Magnetoelectric Multiferroic Composites

Magnetoelectric (ME) multiferroics are materials in which ferromagnetism and ferroelectricity occur simultaneously and coupling between the two is enabled. Applied magnetic field H gives rise to an induced polarization P which can be expressed in terms of magnetic field by the expression, P=┙H, where ┙ is the ME-susceptibility tensor. Most of the known single-phase ME materials are known to show a weak ME coupling (Fiebig, 2005; Kita et al., 1988; Wang et al., 2003; Prellier et al., 2005; Cheong et al., 2007). A composite of piezomagnetic and piezoelectric phases is expected to have relatively strong ME coupling. ME interaction in a composite manifests itself as inducing the electrical voltage across the sample in an applied ac magnetic field and arises due to combination of magnetostriction in magnetic phase and piezoelectricity in piezoelectric phase through mechanical coupling between the components (Ryu et al., 2001; Nan et al., 2008; Dong et al., 2003; Cai et al., 2004; Srinivasan et al., 2002). In last few years, strong magneto-elastic and elasto-electric coupling has been achieved through optimization of material properties and proper design of transducer structures. Lead zirconate titanate (PZT)-ferrite and PZT-Terfenol-D are the most studied composites to-date (Dong et al., 2005; Dong et al.,2006b; Zheng et al., 2004a; Zheng et al., 2004b). One of largest ME voltage coefficient of 500 Vcm-1Oe-1 was reported recently for a high permeability magnetostrictive piezofiber laminate (Nan et al., 2005; Liu et al., 2005). These developments have led to magnetoelectric structures that provide high sensitivity over a varying range of frequency and DC bias fields enabling the possibility of practical applications. In this paper, we focus on four broad objectives. First, we discuss detailed mathematical modeling approaches that are used to describe the dynamic behavior of ME coupling in magnetostrictive-piezoelectric multiferroics at low-frequencies and in electromechanical resonance (EMR) region. Expressions for ME coefficients were obtained using the solution of elastostatic/elastodynamic and electrostatic/magnetostatic equations. The ME voltage coefficients were estimated from the known material parameters. The basic methods developed for decreasing the resonance frequencies were analyzed. The second type of resonance phenomena occurs in the magnetic phase of the magnetoelectric composite at much higher frequencies, called as ferromagnetic resonance (FMR). The estimates for electric field induced shift of magnetic resonance line were derived and analyzed for