Local spin dynamic arising from the non-perturbative SU(2) gauge field of the spin orbit effect

We use the non-perturbative gauge field approach to study the effects of spin orbit coupling on the dynamic of magnetic moment. We present a general equation of motion (EOM) which unifies i) the spin orbit coupling effect derived from the SU(2) spin gauge field, and ii) the moment chirality effect previously derived from the topological U(1)xU(1) rotation gauge under the adiabatic condition. We present a modified Landau-Liftshitz-Gilbert equation and discuss the implication of the modified EOM in various technological applications, such as current-induced switching and trajectory of magnetic moments in spin-valve multilayers, magnetic memory and diluted magnetic semiconductor.