Thin films with perpendicular magnetic anisotropy (PMA) play an essential role in the development of technologies due to their excellent thermal stability and potential application in devices with high density, high stability, and low energy consumption.

We report a current-induced four-state magnetization reversal under zero magnetic field in a wedged Ta/MgO/CoFeB/MgO heterostructure with a perpendicular magnetic anisotropy. Anomalous Hall effect and magneto-optical Kerr effect microscopy measurements were performed to demonstrate that the field-free multi-level reversal is jointly determined by the spin–orbit torque effective field that originates from the lack of the lateral inversion symmetry in the wedged stacking structure and the current-induced Oersted field. Moreover, the creation of robust intermediate Hall resistance states in the multi-state switching strongly depends on the current-induced Joule heating. Our results provide a route for the field-free multi-level state reversal, which is significant for fabricating the non-volatile and energy-efficient multi-level memories or artificial neuron devices.

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