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Implicit in the study of magnetic materials is the concept of spin Hamiltonians, which emerge as the low‐energy theories of correlation‐driven insulators. In order to predict and establish such Hamiltonians for real materials, a variety of first principles ab initio methods have been developed, based on density functional theory and wavefunction methodologies. In this Feature Article, a basic introduction to such methods and the essential concepts of low‐energy Hamiltonians is provided, with a focus on their practical capabilities and limitations. Furthermore, recent efforts toward understanding a variety of complex magnetic systems that present unique challenges from the perspective of ab initio approaches are discussed.

Ab Initio Approaches for Low‐Energy Spin Hamiltonians