Identifying the origin of the nonmonotonic thickness dependence of spin-orbit torque and interfacial Dzyaloshinskii-Moriya interaction in a ferrimagnetic insulator heterostructure

Electrical manipulation of magnetism via spin-orbit torques (SOTs) promises efficient spintronic devices. In systems comprising magnetic insulators and heavy metals, SOTs have started to be investigated only recently, especially in systems with interfacial Dzyaloshinskii-Moriya interaction (iDMI). Here, we quantitatively study the SOT efficiency and iDMI in a series of gadolinium gallium garnet (GGG)/thulium iron garnet (TmIG)/platinum (Pt) heterostructures with varying TmIG and Pt thicknesses. We find that the nonmonotonic SOT efficiency as a function of the magnetic layer thickness is not consistent with the 1/thickness dependence expected from a simple interfacial SOT mechanism. Moreover, considering the insulating nature of TmIG, our results cannot be explained by the SOT mechanism established for metallic magnets where the transverse charge spin current can inject and dephase in the magnetic layers. Rather we can explain this nonmonotonic behavior by a model based on the interfacial spin mixing conductance that is affected by the thickness-dependent exchange splitting energy by determining the phase difference of the reflected spin-up and spin-down electrons at the TmIG/Pt interface. By studying the Pt thickness dependence, we find that the effective DMI for GGG/TmIG/Pt does not depend on the Pt thickness, which indicates that the GGG/TmIG interface is the source of the iDMI in this system. Our work demonstrates that SOT and DMI can originate from two different interfaces, which enables independent optimization of DMI and SOT for advanced chiral spintronics with low damping magnetic insulators.