Accurate estimation of spin-orbit torque in heavy-metal multilayers with account of thermoelectric effects

Heavy metal (HM) multilayers with opposite spin-Hall angle have attracted extensive attentions due to their rich physical properties and controversial reported results. Here, we systematically investigated the spin-orbit torque (SOT) efficiency in $\mathrm{Ta}(1)/{[\mathrm{Pt}({t}_{\mathrm{Pt}})/\mathrm{Ta}(1\ensuremath{-}{t}_{\mathrm{Pt}})]}_{5}/\mathrm{Pt}(1.3)/\mathrm{Co}$ multilayers using harmonic Hall voltage response methods. We observed that the SOT efficiency of Pt/Ta multilayer can be continuously tuned with varying Pt or Ta thickness, and the strong thermoelectric effect in Pt/Ta multilayers causes a large mismatch of low-field and high-field harmonic results. Combined with finite element analysis, we demonstrated the enhanced thermoelectric effect in Pt/Ta multilayers originates from the increased resistivity of HM layers and shunt effect, as well as the change of anomalous Nernst coefficient. Furthermore, the accurate SOTs strength can be obtained by ruling out the thermoelectric effect. Our work not only confirms the importance of thermoelectric effect in electrical transport measurements, but also holds significant implications for the precise determination of SOT strength and the application of SOT devices.