Orientation dependence of magnetoelectric coefficient in 1-3–type BaTiO3/CoFe2O4

Highlights: • Dependence of α_E33 in 1-3 BaTiO₃/CoFe₂O₄ on arbitrary orientations is investigated. • ^pc₁₁′, ^pc₁₂′, e₃₁′ for BaTiO₃ and ^mc₁₁′, ^mc₁₂′, q₃₁′ for CoFe₂O₄ are calculated separately. • The optimal orientations for achieving the largest α_E33′ are specified. Orientation dependence of magnetoelectric coefficient α_E33 in 1-3–type BaTiO₃/CoFe₂O₄ composites was calculated in arbitrary directions by three-dimensional coordinate transformation method. The space distributions of ^pc₁₁′, ^pc₁₂′, e₃₁′ for piezoelectric phase and ^mc₁₁′, ^mc₁₂′, q₃₁′ for magnetic phase were obtained independently using relative experimental data and original matrices for 4mm BaTiO₃ and m3m CoFe₂O₄. Elastic stiffness coefficients show little orientation differences, while e₃₁′ and q₃₁′ exhibit high dependence on crystal orientation, with the MAX absolute e₃₁′ = 2.96 C/m² and the MAX q₃₁′ = 556 × 10⁻¹² m/A are found at θ = 0° and θ = 0°, ϕ = 45°, respectively. For space distribution of α_E33′, BaTiO₃||[0 0 1]/CoFe₂O₄||[0 0 1] combination has the maximum value which applies to both 1-3 p/m (1.485 V/A) and 1-3 m/p composites (1.529 V/A). Volume fraction is quite independent of orientations of both piezoelectric and magnetic phases and the volume fraction for magnetic phase f around 0.5 obtains the largest α_E33. The results suggest an approach to significantly enhancing magnetoelectric coefficient of composite multiferroic materials through crystal orientation controls of single crystals and textured ceramics.