Predicting effective magnetoelectric response in magnetic-ferroelectric composites via phase-field modeling

A phase-field model coupled with constitutive equations is formulated to investigate the magnetoelectric cross-coupling in magnetic-ferroelectric composites. The model allows us to obtain equilibrium piezoelectric, piezomagnetic, dielectric, and magnetoelectric properties under a given magnetic or electric field, from the local distributions of polarization, magnetization, and strain in the composites. As an example, effective magnetoelectric coupling coefficient, i.e., magnetic-field-induced voltage output (or changes in polarization), of the CoFe₂O₄-BaTiO₃ composites is numerically calculated. Influences of the phase connectivity and the phase fraction of the composites on the magnetoelectric coupling coefficient are discussed.