Enhanced magnetoelectric response in nanostructures due to flexoelectric and flexomagnetic effects

This paper presents the constitutive modeling of the piezoeffect- (piezoelectric and piezomagnetic effects) and flexoeffect- (flexoelectric and flexomagnetic effects) induced magnetoelectric (ME) coupling in multiferroic nanocomposites. The governing equations and associated boundary conditions involving in both piezoeffect and flexoeffect are solved to evaluate ME response of a nano-structure under extensional-bending coupling vibration. The enhanced ME coupling via flexoeffect has been noted for thin structures with nanoscale thickness. In addition, an obvious ME coupling due to flexoeffect is observed even though the piezoelectric and piezomagnetic effects vanish simultaneously. Particularly, ME coupling in magnetoelectric-like nano-structures is expected to reach 78% of that in a typical ME structure CoFe₂O₄-PZT for ${\mu }_{3113}=3\times {10}^{\text{-}7}\text{C/m}$. The output power density of ME energy can be improved by decreasing the thickness, increasing flexoeffect constant, and using a proper load impedance. The most important is that an appreciable output power density of 18.3 W/m³ is available for magnetic energy harvester composed of dielectric layer without piezoelectricity and magnetic layer without piezomagnetism. Given the significance of the new coupling mechanism based on flexo-coupling, the theory proposed in this paper may be utilized in developing high-performance ME nano-structures without using any conventional piezoelectric and piezomagnetic materials.