Magnetically-induced electromechanical fields in a flexoelectric semiconductor layer between two piezomagnetic dielectric layers

We study magnetically-induced electromechanical fields in a sandwich plate of a flexoelectric semiconductor layer between two piezomagnetic dielectric layers under a transverse magnetic field. A set of two-dimensional equations for the bending of the plate is derived from the three-dimensional macroscopic theory of piezomagnetics and flexoelectric semiconductors. A few solutions from the plate equations are obtained for static and time-harmonic magnetic loadings. Results show that various distributions of mobile charges and electric fields can be created by different magnetic fields, which is the foundation for flexotronics when magnetic fields are involved. In the case of pure bending under a uniform magnetic field, a combination of physical and geometric parameters is identified as a coefficient characterizing the strength of the interaction between the applied magnetic field and the mobile charges. The coefficient assumes a maximum for a particular thickness ratio between the two types of material layers. The frequency dependence of the coupling coefficient in time-harmonic motions is also obtained.