Spin–Gauge-Field Duality and Its Influence on the Magnetic Moment: A Yang–Mills-Based Theoretical Framework

This theoretical study develops a unified framework for investigating the influenceof the duality between spin fields and gauge fields on the magnetic moment ofquantum particles and magnetic materials. The central hypothesis is that spin shouldnot be treated exclusively as an intrinsic angular-momentum variable, but also as adynamical internal degree of freedom coupled to a non-Abelian gauge connection.Within this approach, local rotations in spin space generate an SU(2) gauge fieldwhose curvature acts as an emergent magnetic field in real and momentum space.The proposed model combines Yang–Mills theory, Pauli and Dirac descriptions,Berry-phase geometry, spin–orbit coupling, effective field theory, and the Landau–Lifshitz–Gilbert equation. The effective magnetic moment is decomposed into conventional Zeeman, anomalous, gauge-curvature, orbital, and topological contributions. The resulting theory predicts that spatially nonuniform spin textures, strong spin–orbit coupling, strain gradients, interfaces, and topological defects can modify the magnetic response of a material even when the external magnetic field remainsunchanged. The framework is applicable to spintronic devices, magnetic multilayers, skyrmionic materials, topological insulators, two-dimensional materials, magneto-mechanical structures, and strain-engineered magnetic composites.