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Spin-orbit-coupling induced torque in ballistic domain walls: Equivalence of charge-pumping and nonequilibrium magnetization formalisms
To study the effect of spin-orbit coupling (SOC) on spin-transfer torque in magnetic materials, we have implemented two theoretical formalisms that can accommodate SOC. Using the ``charge-pumping'' formalism, we find two contributions to the out-of-plane spin-transfer torque parameter $\ensuremath{\beta}$ in ballistic Ni domain walls (DWs). For short DWs, the nonadiabatic …