Two Strategies to Measure Spin-Orbit-Torque Efficiency Acting on the Insulating Magnet Li$_{0.5}$Al$_{0.7}$Fe$_{1.8}$O$_4$
For insulating magnets, widely-used electrically-based techniques to measure spin-orbit-torque efficiency can suffer from poor signal-to-noise ratios and unwanted artifacts, while optical measurements based on conventional magneto-optical Kerr effect (MOKE) imaging often lack sufficient sensitivity. Here we analyze two strategies for measuring the spin-torque efficiency acting on an insulating magnet, focusing on the torque from Pt acting on thin films of the low-damping magnet lithium aluminum ferrite (LAFO). First, lateral + longitudinal spin-torque ferromagnetic resonance (ST-FMR) allows separation of the spin-torque signal from artifacts due to spin-pumping and resonant heating. With this technique, we measure a spin-torque efficiency $ξ^\text{ST-FMR}_\text{DL}\sim\ 0.07$, comparable to but a bit less than for Pt acting on metallic ferromagnets. Second, we attempted optical measurements of spin-orbit-torque-induced magnetic deflection using Sagnac interferometry. We find that Sagnac interferometry provides sufficient sensitivity to measure signals from 14.4 nm LAFO thin films, but the inferred torque efficiency is much weaker than the result from lateral + longitudinal ST-FMR. We speculate that there may be another contribution to the Sagnac signal other than current-induced magnetic deflection, perhaps an out-of-plane component of itinerant electron spins. This becomes relevant for insulating magnets in which the magneto-optic coupling coefficient is very weak.