Theory of magnetoelectric effects in ferrite piezoelectric nanocomposites

A model is presented for low-frequency magnetoelectric (ME) effects in nanobilayers, nanopillars, and nanowires of nickel ferrite (NFO) and lead zirconate titanate (PZT) on MgO substrates or templates. The clamping effect of the substrate for the bilayer and pillars and of the template for the wires have been considered in determining the ME voltage coefficient. The ME interactions have been found to be the strongest for field orientations corresponding to minimum demagnetizing fields, i.e., in-plane fields for bilayers and axial fields for pillars and wires. It is shown that the coupling strength decreases with increasing substrate clamping. For increasing volume of MgO substrate in a bilayer, (i) the ME coefficient drops exponentially and (ii) the PZT volume required for maximum ME effects increases. For nanopillars of NFO in PZT matrix on MgO, the substrate pinning effects are negligible only when the length of the pillar is much greater than its radius. In the case of NFO-PZT nanowires grown on a MgO nanowire template, the ME coefficient is predicted to decrease from a maximum to approaching zero as the radius of the template layer is increased.