Self-biased magnetoelectric coupling mediated by hysteretic dependence of the magnetization in (BaTi⁢O3)(1−????)−CoF⁢e2⁢O4⁢(????) ceramic composites

The application of most multiferroic ceramic composites is severely hindered by their zero or near-zero magnetoelectric response under zero magnetic field. Currently, there has been no in-depth theoretical exploration into the causes of self-biased magnetoelectric coupling effects in these ceramics or how to regulate them. In this study, we report the observation of self-biased magnetoelectric coupling effect in a $(1\ensuremath{-}x)\mathrm{BaTi}{\mathrm{O}}_{3}\ensuremath{-}(x)\mathrm{CoF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}(x=0.1,0.2,0.3,0.4\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}0.5)$ particle composites. P-E and M-H hysteresis loops confirmed the presence of both ferroelectricity and ferromagnetism in the $(1\ensuremath{-}x)\mathrm{BaTi}{\mathrm{O}}_{3}\ensuremath{-}(x)\mathrm{CoF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}$ composites. By measuring the magnetoelectric voltages of the composites, we confirmed the existence of self-biased magnetoelectric coupling effects in the $\mathrm{BaTi}{\mathrm{O}}_{3}$ and $\mathrm{CoF}{\mathrm{e}}_{2}{\mathrm{O}}_{4}$ phases. The highest self-biased magnetoelectric coupling coefficient (1.65 mV/(Oe cm)) was found at $x=0.3$ composite sample. Based on nonlinear magnetoelectric coupling theory, we established a correlation model between magnetic parameters and magnetoelectric coupling coefficients. We demonstrated that the origin of self-biased magnetoelectric coupling lies in the hysteresis dependence of magnetization and proposed that regulating magnetic parameters can effectively control the self-biased magnetoelectric coupling effect. Finite element simulations visually demonstrate displacement variations under different magnetic field conditions, enabling more intuitive observation of changes in internal magnetization and displacement within the material. This lays the foundation for developing high-performance self-biased magnetoelectric coupling devices.