Realistic microscopic models are derived from first‑principles electronic‑structure calculations for the specific groups of electronic states that govern the phenomena of interest. This approach retains the full material specificity of first‑principles methods while providing microscopic insight through model analysis. The methodology has been successfully applied to a broad range of materials and properties, including the mutual control of ferroelectricity and magnetism in multiferroic systems, the manipulation of electric polarization and magnetic textures in compounds with complex skyrmionic structures, and the design of magnetic materials without conventional 3d elements. It further enables the microscopic description of time‑reversal symmetry breaking in unconventional antiferromagnets, as well as the identification of ferromagnetic ferroelectricity driven by orbital ordering.

Explaining the anomalous Hall effect (AHE) in antiferromagnetic materials remains a central challenge in condensed‑matter physics. A symmetry‑based microscopic framework has been developed to clarify why certain centrosymmetric antiferromagnets nevertheless exhibit a finite AHE. In antipolarly distorted lattices, the inversional invariance of the relativistic spin–orbit interaction permits the antiferromagnetic state to be mapped onto an effective ferromagnet within an appropriate local coordinate frame. This mapping naturally accounts for the emergence of conventionally ferromagnetic responses—including the AHE and a net orbital magnetization—even though the spin magnetization vanishes in the global frame.