Unraveling spin-orbit torque-induced multistate magnetization switching in Co/Gd ferrimagnetic multilayers for physically unclonable functions.

Ferrimagnetic materials driven by spin-orbit torque (SOT) exhibit a distinctive characteristic of multistate magnetization switching and enable versatile applications. However, the underlying mechanism governing multistate magnetization switching in ferrimagnetic materials remains unelucidated. Here, by studying SOT-induced magnetization switching in Co/Gd ferrimagnetic multilayers with perpendicular magnetic anisotropy (PMA), we demonstrate that the multistate magnetization switching behavior is observed not only in [Co/Gd]n but also in [Co/Gd]L/CoFeB stacks and size-shrinking dot devices. Under the stimuli of numerous pulsed SOT currents, the anomalous Hall resistance of our devices is found to change successively and finally saturate at a specific value, depending on the SOT current density. This behavior suggests a substantial pinning effect that prevents the domain wall from expansion, as verified by magneto-optical Kerr experiments. Because the pinning effect is intrinsic and specific to each Hall-bar device, we further realized analogue physically unclonable functions (PUFs) in a 10 × 10 Hall-bar array and generated multiple PUFs using SOT pulse currents of different amplitudes. Our work unravels the underlying mechanism of SOT-driven multistate switching in ferrimagnets and provides insights into materials engineering to realize high-density memory devices and spintronic analogue PUFs.