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.
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