Magnetic and magnetoelectric susceptibilities of a ferroelectric/ferromagnetic composite at microwave frequencies

A phenomenological theory of magnetic and magnetoelectric (ME) susceptibilities of ferroelectric/ferromagnetic composites is presented and applied to the special case of layered structures. Expressions have been obtained relating the magnetic and ME susceptibility tensor components of the composite (symmetry point group $3m$ and $4mm)$ to ME coupling constants. The theory predicts a unique resonance in the electric-field dependence of the magnetic susceptibility. It is shown that the ME susceptibility is the product of magnetic susceptibility, composite magnetization, and ME coupling constants. The model is used to obtain the magnetic and ME susceptibilities versus electric-field profiles for three bilayer composites of importance: lithium ferrite (LFO)--lead zirconate titanate (PZT), nickel ferrite (NFO)-PZT, and yttrium iron garnet (YIG)-PZT. Our calculations reveal the largest electric-field effects for NFO-PZT and the weakest effect for YIG-PZT. Three measurement methods for ME susceptibility, resonant ME coupling, electrical dipole transitions, and ME effect at ferromagnetic resonance (FMR) are proposed. As an example, we consider multilayers of LFO-PZT and determine the ME constants from data on electric-field influence on FMR. The ME parameters are then used to calculate the susceptibilities. The results indicate strong high-frequency ME effects in the composite. The theory is useful for measurements of ME susceptibility and for the design and analysis of electrically controlled high-frequency magnetic devices.