In Fig. 2 the magnetic signal and piezoelectric voltage are shown versus the excitation frequency when connecting the electrodes directly to the Metglas/P(VDF-TrFE) laminate.
From Fig. 2 we can see the effect of the magnetoelastic resonance in the frequency range of 105 kHz and 120 kHz. The magnetoelastic resonance effect in magnetostrictive films and its applications have been studied and reported earlier [2, 3, 8, 9]. There is a large increase in the magnetic response at about 109 kHz where the magnetoelastic resonance is located, and it drops down to almost zero at 115 kHz where the antiresonance is located and then the magnetic response signal increase again with increasing frequencies. At the magnetoelastic peak resonance frequency of 109 kHz we have the first mode of an elastic standing wave with a node in the middle of the film. This mode gives maximum lateral displacements at the ends of the film as well as the largest magnetic response. At the resonance peak frequency, lateral strain amplitudes in the laminate structure are at maximum, which translates into the P(VDF-TrFE) layer and results in a maximum voltage amplitude from the piezoelectric layer, as we can see in Fig. 2. From the maximum piezoelectric voltage we can determine the magnetoelectric coupling coefficient at resonance using Eq. 1. The non-resonant magnetoelectric coupling can also be determined by using the piezoelectric voltage outside the resonance range in the range of 90 kHz, since the Metglas material have magnetostrictive properties even when the film is not in resonance. We also measured on a P(VDF-TrFE) layer that was unpoled (non-piezoelectric active) and obtained piezoelectric voltages in the range of 1.5 mV peak-to-peak voltage which is the background signal due to induced voltages in electrodes and cables close to the detection zone. The background signal was subtracted from the measured piezoelectric response. From this result we obtain a measured magnetoelectric coupling at resonance of the structure of about 1445 V/(cm⋅Oe) and about 100 V/(cm⋅Oe) at non-resonance (90 kHz). The coupling value at resonance is more than 4 times higher than previously reported values for magnetostrictive and PVDF layers in a laminate structure [2, 4]. Further, from Fig. 2 the piezoelectric voltage peak (the elastic part) is somewhat broader than the magnetoelastic resonance response peak. This is probably due to mechanical losses in the P(VDF-TrFE) and PEDOT:PSS layer. The measured phase for the magnetic response (relative to the applied magnetic field) is about 165 degrees, which is in good agreement with the theoretical phase shift of 170 degrees that returns to zero phase above the resonance. The phase of the piezoelectric response (the elastic part) changes also its phase at the resonance by about 180 degrees, according to theory [12, 13]. This shows that the piezoelectric voltage below and above the resonance is not only a background signal but instead also originates from the magnetoelectric coupling.
The result and measurement setup when using the non-contact capacitive coupling electrode above the PEDOT:PSS layer can be seen in Fig. 3.
In the experiment with non-contact measurements, we were careful that the Au-wire (that was connected to the graphite dot) did not touch the reading electrode above the PEDOT:PSS layer and not build up a close approach to the reading electrode. As can be seen in Fig. 3b even when we have a non-contact reading electrode above the PEDOT:PSS (not in physical contact with the sample), we have a piezoelectric peak voltage of about 28 mV (peak-to-peak). The peak of the piezoelectric voltage is somewhat broader in frequency than compared with the case of direct contacting the PEDOT layer (see Fig. 2), indicating a higher damping of the system. For the non-contact readout case we obtain a magnetoelectric coupling of about 950 V/(cm⋅Oe) at resonance, which is also higher than previously reported values using contact measurements of the sample.
As previously shown in the literature, the magnetoelectric coupling coefficient can be compensated for the high demagnetization fields in the Metglas film when excited with a magnetic field . In this case the internal AC magnetic field amplitude is calculated by considering the demagnetization field in the Metglas film and the determined magnetoelectric coupling coefficient will be an intrinsic value. When using data of measured magnetic properties of the used Metglas film  and demagnetization factors for thin magnetic films  together with the Metglas dimensions, we get a compensation of 0.23, which gives an intrinsic magnetoelectric coupling coefficient of 6200 V/(cm⋅Oe) at resonance for the measurements with physical contact to the laminate sample.
Through LDV (laser Doppler vibrometry) we examined the vibrations in the laminated sample when it is excited by an AC magnetic field at the magnetoelastic resonance frequency of 109 kHz (Fig. 4). We also swept the frequency over the resonance frequency and measured the LDV response. We used exactly the same set up as in the previous magnetic/piezoelectric measurements for applying AC field and DC bias. The measurements were performed with the PEDOT:PSS side facing the LDV. During excitation, the LDV measured 18090 points spread over a rectangular matrix on the laminate sample presented in Fig. 4a and measured 3810 points presented in Fig. 4b and Fig. 4c.
In Fig. 4a there are multiple small vertical displacement amplitudes between 0 and 8 nm (red is 0 and yellow is 8 nm) in a 2D lattice structure resulting from a complex bending mode in the film when the film is excited at the magnetoelastic resonance (109 kHz). Since the vertical displacements shown in Fig. 4a give both positive and negative vertical strains, the resulting piezoelectric voltage from these modes will be zero. The horizontal lateral strains originating from the magnetoelastic resonance cannot be visualized in this LDV analysis since the setup is only sensitive to vertical displacements. The vertical displacement pattern shows that the laminate sample does not bend during excitation, as the vertical displacement does not gradually increase from the middle of the film towards the outer free ends of the film.
The first magnetic resonance mode in the film when clamping the film in the middle is a lateral node in the middle with largest lateral displacements at the ends of the film. Instead, from Fig. 4a, we can see a small vertical displacement pattern in the laminate sample with maximum vertical displacement amplitudes of about 8 nm. This pattern can be due to higher order mechanical surface vibrational modes [15, 16]. Since we get a more or less zero vertical displacement without excitation, see Fig. 4c, it is not a surface roughness.
To get a better view of the longitudinal motion on the laminated sample, a wedge was placed below one side, giving the laminated sample a tilt angle of 2.3ᵒ. In Fig. 4b the vertical displacement pattern becomes clearer and the mode shapes on the surface from higher order surface modes is highly visible as green islands. FE simulations (using COMSOL Multiphysics®) at an excitation frequency equal to the measured magnetoelastic resonance frequency, as presented in Fig. 4d, verify that the magnetic longitudinal mode couples to a higher order of mechanical resonance frequency.
When we swept the frequency of the magnetic AC field we could see a vertical displacement amplitude (from frequency analysis of the LDV signal) and large magnetic response when we entered the resonance frequency range (between 100 kHz and 120 kHz), correlating to the frequency of the magnetic excitation field where we have the piezoelectric response as seen in Fig. 2 and Fig. 3. Thus, no vertical displacements were measured when exciting the Metglas/P(VDF-TrFE) composite at frequencies below or above this resonance frequency range. It is also interesting that we can see the graphite dot even in the background signal from the LDV image, see Fig. 4c.