamental bending resonance (\(Q\,\text@frac{\text@frac{\text@frac{\text@math{}}}{\text@math{r}_{1}}}{ \text@math{r}_{1}}\approx 20\)) was roughly two times higher than the typical quality factor of the second bending resonance (\(Q\,\text@frac{\text@frac{\text@math{}}}{\text@math{r}_{2}}\approx 10\)). However, there seemed to be an optimum thickness for the MAE layer, at which the ME coupling at the fundamental resonance frequency was the greatest. At the same time, for the second mode of bending oscillations, an increase in MAE thickness led to a decrease in maximal \(\alpha\) (Figure 8).