Parametric Generation of Subharmonics in a Composite Multiferroic Resonator

Parametric generation of subharmonics in a composite multiferroic resonator is observed and investigated. The resonator has the form of a disk and contains two mechanically coupled layers, one of which is amorphous ferromagnet $\mathrm{Fe}\text{\ensuremath{-}}\mathrm{B}\text{\ensuremath{-}}\mathrm{Si}\text{\ensuremath{-}}\mathrm{C}$ and the other piezoelectric lead zirconate titanate. The resonator is placed inside two planar electromagnetic coils with orthogonal axes. A static magnetic field of 0--100 Oe is applied parallel to the plane of the resonator. The resonator is excited in the frequency range f = 9--10 kHz by either a harmonic magnetic field with an amplitude of up to 5 Oe generated by one of the coils, or a harmonic electric field with an amplitude of up to 500 V/cm applied to the piezoelectric layer. When the pump field is above a certain threshold, generation of a subharmonic of half-frequency (f/2) is observed for three different excitation methods. The first two employed either the direct magnetoelectric effect or the converse magnetoelectric effect, while in the third a transformer system is utilized. The subharmonic is generated in a limited range of pump frequencies and its amplitude is a nonlinear function of both the pump-field amplitude and the strength of static magnetic field. A theory of parametric generation of the subharmonic in a multiferroic resonator is developed, taking into account the magnetoacoustic nonlinearity of the ferromagnetic layer of the structure and excitation of acoustic resonances near the pump and subharmonic frequencies. The theory qualitatively describes the main characteristics of the subharmonic generation.