Equivalent Circuit Model of Magnetoelectric Composite Nanoparticles

This study presents an analysis of magnetoelectric nanoparticles (MENPs) through the development of equivalent circuits to predict the frequency-dependent magnetoelectric coefficient, with a focus on the widely utilized CoFe₂O₄@BaTiO₃ core–shell configuration. This approach involves –derivation of phenomenological expressions that capture the dynamic behavior of MENPs under varying magnetic and electric fields. By integrating piezoelectric and magnetostrictive constitutive equations, along with consideration of dynamic effects and bio-load conjugation, a magneto-elasto-electric effect equivalent circuit has been constructed. This circuit model not only facilitates the investigation of longitudinal data in cube-shaped MENPs but also offers insights into fundamental biological processes. The versatility of this model is shown through translation to other core–shell nanoparticles, composite structures, and multiferroic nanostructures. This analysis provides quantitative predictions of the magnetoelectric coefficients, enhancing general understanding of MENP characteristics across a broad frequency range. Furthermore, the study highlights the framework for future refinement to incorporate intrinsic composition-specific resonances, such as ferromagnetic and ferroelectric resonances, to further significantly improve the nanoparticles’ performance. Overall, this work lays the groundwork for future technology to intelligently and wirelessly control biological processes using MENPs, thus paving a way for innovative biomedical applications. This quantitative approach may facilitate further interdisciplinary research and contribute to advancement of magnetoelectric materials and their applications.