Homogenization method for microscopic characterization of the composite magnetoelectric multiferroics

Tuning of magnetization or electrical polarization using external fields other than their corresponding conjugate fields (i.e., magnetic field for the former or electric field for the latter response) attracts renewed interest due to its potential for applications. The magnetoelectric effect in multiferroic 1-3 composite composed of alternating magnetic and ferroelectric layers operating in linear regime consequent to external biasing fields is simulated and analysed theoretically. Two-scale homogenization procedure to arrive at the equilibrium overall physical properties of magnetoelectric multiferroic composite is formulated using variational analysis. This procedure is extended to quantify the underlying local (microscopic) electric, magnetic and elastic fields and thereby compute local distribution of stresses and strains, electrical and magnetic potentials, the electric and magnetic fields as well as the equivalent von Mises stresses. The computational model is implemented by modifying the software POSTMAT (material postprocessing). Computed local stress/strain profiles and the von Mises stresses consequent to biasing electrical and magnetic fields provide insightful information related to the magnetostriction and the ensuing electrical and magnetic polarization. Average polarization and magnetization against magnetic and electric fields respectively are computed and found to be in reasonable limits of the experimental results on similar composite systems. The homogenization model covers multiferroics and its composites regardless of crystallographic symmetry (with the caveat of assuming an ideal and semi-coherent interface connecting the constituent phases) and offer computational efficiency besides unveiling the nature of the underlying microscopic field characteristics.