Electron dynamics in slowly varying antiferromagnetic texture

Adiabatic dynamics of conduction electrons in antiferromagnetic (AFM) materials with slowly varying spin texture is developed. Quite different from the ferromagnetic (FM) case, adiabaticity in AFM texture does not imply perfect alignment of conduction electron spins with background profile, instead, it introduces an internal dynamics between degenerate bands. As a result, the orbital motion of conduction electrons becomes spin dependent and is affected by two emergent gauge fields: one of them is the non-Abelian version of what has been discovered in FM systems; the other leads to an anomalous velocity that has no FM counterpart. Two examples with experimental predictions are provided.