Deficiency of the Bulk Spin Hall Effect Model for Spin-Orbit Torques in Magnetic Insulator/Heavy Metal Heterostructures

Abstract: Electrical currents in a magnetic insulator/heavy metal heterostructure can induce two simultaneous effects, namely, spin Hall magnetoresistance (SMR) on the heavy metal side and spin-orbit torques (SOTs) on the magnetic insulator side. Within the framework of the pure spin current model based on the bulk spin Hall effect (SHE), the ratio of the spin Hall-induced anomalous Hall effect (SH-AHE) to SMR should be equal to the ratio of the field-like torque (FLT) to damping-like torque (DLT). We perform a quantitative study of SMR, SH-AHE, and SOTs in a series of thulium iron garnet/platinum or Tm3Fe5O12/Pt heterostructures with different Tm3Fe5O12 thicknesses, where Tm3Fe5O12 is a ferrimagnetic insulator with perpendicular magnetic anisotropy. We find the ratio between measured effective fields of FLT and DLT is at least 2 times larger than the ratio of the SH-AHE to SMR. In addition, the bulk SHE model grossly underestimates the spin torque efficiency of FLT. Our results reveal deficiencies of the bulk SHE model and also address the importance of interfacial effects such as the Rashba and magnetic proximity effects in magnetic insulator/heavy metal heterostructures.