Angular characterization of spin-orbit torque and thermoelectric effects

Abstract

Arising from the interplay between charge, spin and orbital of electrons, spin-orbit torque (SOT) has attracted immense interest in the past decade. Despite vast progress, the existing quantification methods of SOT still have their respective restrictions on the magnetic anisotropy, the entanglement between SOT effective fields, and the artifacts from the thermal gradient and the planar Hall effect, etc. Thus, accurately characterizing SOT across diverse samples remains as a critical need. In this work, with the aim of removing the afore-mentioned restrictions, thus enabling the universal SOT quantification, we report the characterization of the sign and amplitude of SOT by angular measurements. We first validate the applicability of our angular characterization in a perpendicularly magnetized Pt/Co-Ni heterostructure by showing excellent agreements to the results of conventional quantification methods. Remarkably, the thermoelectric effects, i.e., the anomalous Nernst effect (ANE) arising from the temperature gradient can be self-consistently disentangled and quantified from the field dependence of the angular characterization. The superiority of this angular characterization has been further demonstrated in a Cu/CoTb/Cu sample with large ANE but negligible SOT, and in a Pt/Co-Ni sample with weak perpendicular magnetic anisotropy (PMA), for which the conventional quantification methods are not applicable and even yield fatal error. By providing a comprehensive and versatile way to characterize SOT and thermoelectric effects in diverse heterostructures, our results pave the important foundation for the spin-orbitronic study as well as the interdisciplinary research of thermal spintronic.