Polarization-Dependent Oxygen Diffusion Barriers and Magnetic Anisotropy in Co/HfO₂ Heterostructures

Multiferroic materials, which combine ferroelectric and ferromagnetic components, exhibit strong magnetoelectric coupling, enabling electric field control of magnetic properties. This characteristic is highly desirable for applications in memory and logic devices, driving extensive research in this field. Recent experiments have demonstrated that applying an electric field to a Co/HfO₂ system induces oxygen migration into the Co layer, accompanied by an asymmetric modulation of the magnetic anisotropy energy (MAE). In this study, we employ density functional theory (DFT) calculations to investigate the oxygen diffusion barrier at the Co/HfO₂ interface under different ferroelectric polarization states and analyze the corresponding changes in MAE. Additionally, since structural imperfections naturally form at the interface, we examine how cobalt vacancies modify the diffusion energy barrier. Using these barriers as inputs, we carry out random-walk simulations of oxygen migration to quantitatively assess how the diffusion behavior can differ between interfaces with opposite polarizations. Our findings provide a theoretical framework for understanding electric-field-induced modifications of MAE in Co/HfO₂ systems.