Enhancement of magnetoelectric coupling in functionally graded ferroelectric and ferromagnetic bilayers

Abstract

A model is presented for magnetoelectric (ME) effects in a functionally graded ferroelectric-ferromagnetic bilayer. A linear grading of the piezoelectric coefficient and permittivity in the ferroelectric and a similar grading of piezomagnetic coefficient in the ferromagnet are assumed. The ME coupling at low frequencies and at mechanical resonance due to bending oscillations have been estimated and applied to the specific case of bilayers of nickel zinc ferrite and lead zirconate titanate with the grading axis perpendicular to the sample plane. Both free-standing bilayers and bilayer on a substrate have been considered. The thickness dependence of piezomagnetic and piezoelectric coefficients leads to an additional flexural strain and the theory predicts an enhancement in the strength of ME coupling compared to homogeneous compositions. The enhancement in the case of a free-standing bilayer is on the order of 50% at low frequencies and at electromechanical resonance (EMR). For the case of a bilayer on a substrate, the low-frequency ME coefficient is maximum when the substrate and the bilayer are of equal thickness. The coupling weakens with increasing substrate thickness. With increasing substrate thickness, the ME coefficient at EMR is expected to show an initial rapid decrease, followed by an increase and a broad maximum. The resonance frequency is predicted to show a linear increase with increasing substrate thickness.