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Characterization of spin-orbit torque and thermoelectric effects via coherent magnetization rotation

Owing to the interplay between charge, spin, and orbits of electrons, spin-orbit torque (SOT) has attracted considerable interest during the past decade. Despite substantial progress, the existing quantification methods of SOT still have their respective restrictions on magnetic anisotropy, entanglement between SOT effective fields, and lack of corrections for the thermal gradient and planar Hall effect. Thus, it is still essential to accurately characterize SOT across diverse samples. In this study, with the aim of removing the above-mentioned restrictions and enabling universal SOT quantification, we report the characterization of sign and amplitude of SOT by angular measurement, during which magnetization coherently rotates as enforced by an external magnetic field. First, we validate the applicability of our angular measurement method in a perpendicularly magnetized [Co-Ni]/Pt heterostructure by showing excellent agreement with the results of conventional quantification methods. Remarkably, the thermoelectric effect, i.e., the anomalous Nernst effect (ANE) arising from the temperature gradient, can be self-consistently disentangled and quantified by field dependence. The superiority of this angular measurement method has been further demonstrated in a Cu/CoTb/Cu sample with large ANE but negligible SOT, and in a [Co-Ni]/Pt sample with weak perpendicular magnetic anisotropy (PMA), for which the conventional quantification methods face difficulty and even yield a fatal error. By providing a comprehensive and versatile way to characterize SOT and thermoelectric effects in diverse heterostructures, our results provide an important foundation for the spin-orbit study and interdisciplinary research of thermal spintronics.