Challenges and Strategies for Firsts-Principle Simulations of Two-Dimensional Magnetic Phenomena

The discovery of intrinsic magnetism in two-dimensional (2D) materials has opened new frontiers in material science and technology. This review offers a detailed guide to modeling 2D magnetic materials using Density Functional Theory (DFT), focusing on both fundamental concepts and practical methodologies. Starting with the principles of magnetism, it examines the unique challenges of 2D systems, including the effects of anisotropy in stabilizing magnetic order, the limitations imposed by the Mermin-Wagner theorem, and the critical role of exchange interactions. The review introduces DFT basics, highlighting approaches to address electron delocalization through methods like DFT+$U$ and hybrid functionals, and emphasizes the importance of incorporating Van der Waals corrections for layered systems. Strategies for determining ground-state spin configurations for both collinear and non-collinear arrangements, are discussed, alongside advanced techniques like spin-constrained DFT and the Generalized Bloch Theorem for spin-spiral states. Methods for extracting magnetic exchange parameters and estimating critical temperatures from first-principles calculations are comprehensively covered. Practical insights are provided for applying these techniques to explore material databases and identify 2D magnets with promising properties for room-temperature applications. This review serves as a resource for theoretical and computational studies of 2D magnetic materials.