Torque engineering in trilayer spin-hall system

A trilayer system with perpendicularly magnetized metallic (FMM) free-layer, heavy metal (HM) with strong spin-hall effect and ferromagnetic insulating (FMI) substrate has been proposed to significantly enhance the torque acting on FMM. Its magnitude can be engineered by configuring the magnetization of the FMI. The analytical solution has been developed for four stable magnetization states (non-magnetic and magnetization along three Cartesian axes) of FMI to comprehensively appraise the anti-damping torque on FMM and the Gain factor. It is shown that the proposed system has much larger gain and torque compared to a bilayer system (or a trilayer system with non-magnetic substrate). The performance improvement may be extremely large for system with a thin HM. Device optimization is shown to be non-trivial and various constraints have been explained. These results would enable design of more efficient spin-orbit torque memories and logic with faster switching at yet lower current.