We use temperature-dependent Hall measurements to identify contributions of spin Hall, magnetic proximity, and sublattice effects to the anomalous Hall signal in heavy metal/ferrimagnetic insulator heterostructures with perpendicular magnetic anisotropy. This approach enables detection of both the magnetic proximity effect onset temperature and the magnetization compensation temperature and provides essential information regarding the interfacial exchange coupling. Onset of a magnetic proximity effect yields a local extremum in the temperature-dependent anomalous Hall signal, which occurs at higher temperature as magnetic insulator thickness increases. This magnetic proximity effect onset occurs at much higher temperature in Pt than W. The magnetization compensation point is identified by a sharp anomalous Hall sign change and divergent coercive field. We directly probe the magnetic proximity effect using x-ray magnetic circular dichroism and polarized neutron reflectometry, which reveal an antiferromagnetic coupling between W and the magnetic insulator. Finally, we summarize the exchange-coupling configurations and the anomalous Hall-effect sign of the magnetized heavy metal in various heavy metal/magnetic insulator heterostructures.

Magnetic insulators (MIs) attract tremendous interest for spintronic applications due to low Gilbert damping and the absence of Ohmic loss. Spin-orbit torques (SOTs) on MIs are more intriguing than magnetic metals since SOTs cannot be transferred to MIs through direct injection of electron spins. Understanding of SOTs on MIs remains elusive, especially how SOTs scale with the MI film thickness. Here, we observe the critical role of dimensionality on the SOT efficiency by studying the MI layer thickness-dependent SOT efficiency in tungsten/thulium iron garnet (W/TmIG) bilayers. We show that the TmIG thin film evolves from two-dimensional to three-dimensional magnetic phase transitions as the thickness increases. We report the significant enhancement of the measured SOT efficiency as the TmIG thickness increases, which is attributed to the increase of the magnetic moment density. We demonstrate the current-induced SOT switching in the W/TmIG bilayers with a TmIG thickness up to 15 nm.