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The current-induced domain wall motion along a ferromagnetic strip with high perpendicular magnetocristalline anisotropy sandwiched in an multilayer stack is theoretically studied, by means of micromagnetic simulations and the one-dimensional model, with emphasis on the roles of the Rashba spin-orbit coupling and the spin Hall effect. The results point out that in the presence of a strong Rashba field the domain wall motion can be either in the direction of the current or opposing to it depending on the amplitude of the spin Hall effect. The predictions are in agreement with the experiments only in a reduced range of positive spin Hall angles under a strong Rashba torque

The influence of the spin-orbit torques on the current-driven domain wall motion