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In our numerical study, we identify the best conditions for efficient domain wall motion by spin-orbit torques originating from the Spin Hall effect or Rashba effect. We demonstrate that the effect depends critically on the domain wall configuration, the current injection scheme and the symmetry of the spin-orbit torque. The best identified configuration corresponds to a N'eel wall driven by spin Hall Effect in a narrow strip with perpendicular magnetic anisotropy. In this case, the domain wall velocity can be a factor of 10 larger than that for the conventional current-in-plane spin-transfer torque.

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