## 1 Introduction  
Today, human beings have entered the era of big data, which is generated not only by industry but also by society. The storage and readout of those big data or information consumes huge quantities of energy and greatly improves the temperature of the storage medium and its surrounding environment, due to the induced magnetic field generated by alternating current in traditional information storage and sensors [1]. The resulting large amount of energy consumption generates a large amount of useless heat energy. Therefore, the demand for saving huge quantities of energy for big data storage and reducing the medium's temperature becomes imperative. However, from this point of view, it has significance for research on low-energy memory and logic devices, in which the field of spintronics focuses on establishing magnetization control without the need for a magnetic field [2], so that the induced magnetic field can no longer be directly generated, thus enabling the device to have the advantages of being faster, smaller, and ultra-low power consuming [3; 4]. Upon this demand, multiferroic materials come into the vision of scientists. As the term suggests, multiferroic materials refer to ones with a variety of ferrous properties, such as ferroelectricity (antiferroelectricity), ferromagnetism (antiferromagnetic, ferrimagnetism), and ferroelasticity [5]. Multiferroic materials have gained so much attention because of their unique magnetoelectric coupling effect. Through magnetoelectric coupling, the magnetic state of the material can be changed under an electric field, thereby reducing the energy consumption, volume, and reaction speed of the device [6; 7; 8; 9; 10]. It could be predicted that complex structures combining multiferroicswith semiconducting and/or spintronics [11; 12; 13; 14] could in the future replace the existing semiconductor-based random access memory and computing technologies [15], leading to a revolution in information storage and computing technology. Recent studies have shown that the dielectric and piezoelectric parameters are greatly improved at room temperature with an increase in grain size. The Curie transition temperature is found to shift slightly towards higher temperatures as the grain increases from 86 nm to 123 nm. The coercive field decreases and the remnant polarization and spontaneous polarization increase as the grain size of BST (Ba\({}_{0.8}\)Sr\({}_{0.2}\)TiO\({}_{3}\)) nanoceramics increases [16; 17]. On the contrary, the diffusion degree of the Curie peak increases with the decrease in grain size [18]. The coherent shift in the magnetic ordering and the dielectric anomalies to high temperature with increasing grain size is related to the suppression of the in-plane lattice parameter [19]. The ME coupling was influenced by the interfacial coupling and the density of the phases. Although it was possible to control the process of interdiffusion, a low density caused by differences in thermal expansion reduced the ME coupling. Consequently, it was concluded that ME coupling could be enhanced by the optimization of the interfacial properties [20; 21]. BiFeO\({}_{3}\) and TbMnO\({}_{3}\), the representative candidates of the revival of multiferroic materials, have always been the most-studied [22; 23]. However, the weak magnetoelectric coupling and low Curie temperature may limit their application prospective. M-type hexagonal ferrite, on the other hand, has been reported to be multiferroic and show a larger room temperature magnetoelectric coupling effect than other compounds [24; 25; 26; 27; 28]. M-type hexagonal ferrite is a traditional ferrimagnetism material and has been widely used in the development of magneto-dielectric devices and fabrication techniques at very low costs [29; 30].