Spin-polarized electric current exerts torque on local magnetic spins, resulting in magnetic domain-wall (DW) motion in ferromagnetic nanowires. Such current-driven DW motion opens great opportunities toward next-generation magnetic devices controlled by current instead of magnetic field. However, the nature of the current-driven DW motion--considered qualitatively different from magnetic-field-driven DW motion--remains yet unclear mainly due to the painfully high operation current densities J_OP, which introduce uncontrollable experimental artefacts with serious Joule heating. It is also crucial to reduce J_OP for practical device operation. By use of metallic Pt/Co/Pt nanowires with perpendicular magnetic anisotropy, here we demonstrate DW motion at current densities down to the range of 10^9 A/m^2--two orders smaller than existing reports. Surprisingly the current-driven motion exhibits a scaling behaviour identical to the field-driven motion and thus, belongs to the same universality class despite their qualitative differences. Moreover all DW motions driven by either current or field (or by both) collapse onto a single curve, signalling the unification of the two driving mechanisms. The unified law manifests non-vanishing current efficiency at low current densities down to the practical level, applicable to emerging magnetic nanodevices.
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