Elimination of thermoelectric artifacts in the harmonic Hall measurement of spin-orbit torque

The harmonic Hall measurement is widely used to determine the equivalent field of current-induced spin-orbit torque in ferromagnet/normal metal bilayers. We report that this method suffers from various thermoelectric artifacts that have not been considered. We propose and experimentally demonstrate how to eliminate major thermoelectric artifacts using, namely, the four-direction (4-D) methods interchanging current and field polarities, which allow us to determine the magnitudes and angular dependences of spin-orbit torques more accurately than a conventional method. The proposed 4-D method will be useful for searching suitable materials for device applications operated by spin-orbit torques.