## 1 Introduction
Both \(\lambda\) and T\({}_{\text{C}}\) are strongly dependent on the crystal and size properties of the ferrite nanoparticles as well as on the substitution of the divalent ion (Co, Ni, Mn) [24; 25], thus allowing for tight control of the magnetostrictive properties. Unfortunately, they have shown that in order to maximize the ME coupling coefficient in these nanocomposites, a high loading of nanoparticles has to be used (over 40 wt%), which inevitably sacrifices the flexibility of the composite material, introduces a high porosity of the hybrid nanostructure, and also compromises the dielectric and piezoelectric properties of the polymer due to the metallic properties of the magnetic nanoparticles. As a matter of fact, an increase in the conductivity of the composite is observed with an increase of the number of nanoparticles agglomerates at the expense of the piezoelectric properties of the hybrid material. A recent article [30] showed that the dispersion of ultra-small CoFe\({}_{2}\)O\({}_{4}\) nanoparticles (i.e., smaller than 7 nm) using a 1H, 1H, 2H, and 2H-perfluorocytltriethoxysilane (POTS) functionalization, not only ensured the flexibility of ME nanocomposites but also enhanced the interplay between the magnetostrictive phase and the piezoelectric one by allowing for the optimization of an ME coupling coefficient of 34 mV cm\({}^{-1}\) Oe\({}^{-1}\) using a low content of magnetic nanoparticles (i.e., 20 wt%). The authors report that POTS' long fluoric chains together with the small size of the nanoparticles (matching the size of PVDF-TrFE crystals) are beneficial for the polar phase crystallization of the polymer and also for the robustness of the 0-3 connectivity among the two phases and, thus, the strain transfer at their interphase. The dielectric measurements showed a stable dielectric constant at low frequency (between 100 Hz and 10 KHz) with low dielectric loss accompanied by optimized ferroelectric polarization cycles. This study confirmed previously published magneto-capacitive measurements reported for Fe\({}_{3}\)O\({}_{4}\)-PVDF composite films [31], showing the importance of the electrical-insulated coating of Fe\({}_{3}\)O\({}_{4}\) nanoparticles obtained using a very thin silica layer. The dielectric properties were again clearly optimized in this case thanks to the control of the current density leakage. The presence of insulated coated metallic nanoparticles enabled the stabilization of the dielectric loss. This was recently confirmed also in the case of a lower loading of the metallic nano-inclusions inside the polymer film [32]. The authors showed the possibility of optimizing the dielectric properties by using an ultra-small load of well-dispersed nanoparticles (i.e., \(<\)1% in volume). Despite these efforts, it is important to underline that all these results were obtained on mainly thick micrometer films (i.e., 30-40 \(\upmu\)m), annealed for 1 or a few hours at high temperature (\(>\)100 \({}^{\circ}\)C) and often poled during the elaboration process at high electric field in order to maximize the crystalline \(\beta\)-phase content. These treatments are well known not to be compatible with the integration of these hybrid films into standard technology processes. In addition, although there have been a considerable number of works measuring their dielectric, piezoelectric, and magnetoelectric properties that undeniably support the idea of their optimization being directly linked to the dispersion of the magnetic nano-inclusions, currently, there is still an important lack of the characterization of the local electroactive and magnetostrictive properties. Several studies have shown the local piezoelectric properties of PVDF-TrFE copolymer neat films [33] as well as hybrid films based on the artificial mixing of the PVDF and copolymer phase with non-magnetic nano-phases (e.g., CNTs, ZnO, (Pb,Ba)(Zr,Ti)O\({}_{3}\), graphene) [34; 35; 36; 37; 38; 39].