Resonant magnetoelectric coupling in trilayers of ferromagnetic alloys and piezoelectric lead zirconate titanate: The influence of bias magnetic field

Abstract

We present the first data and theory for the bias magnetic field dependence of magnetoelectric coupling in the electromechanical resonance (EMR) region for ferromagnetic-piezoelectric heterostructures. Trilayers of Permendur, a $\mathrm{Co}\ensuremath{-}\mathrm{Fe}\ensuremath{-}\mathrm{V}$ alloy, and lead zirconate titanate were studied. Measurements of the magnetoelectric (ME) voltage coefficient ${\ensuremath{\alpha}}_{E}$ indicate a strong ME coupling in the low-frequency range and a giant ME effect due to EMR at $200--300\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$ for radial modes and at $\ensuremath{\sim}2.7\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ for thickness modes. Data were obtained for the bias field $H$ dependence of two key parameters, the EMR frequency ${f}_{r}$ and the ME coefficient ${\ensuremath{\alpha}}_{E,R}$ at resonance. With increasing $H$, an increase in ${f}_{r}$ and a rapid rise and fall in ${\ensuremath{\alpha}}_{E,R}$ are measured. In our model we consider two mechanisms for the magnetic field influence on ME interactions: (i) a shift in the EMR frequency due to changes in compliance coefficients ($\ensuremath{\Delta}E$ effect) and (ii) variation in the piezomagnetic coefficient that manifests as a change in ${\ensuremath{\alpha}}_{E,R}$. Theoretical profiles of ${\ensuremath{\alpha}}_{E}$ vs frequency and estimates of frequency shift based on the $\ensuremath{\Delta}E$ effect are in excellent agreement with the data.