A predictive design framework for optimizing CoFe2O4@BaTiO3 magnetoelectric nanoparticles for noninvasive brain stimulation

Abstract

Magnetoelectric nanoparticles (MENs) are emerging as promising candidates for wireless and minimally invasive deep brain stimulation, yet rational design strategies to maximize their magnetoelectric (ME) efficiency remain elusive. Here, we present a comprehensive computational study of a single MEN with spherical core@shell geometry (CoFe2O4@BaTiO3) in cerebrospinal fluid to identify the fundamental principles governing its ME coefficient (alpha ME). Unlike prior approaches treating parameters in isolation, we systematically vary geometry, external fields, and material properties to reveal their complex coupled effects. Specifically, our simulations identify a size-independent optimal core-to-MEN diameter (core-MEN) ratio of 0.869, where the dynamic modulation of magnetostrictive strain and piezoelectric transduction are simultaneously maximized. Furthermore, we demonstrate that the ME response is not maximized by arbitrarily increasing the DC magnetic field (B-DC) or saturation magnetization (M-s), but rather by tuning them to optimal ranges determined by the core's intrinsic magnetic properties. For example, in our reference model (magnetization reversibility of 0.5, domain wall density of 150 kA/m, and M-s of 400 kA/m), alpha(ME) peaks at B-DC similar to 120 mT when MEN diameter was set 30 nm. Moreover, our analysis highlights that increasing magnetic reversibility and saturation magnetostriction offers a direct pathway to further boost the ME response. Collectively, these results establish a predictive design framework that integrates geometry, field protocols, and intrinsic material tuning, providing actionable guidelines for synthesizing high-performance MENs for noninvasive neuromodulation.