Theoretical Model of Electric Field Tunable FMR Frequency of Magnetoelectric Tri-Layered Structure
To study the magnetic-electrical-mechanical coupling mechanism of microwave ME (magnetoelectric) tri-layered structures, we proposed a theoretical model of electric tunable FMR (Ferromagnetic Resonance) frequency shift for bias magnetic field in different directions through the theory of Smith-Beljers and free energy density of ferrite. A deformation produced by the applied electric field called strain could be obtained through the theory of classical laminated plate. This model effectively predicts the stress of laminated structure increases when the piezoelectric coefficient increases, the shift of electric field tunable FMR frequency is more obvious when saturation magnetization and magnetostriction coefficient of ferrite increase. Moreover, it qualitatively explains the experimental phenomena that the directions of FMR frequency shift are opposite when apply the in-plane and out-of-plane magnetic field respectively, and provides a theoretical basis for electric field and magnetic field dual tunable microwave devices.