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Neuromorphic computing (NC) is gaining wide acceptance as a potential technology to achieve low-power intelligent devices. To realize NC, researchers investigate various types of synthetic neurons and synaptic devices, such as memristors and spintronic devices. In comparison, spintronics-based neurons and synapses have potentially higher endurance. However, for realizing low-power devices, domain wall (DW) devices that show DW motion at low energies─typically below pJ/bit─are favored. Here, we demonstrate DW motion at current densities as low as 10 6 A/m 2 by engineering the β-W spin-orbit coupling (SOC) material. With our design, we achieve ultralow pinning fields and current density reduction by a factor of 10 4 . The energy required to move the DW by a distance of about 18.6 μm is 0.4 fJ, which translates into the energy consumption of 27 aJ/bit for a bit-length of 1 μm. With a meander DW device configuration, we have established a controlled DW motion for synapse applications and have shown the direction to make ultralow energy spin-based neuromorphic elements.