Laminate composite magnetoelectric multiferroics optimized by global derivative-free optimization method

Abstract

The magnetoelectric multiferroics where magnetism and ferroelectricity coexist in one material have recently attracted renewed interest due to its potential applications in novel functional devices. Natural multiferroic single-phase compounds are rare and an alternative approach to obtain a magnetoelectric (ME) effect is through multilayered composites of a ferroelectric and a ferromagnetic material. An applied electric field creates a piezoelectric strain in the ferroelectric, which produces a corresponding strain in the ferromagnetic material and a subsequent change in magnetization. Various efforts to improve the value of ME coupling coefficient α have been made by modifying preparation techniques of the samples, by the proper choice of materials or different structures and by choosing different thickness of the samples. In this study, we have applied numerical optimization for arriving at the solution for maximum ME coupling coefficient α of a laminar ME composite by making use of the anisotropy of the ferroelectric phase. We have used a global derivative-free optimization method based in directional direct search coupled with specific multistart strategies for setting up the optimization problem. The effective ME couping coefficients αij∼ are computed using the asymptotic homogenization method. Optimal composite microstructure with a range of the constituent ferroelectric single-crystal configurations that enhances the overall α is identified. Optimal composite would have the [001]-axis of the ferroelectric phase oriented out-of-plane of the lamina. Yet the elasticity of the composite is found to be anisotropic at the optimal orientations of the ferroelectric phase. Stress-mediated enhancement of the ME coupling is demonstrated using the analysis of the inplane elastic stiffness of the composite.