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Abstract
Electrical control of magnetization offers an extra degree of freedom in materials possessing both electric and magnetic dipole moments. A stochastic optimization combined with homogenization is applied for the solution for maximum magnetoelectric (ME) coupling coefficient α of a laminar ME composite with the thickness and orientation of ferroelectric phase as design variables. Simulated annealing with a generalized Monte Carlo scheme is used for optimization problem. Optimal microstructure with single and poly-crystalline configurations that enhances the overall α is identified. It is found that juxtaposing a preferentially oriented ferroelectric material with a ferromagnetic ferrite into a composite would result in manifold increase in magnetoelectric coupling. The interface shear strains are found to be richly contributing to the ME coupling. The preferential orientation of the ferroelectric phase in the optimal ME composite laminate is demonstrated using the optimal pole figure analyses.
Highlights
Magnetoelectric (ME) multiferroics have recently drawn increasing interest due to their potential applications in multifunctional devices such as nonvolatile memory elements, nano-electronics, etc.[1,2]
Theoretical characterization of equivalent material properties of complex material systems such as multiferroics is pursued as an alternative to experiments which are hampered by a host of factors affecting the sample such as demagnetization, debonding, microcracks, interdiffusion, depoling etc.[7,8,9,10]
The product property in a composite is defined as an effective property which is not present in either of the constituent phases[13]
Summary
The general homogenization method applied to magnetoelectric composite is based upon assumptions of periodic boundary conditions on the microstructure and the separation of the microstructure scale through asymptotic expansion. This signifies the fact that majority of [001] axes, the spontaneous polarization direction of BTO, are oriented parallel to the y3 direction of the lamina This implies that in order to achieve the enhanced out of plane coupling, one needs to have a texture which favours the alignment of maximum number of grains (or rather its spontaneous polarizations) towards the y3 axis. For the out-of-plane ME voltage coefficient α E33 = α 33/κ 33 at the optimal configuration[8], we get a value of α E33 ≈ 193 V/cmOe for single crystal BTO-ceramic CFO laminate. A recent report[49], presents an approach namely combinatorial substrate epitaxy (CSE) relies on the creation of polycrystalline substrates and provide access to a wide range of materials and numerous orientations in a single pass Studies in this direction would plausibly promote experiments aimed at realizing optimal multiferroic material geometries where the ME coupling is maximized as is manifested in the present study. See Supplementary material for the details on the multiferroic homogenization, convergence analysis for representative volume element and the optimization algorithm
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