Present status of theoretical modeling the magnetoelectric effect in magnetostrictive-piezoelectric nanostructures. Part I: Low frequency and electromechanical resonance ranges

Mechanical deformations of a magnetostrictive-piezoelectric bilayer result in the interaction between the magnetic and electric subsystems. This review reports the models for describing the distinctive features of magnetoelectric (ME) interactions in ferrite-piezoelectric nanostructures at low-frequencies and in electromechanical resonance region. Expressions for ME coefficients are obtained using the solution of elastostatic/elastodynamic and electrostatic and magnetostatic equations. The ME voltage coefficients are estimated from known material parameters. The models take into account the clamping effect of substrate, flexural deformations, and the contribution of lattice mismatch between composite phases and substrate to ME coupling. Lattice mismatch effect has been taken into account by using the classical Landau–Ginsburg–Devonshire phenomenological thermodynamic theory. For a nickel ferrite-lead zirconate titanate nanobilayer on SrTiO₃ substrates, the strength of low-frequency ME interactions is shown to be weaker than for thick film bilayers due to the strong clamping effects of the substrate. However, flexural deformations result in the considerably lower rate of change in ME voltage coefficient with substrate thickness compared to the case when neglecting the flexural strains. To avoid the strong clamping effects of the substrate, nanopillars of a magnetostrictive material in a piezoelectric matrix can be used as an alternative. The further methods of increasing the ME coupling in nanostructures are discussed.