(577h) Intelligent Design of Substituted Ferrite Materials for Magnetically Modulated Energy Delivery Applications: Density Functional Theory and Machine Learning Study

We use computational methods to drive the design of substituted ferrites. Substituted ferrites are magnetic materials based off of the bulk structure of magnetite, i.e., Fe₃O₄ (Figure 1a). In this structure, two of the Fe ions are octahedrally coordinated with formal charges of +2 or +3, and one is tetrahedrally coordinated with a formal charge of +3 (Figure 1b). Substituted ferrites have the formula M_xFe_(3-x)O₄,where M is the substituent and can be Mn, Co, Ni, Cu, or Zn. Capitalizing on their strong and tunable magnetic properties (e.g., magnetic saturation and magnetic anisotropy), substituted ferrites can be used for energy delivery when placed in a magnetic field. For biomedical applications, a goal is to optimize the magnetic saturation and anisotropy so that energy can be delivered (e.g., to cancer cells) effectively and safely. Recent literature suggests that the magnetic properties of substituted ferrites can be tuned via their compositions. In this work, we use a combination of Density Functional Theory (DFT) and machine learning (ML) to learn the relationship between composition and magnetic performance of substituted ferrites. Magnetic saturations and anisotropies are calculated for ~1,000 substituted ferrite bulk structures (with x ranging from 0.0625 to 1) using DFT. Substitutions are made at the octahedrally coordinated Fe²⁺ sites, which are highlighted in gray in Figure 1b. DFT values are input to machine-learning (ML) to correlate the magnetic properties to composition. Specifically, an XGBoost algorithm is used to correlate the magnetic performance to tabulated properties of the substituents, such as electronic properties, nuclear properties, atomic sizes, and redox energies. All of these "features" of the substituents are taken from established databases and do not require further calculations. Figure 1c shows a parity plot comparing the magnetic saturation as computed with DFT and predicted with our ML model, and Figure 1d is a radar chart illustrating features selected with the Recursive Feature Elimination with Cross-Validation (RFECV) algorithm that have the strongest influence on the magnetic saturation. The developed ML model enables the screening of vast chemical spaces with surrogate ML models, which can be used to identify design rules and guide materials selection for substituted ferrites.