A Predictive Framework for Discovering New Materials Combining Topology and Programmable Magnetism: An Effective Yang–Mills–Inspired Materials-Design Strategy

The discovery of materials that simultaneously exhibit nontrivial electronictopology and controllable magnetic order is one of the central challenges inquantum materials science. Such systems may support quantum anomalous Hallstates, magnetic Weyl fermions, axion electrodynamics, topological Hall transport,nonreciprocal responses, and low-dissipation spintronic functionality.This work proposes a unified predictive framework in which electronic topologyand magnetism are represented as coupled geometric structures in momentumspace, real space, and internal spin–orbital space. The framework combines densityfunctional theory, magnetic-space-group symmetry, Wannier interpolation, Berryphase calculations, magnetic exchange modeling, machine learning, active learning,and an effective Yang–Mills-inspired gauge formulation.In the proposed theory, electronic wave functions are treated as sections of avector bundle over the Brillouin zone, whereas magnetic order parameters generatean emergent non-Abelian connection. The resulting gauge field modifies the Berrycurvature and therefore affects the Chern number, Weyl-node chirality, anomalousHall conductivity, and topological phase transitions.A dimensionless Topological–Magnetic Compatibility Index is introduced torank candidate materials according to their topological gap, magnetic stability, ordering temperature, anomalous Hall response, chemical stability, and synthesisfeasibility. Several hypotheses are also proposed, including the possibility thatnoncommuting local spin rotations can enhance Berry curvature and stabilizetopological gaps without requiring exceptionally large atomic spin–orbit coupling.