Spin dynamics under local gauge fields in chiral spin–orbit coupling systems

We present a theoretical description of local spin dynamics in magnetic systems with a chiral spin texture and finite spin–orbit coupling (SOC). Spin precession about the relativistic effective magnetic field in a SOC system gives rise to a non-Abelian SU(2) gauge field reminiscent of the Yang–Mills field. In addition, the adiabatic relaxation of electron spin along the local spin yields an U(1) ⊗ U(1) topological gauge (Berry) field. We derive the corresponding equation of motion i.e. modified Landau–Lifshitz–Gilbert (LLG) equation, for the local spin under the influence of these effects. Focusing on the SU(2) gauge, we obtain the spin torque magnitude, and the amplitude and frequency of spin oscillations in this system. Our theoretical estimates indicate significant spin torque and oscillations in systems with large spin–orbit coupling, which may be utilized in technological applications such as current-induced magnetization-switching and tunable microwave oscillators.

Research highlights► We derive a modified LLG equation in magnetic systems with spin–orbit coupling (SOC). ► Our results are applied to magnetic multilayers, and DMS and magnetic Rashba systems. ► SOC mediated magnetization switching is predicted in rare earth metals (large SOC). ► The magnetization trajectory and frequency can be modulated by applied voltage. ► This facilitates potential application as tunable microwave oscillators.