The spin Hall effect originating from 5d heavy transition-metal thin films such as Pt, Ta, and W is able to generate efficient spin–orbit torques that can switch adjacent magnetic layers. This mechanism can serve as an alternative to conventional spin-transfer torque for controlling next-generation magnetic memories. Among all 5d transition metals, W in its resistive amorphous phase typically shows the largest spin–orbit torque efficiency ≈0.20–0.50. In contrast, its conductive and crystalline α phase possesses a significantly smaller efficiency of ≈0.03 and no spin–orbit torque switching is realized using α-W thin films as the spin Hall source. Herein, through a comprehensive study of high-quality W/CoFeB/MgO and the reversed MgO/CoFeB/W magnetic heterostructures, it is shown that although amorphous-W has a greater spin–orbit torque efficiency, the spin Hall conductivity of α-W (|σSHα-W| = 3.71 × 105 Ω-1 m−1) is ≈3.5 times larger than that of amorphous W (|σSHamorphous-W| = 1.05 × 105 Ω-1 m−1). Moreover, spin–orbit torque-driven magnetization switching using a MgO/CoFeB/α-W heterostructure is demonstrated. The findings suggest that the conductive and high spin Hall conductivity α-W is a potential candidate for future low-power consumption spin–orbit torque memory applications.