Theoretical advances in bilayer van der Waals magnetic materials

<sec><p indent="0mm">Two-dimensional (2D) magnetic materials have emerged as promising candidates for next-generation spintronic devices, owing to their distinct characteristics and potential for efficient low-power information processing. Since the successful exfoliation of graphene, extensive efforts have focused on realizing intrinsic magnetism in 2D materials. The experimental breakthrough occurred in 2017 with the discovery of intrinsic magnetism in monolayer CrI₃ and bilayer Cr₂Ge₂Te₆, leading to the synthesis of diverse 2D van der Waals (vdW) magnetic materials. These materials consist of atomically thin layers stacked together by weak vdW interactions. The weak interlayer coupling enables precise control over the relative crystal alignment between layers, resulting in diverse stacking configurations. Recent advances in synthesis methods and polymer-assisted transfer techniques have made on-demand stacking of vdW layers feasible, revealing novel physical phenomena such as stacking-dependent magnetic ordering and non-collinear spin textures in moiré superlattices. Moreover, sliding ferroelectricity, arising from polar stacking of nonpolar monolayers, provides alternative pathways for realizing magnetoelectric coupling, leading to novel correlated physics and device applications. These discoveries demonstrate that stacking order significantly influences the charge and spin redistribution between adjacent layers, thus affecting the topological properties, electronic correlations, and spin behaviors. Recent studies have focused on modulating the stacking order of 2D vdW magnetic materials, particularly through the manipulation of structural degrees of freedom such as interlayer sliding and twisting. These tunable variables provide a comprehensive platform for exploring and engineering novel quantum states in bilayer magnetic systems. </sec><sec> First-principles calculations based on fundamental quantum mechanical laws play a crucial role in materials simulation, particularly in predicting stacking configurations of bilayer magnetic materials through interlayer coupling analysis. The emergence of data-driven paradigms has transformed materials science research through the integration of high-throughput calculations and deep learning methods. High-throughput computational materials design enables efficient generation and analysis of extensive materials databases, overcoming traditional computational limitations. Simultaneously, advances in deep learning have enabled artificial neural networks to efficiently process large-scale datasets and establish structure-property relationships without requiring first-principles calculations. This approach, integrating first-principles calculations, high-throughput computation, and deep learning, significantly accelerates the discovery of novel bilayer magnetic materials with desired properties. </sec><sec> In this review, we first introduce the intriguing physical phenomena observed in bilayer vdW magnetic materials controlled through interlayer sliding and twisting, including stacking-dependent magnetism, magnetoelectric coupling, and the emergence of noncollinear spins in moiré superlattices. We then present recent progress in high-throughput computational design and deep learning applied to bilayer magnetic materials. Through these studies, we systematically describe the fundamental mechanisms of interlayer exchange coupling, stacking order modulated electronic and magnetic properties, and data-driven research in magnetic materials. Finally, we provide insights into future directions for material design and artificial intelligence-enabled research in 2D magnetic materials. </sec>