Current induced magnetization switching in ferrimagnetic insulators with perpendicular magnetic anisotropy: A macrospin modeling

Spin-orbit torque (SOT) assisted magnetization switching by in-plane current in heavy-metal (HM)/ferrimagnetic insulators (FMIs) heterostructure with perpendicular magnetic anisotropy (PMA) has attracted more attention than in HM/FM (ferromagnetic) heterostructure due to it's low magnetic losses and electric insulation. Here, macrospin modeling was employed to study the current-induced magnetization switching in Bi doped Y3Fe5O12 (BiYIG), Tm3Fe5O12 (TmIG) and Eu3Fe5O12 (EuIG) FMIs layers with heavy metal on to explore promising FMIs materials for SOT-based fast and efficient devices. The magnetization switching phase diagram (MSPD) of BiYIG, TmIG, EuIG1 and EuIG2 was calculated. It is found that the distribution of MSPD is strongly dependent both on the PMA field Hk and Gilbert damping parameter & alpha;. The larger the PMA field Hk is, the greater the damping-like effective field HDL (proportional to the current density) and in-plane magnetic field Hx required to realize magnetization switching in HM/FMIs. Furthermore, switching trajectories and diagrams of BiYIG, TmIG, EuIG1 and EuIG2 with variable Hx and HDL were calculated. The results show that compared with spin transfer torque (STT) and SOT-assisted magnetization switching in all-metallic heterostructures, the switching speed in HM/ FMIs system has great advantages. Besides, presence of an external field-like effective field (HFL) can improve switching reliability for low Gilbert damping heterostructure like HM/BiYIG. It is noteworthy that although small damping coefficient is not conducive to the stability of magnetization switching, a huge advantage of smaller damping coefficient is that it can reduce the critical switching current density, which is of great significance to the application of SOT devices. In the end, the SOT-assisted magnetization switching loops of four kinds of FMIs were calculated. This study provides a new perspective for further exploring the current-induced magnetization switching in HM/FMIs system.