Integrative Analysis of Magnetic Anisotropy Energy Density in CoZr₂, NiZr₂, and FeZr₂: Empirical Models and Crystallographic Perspectives

The exploration of magnetic anisotropy energy density (MAED) in intermetallic compounds is essential for tailoring advanced magnetic materials with tunable properties for spintronics, magnetic storage, and high-frequency applications. This study presents a comprehensive and comparative analysis of MAED in three transition metal-zirconium compounds—CoZr₂, NiZr₂, and FeZr₂. By integrating crystallographic data with empirical and semi-empirical models, the work investigates how variations in crystal structure, atomic coordination, and spin-orbit coupling influence the anisotropy behavior of each compound. High-resolution structural data were analyzed using density functional theory (DFT) simulations, complemented by experimentally reported crystallographic parameters. The electronic structure, magnetization directionality, and site-specific contributions to anisotropy were evaluated using projected density of states (PDOS) and magnetic force theorem-based calculations. The study further employs analytical models such as Bruno’s relation and second-order perturbation theory to correlate orbital moment anisotropy with MAED. Results indicate that FeZr₂ exhibits higher magnetic anisotropy due to stronger exchange interactions and tetragonal distortion, while NiZr₂ shows near-isotropic magnetic behavior owing to its more symmetric structure and weaker spin-orbit coupling. CoZr₂ demonstrates intermediate characteristics with potential for tunability via strain engineering. This integrative framework not only enhances understanding of intrinsic magnetic anisotropy in these intermetallics but also provides a predictive basis for designing novel magnetic materials through crystallographic control.