Interpretable Graph Neural Networks for Classifying Structure and Magnetism in Delafossite Compounds

Abstract

Delafossites (ABC2, where A and B are metals and C is a chalcogen) are a versatile family of quantum materials and layered oxides/chalcogenides whose properties are highly sensitive to atomic composition and stacking geometry. Their broad chemical tunability makes them an ideal platform for large-scale combinatorial exploration and high-throughput computational screening with desirable quantum properties. In this work, we employ a Concept Whitening Graph Neural Network, a gray-box AI model, to classify delafossite structures by stacking sequence and magnetic states. By aligning learned representations with human-interpretable physical concepts, this gray-box approach enables both accurate prediction and insight into the structural and chemical features driving magnetic behavior. The magnetic-ordering models achieved validation accuracies exceeding 80 percent, with a further slight uptick observed in the model incorporating the largest number of concepts. Concept alignment analysis revealed measurable learning across nine physically meaningful descriptors, with coefficients of determination ranging from approximately 0.6 for the d-shell valence-electron concepts to 0.4-0.5 for the magnetic coupling parameters. Furthermore, we mapped the concept importances onto the material graph representation, elucidating interpretable physical trends and the progression of stable concept-aligned regions across training. These results demonstrate the potential of interpretable graph-based learning to capture the underlying physics of complex materials systems and provide an interpretable framework for accelerating the discovery and understanding of delafossites and related crystalline materials.

Figures (15)

• Figure 1: Crystal structures of delafossites with direct, tilt, and crednerite stacking (top row) and their corresponding graph representations (bottom row), generated using the workflow described in Section \ref{['sec:methods_graph_construction']}. In the graph representations, atoms are shown as nodes (circles color-coded by site type: A, B, or C) and bonds as edges (lines between nodes). Each node contains one self-loop to encode its own features, with additional self-loops representing connections to its periodic images. The bottom row shows histograms of the three atomic triplet angles: (a) $\angle ABC$, (b) $\angle BCA$, and (c) $\angle CAB$, color-coded by stacking type.
• Figure 2: Periodic table heatmaps showing the distribution of elements across the A-, B-, and C-sites in delafossite structures. Rows correspond to stacking types (Direct, Tilt, and Crednerite). Site assignments are indicated by geometric shapes (A-site: lower-left triangle; B-site: upper-right triangle; C-site: full square). Colormap hue (coolwarm) encodes the normalized frequency of occupancy for each site type, with A-, B-, and C-sites normalized separately. Roman numerals above each table denote group numbers. The legend and colorbar provide site definitions and the quantitative scale.
• Figure 3: Periodic table heatmaps showing the normalized frequencies of element occupancy across magnetic orderings and stacking types for 33,520 relaxed delafossite structures. Rows correspond to non-magnetic, ferromagnetic, and antiferromagnetic orderings, while columns correspond to Direct, Tilt, and Crednerite structures. Site occupancies are distinguished by plotting conventions: A-site (lower-left triangle), B-site (upper-right triangle), and C-site (full square). Colors follow the coolwarm colormap, with the gradient representing normalized occupancy frequencies, computed separately for A-, B-, and C-sites.
• Figure 4: Distribution of magnetic orderings across the three stacking types of delafossites. Each pie chart corresponds to a stacking type (direct, tilt, and crednerite), partitioned into fractions of non-magnetic, ferromagnetic, and antiferromagnetic orderings. The relative wedge sizes represent the observed proportions of each ordering within that stacking type.
• Figure 5: Concept-specific node and edge importance visualizations for the FeCuO$_2$ direct stacking type delafossite's graph representation across training epochs. The top panel shows learned importance for two representative concepts: sum_J (first row) and J1 (second row), at epochs 1, 10, and 80. Node colors represent relative node importance with color scales normalized globally (0--1) for comparability across epochs. The rightmost column contains the shared colorbar. The bottom section of the figure shows the evolution of the $R^2$ values with each epoch for the nine physical concepts used in training the CW-GNN for magnetic ordering classification. Higher $R^2$ values indicate stronger alignment between the learned latent features and the corresponding physically meaningful concepts.