## 1 Introduction  
The direct magnetoelectric (ME) effect is defined as the induced electric polarization of a material in an applied magnetic field. The strain-mediated ME phenomena of importance in layered multiferroic composites are giant low-frequency coupling and resonance enhancement of ME effects that are anticipated for bending and other oscillation modes [1]. Soft (Young's modulus \(Y<10^{9}\) Pa) ME materials are absent in nature and conventional multiferroic layered heterostructures mostly involve rigid (\(Y\)-\(10^{11}\) Pa) constitutive materials, e.g., alloys and ceramics. Soft ME materials are expected to have a number of promising applications in wireless energy harvesting and transfer, non-volatile memories, and electronics [2; 3]. In sensor technology, highly sensitive ME magnetic-field sensors usually operate at the electromechanical resonance frequency, taking advantage of the increased amplitude of mechanical deformation. As the employed materials are rigid, the resonance frequency of a layered multiferroic heterostructure is usually in the range of 1-100 kHz. A soft ME sensor material would allow one to lower the resonance frequency to the range of 1 to 100 Hz, which would be of a particular advantage for biomedical and (vibration) energy harvesting applications because it would better match the frequency range there. To the best of our knowledge, the lowest reported fundamental bending resonance frequency of 27.8 Hz was achieved in ME sensors using the thin-film approach by direct spin coating of polyvinylidene fluoride-trifluoroethylene (PVDF-TrFE) onto a Metglas substrate [4]. A NdFeB magnet/piezoelectric composite cantilever with varying cross sections demonstrated a bending resonance frequency of 29 Hz and a high value for its ME voltage coefficient (\(\approx\)500 V/A) [5]. A low resonance frequency in [5] was realized by employing a NdFeB permanent magnet as a tip mass. Several authors reported ME sensors operating at bending resonance frequency in the 100 Hz range by employing thin-film constituents [6; 7; 8; 9; 10] where the ferromagnetic material was an alloy. ME sensors working at a frequency of \(\approx\)1 Hz were also reported, but they did not operate at resonance frequency [11; 12]. It is also known that if a multiferroic bilayer is either free to vibrate at both ends, or simply supported at both ends or fixed at one end, the enhancement of ME coupling occurs at the lowest frequency for a bilayer that is fixed at one end and free at the other end (i.e., for a cantilever configuration) [13]. Very recently a new, alternative group of ferromagnetic materials came into play --the magnetoactive elastomers (MAEs)--in which micrometer-sized ferromagnetic particles are dispersed in a compliant polymer matrix [14; 15; 16; 17]. MAEs are intrinsically soft (\(Y\approx\) 3-300 kPa in the absence of a magnetic field) and exhibit extraordinary magnetomechanical effects, such as giant (\(\sim\)10\({}^{-1}\)) magnetostriction [18]. Therefore, it was a logical step to combine an MAE with another well-known piezoelectric polymer (PEP), namely polyvinylidene fluoride (PVDF), to fabricate layered composites with an ME response [19]. Hitherto, MAE-PEP composites were studied only in the transverse electric and transverse magnetic field (T-T) configuration, where both the electric and magnetic fields were perpendicular to the plane of the sample [19; 20]. The direct ME response was observed in pulsed magnetic fields and a quasi-static ME voltage coefficient (\(\alpha_{\text{E33}}\approx\) 50 V/A) was estimated in [20]. Hitherto, the exploration of MAEs in mechanically soft ME multiferroic composites is in the early stages, although the published results are very promising. The purpose of this paper was to report the characterization of laminated multiferroic structures comprising an MAE layer and a PEP multilayer, as described in [20], by the standard method of sinusoidal field excitation [21] for the first time.