## 2 Materials and Methods
### The Lock-In Technique  
Magnetoelectric properties of the samples were investigated with the lock-in technique. The technique, also known as the dynamic method, involves exposing a sample to a DC magnetic field with a superimposed AC magnetic field generated by a pair of Helmholtz coils with the sample inside. The voltage induced across the sample is measured with a lock-in amplifier attuned to the frequency of the AC field. Importantly, the sample should be shielded from electromagnetic interference. The magnetoelectric coupling coefficient \(\alpha\) can then be calculated from Equation (1). It should be noted that the coupling linearity in this type of measurement is an acceptable approximation. In fact, the measured quantity is the pseudo-linear ME coupling coefficient. The relation between an external field (e.g., magnetic field) and material property (e.g., polarization) depends on several factors, such as composite phase (piezomagnetic/magnetostriction coupling coefficient), strain direction, layer thickness ratio, and magnetic field type. The DC bias is usually required; however, it may influence the linearity of the final ME signal due to higher-order coupling effects [4; 20; 21]. The experimental setup is shown in Figure 3.  
The lock-in amplifier is the key component of the setup. The device is useful in detection and tracking of weak, noisy AC signals. The principle of operation is based on the phase-sensitive detection (PSD). In essence, the amplifier continuously compares the input signal with the external reference signal (used to stimulate the experiment). The signals are  
Figure 3: The lock-in technique experimental setup.  
Figure 2: Model of the prepared magnetoelectric composite with three layers of Terfenol-D (sample S2), where: 1—sheet of a piezoelectric patch, 2—magnetostrictive material (black color), 3—a layer of the X60 glue (gray color), 4—signal wiring.  
said to be phase-locked, so that their frequencies match and the phase difference remains constant. Once the AC input signal from the sample is amplified and passes through a specifically tuned band pass filter, it is multiplied by the reference signal. The resultant signal passes through a low-pass filter which removes the remaining AC components. The DC output signal is proportional to the input and its value can be taken from the device's front display.  
The SR830 DSP lock-in amplifier working in the differential mode was utilized in our experiment. All measurements were carried out at room temperature. Two types of measurement were performed in the present study: (i) magnetoelectric voltage depending on AC field frequency and characteristic U\({}_{\text{OUT}}\)(f) in various DC fields, and (ii) the measurements of magnetoelectric voltage versus DC magnetic field, U\({}_{\text{OUT}}\)(H\({}_{\text{DC}}\)), for selected frequencies. The multilayered PZT/Terfenol-D composite samples were placed inside a pair of Helmholtz coils, between the poles of the DC magnet. To generate the required DC magnetic field, two types of magnets were used. An electromagnet with a fixed gap was employed in the low-field region (up to 0.13 T). In the high-field region (0.3-0.5 T), the samples were examined inside a permanent magnet with a variable gap. The samples were oriented with their flat surface perpendicular to the magnetic field lines. The AC magnetic field was monitored with an ammeter and, based on previous coil calibration, 4 Oe was set throughout all experiments. The DC field was measured with a Gaussmeter. Additionally, the reference characteristics on a sheet of piezoelectric patch (reference sample R) were registered for both types of measurement.