## 1 Introduction  
Materials with magnetoelectric (ME) coupling have numerous applications and can be utilized as components of electronic and spintronic devices, e.g., transducers, logic gates, and nonvolatile memory. As far as commercial applications are concerned, possible fields of interest include metrology (AC magnetic field sensors), renewable energy engineering (photovoltaics and energy harvesting), computer science, and medicine (drug delivery methods) [1, 2]. Currently, the main research goal of many scientific groups in the world is to obtain materials with strong, room-temperature ME effect [2, 3, 4]. The ME effect is a coupling between the magnetic and ferroelectric order of a material. In the presence of an external magnetic field, such a material becomes electrically polarized. Conversely, an external electric field results in material magnetization [2, 3]. The linear ME effect is observed when the field intensity and material property change proportionally. The coupling strength (material response to external stimulus) is then denoted by the linear ME coupling coefficient \(\alpha\)[4, 5]. In the simplest terms, the magnetoelectric coupling coefficient can be approximated by the formula:  
\[\alpha=\frac{1}{d}\frac{U_{OUT}}{H_{AC}}, \tag{1}\]  
where \(U_{OUT}\) denotes the voltage generated across the sample due to magnetoelectric coupling, \(H_{AC}\) is the amplitude of the sinusoidal magnetic field, and \(\mathrm{d}\) is the thickness of the sample. Materials exhibiting magnetoelectric coupling can be divided into two groups, i.e., (i) multiferroics in which ME is due to the long-range ordering of magnetic moments and electric dipoles, and (ii) composites where ME is the result of magnetostrictive and piezoelectric properties of the components. The search for single-phase multiferroics with a high magnetoelectric coupling coefficient is still ongoing. However, their number is restricted by symmetry laws imposed by [PERSON]'s principle [5; 6]. Additionally, the coexistence of ferroelectric and magnetic order in one phase is mutually exclusive and depends on a number of phenomena (e.g., lone-pair mechanism, geometric ferroelectricity, inverse Dzyaloshinskii-Moriya interaction) [3; 7; 8]. Ultimately, the key argument against single-phase materials is that the ME effect is generally weak and observable under cryogenic conditions [3; 8]. On the other hand, composite materials can be readily produced by joining two ferroic phases, e.g., piezoelectric and magnetostrictive, which are mechanically coupled [3; 5; 9]. The piezoelectric effect was proven in 1880 by [PERSON] and [PERSON] and is caused by the relocation of electric charges under mechanical deformation of the material (direct effect). Magnetostriction is a physical phenomenon defined as a change in material dimensions in one or many directions under the influence of the magnetic field (direct effect discovered by [PERSON] in 1842). Both phenomena can occur in the opposite way. Specifically, when the voltage is applied to the piezoelectric material, it causes its strain (inverse piezoelectric effect, discovered in 1881 by [PERSON], also named electrostriction). In the case of the inverse magnetostriction effect, i.e., Villari effect or magnetoelastic effect (proven in 1865 by [PERSON]), the change in the magnetization (magnetic susceptibility) of the material occurs as a result of mechanical deformation. The ME coupling in composites is not limited to low temperatures. Furthermore, the effect can be several orders of magnitude larger in comparison to that in single-phase materials. The coupling coefficient \(\alpha\) reaches values from a few to several tens of mVcm\({}^{-1}\) Oe\({}^{-1}\) in single-phase multiferroics [10], while in composites/laminates it can be up to hundreds of Vcm\({}^{-1}\) Oe\({}^{-1}\), especially in resonance state [5; 11]. Regardless of whether the material is a single-phase multiferroic or a piezoelectric-magnetostrictive composite, it is difficult to obtain a proper ME material due to several persistent challenges.