# Magnetoelectric Composites: Engineering for Tunable Filters and Energy Harvesting Applications
## 3 Results
Generally, for all the compositions, the diameter of semicircles lowered significantly with the increase in measuring temperature, which illustrated a strong temperature dependence of the conductivity mechanism. In our opinion, this effect indicates that the mobility of the space charge became easier, and the accumulated charge carriers in the vicinity of the grain interior had sufficient energy to pass through the ferrite phase, which led to an enhanced conductivity with the reduction in impedance that was also presented in [51; 52]. In correlation to the presented complete temperature range characteristics, the more detailed impedance spectra recorded at the temperature range from 200 to 300 \({}^{\circ}\)C of the P-F multiferroic composites are presented in Figure 6. Similarly, two semicircular arcs are very distinctly visible in the Nyquist plot of high ferrite content samples in low and high frequencies, indicating the presence of two parallel relaxation processes (Figure 6a-c). Although for almost all compositions there is a weaker grain boundary effect reflected in the shape of the smaller semicircle at low frequency, for the P60-F40 sample, the dominant is the grain effect (Figure 6c) [53]. A deviation from the double semicircle form of the P-F composite samples has been recorded with decreasing ferrite content (Figure 6d-f). Figure 5: Complex impedance plots in temperatures range from 40 to 400 \({}^{\circ}\)C for multiferroic composite samples: P20-F80 (**a**), P40-F60 (**b**), P60-F40 (**c**), P80-F20 (**d**), P85-F15 (**e**), and P90-F10 (**f**). In order to calculate the activation energies of these relaxations, the additional charts are constructed and presented in Figure 7 that showed the frequency dependence of the normalized imaginary part of the impedance calculated as a \(Z^{\prime\prime}\) to \(Z^{\prime}{}_{\text{max}}\) ratio in the same temperature range as in Figure 6. The most exciting thing that is visible is the apparent frequency shift to a higher frequency range of the grain boundaries' peaks with an increasing amount of ferrite phase in the investigated P-F composite material. For the sample with only 10% of ferrite content (P90-F10), the frequency range is from 100 Hz to 3 kHz, whereas, for example, for the sample with 40% of ferrite content analogical range is from 1 kHz to 12 kHz. Consequently, we can draw significant conclusions from the application's point of view because we can tune the resonant frequency with composition. Hence, in the case of antennas or band filters, we can fabricate appropriate filters for a specific frequency band through material engineering. Only for the 10, 15, and 20% ferrite content samples (P90-F10, P85-F15, and P80-F20, respectively), single Debye-like peaks are visible, whereas a secondary peak has appeared for a higher ferrite content. From these peaks, the relaxation time can be obtained as the inverse of \(f_{\text{max}}\):  
\[\tau=\frac{1}{2*\pi f_{\text{max}}} \tag{1}\]  
Consequently, from the plots of \(\ln(\tau)\) vs. \(1/T\), that obey the Arrhenius equation, the \(E_{\text{R}}\) value was calculated for the investigated P-F composite materials and listed in Table 2. Considering the obtained \(E_{\text{R}}\) values for these composites, it seems that charge movement involves only released electron conductivity because for oxygen vacancies V\({}_{\text{O}}\) the activation energy for V\({}_{\text{O}}\) is much higher, namely in the range of 0.7-1.1 eV [54]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Composition** & \(E_{\text{R1}}\) **for I Peak** & \(E_{\text{R2}}\) **for II Peak** \\ \hline P20-F80 & \(0.18\pm 0.1\) eV & \(0.17\pm 0.1\) eV \\ P40-F60 & \(0.16\pm 0.1\) eV & \(0.15\pm 0.1\) eV \\ P60-F40 & \(0.18\pm 0.1\) eV & \(0.17\pm 0.1\) eV \\ P80-F20 & \(0.17\pm 0.1\) eV & - \\ P85-F15 & \(0.15\pm 0.1\) eV & - \\ P90-F10 & \(0.16\pm 0.1\) eV & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inverse of the peak frequency (relaxation times) as a function of P-F composition.