Comments on the formula to extract current-induced torques from the harmonic Hall voltage measurements

Abstract

We examine the formulas commonly used to estimate current-induced spin-orbit torques from harmonic Hall voltage measurements. In particular, we focus on the factor of two discrepancy among expressions employed to fit harmonic Hall signals measured under an in-plane rotating magnetic field. By explicitly deriving the relevant relations, we clarify the origin of this discrepancy and present the correct form of the fitting formula. We further discuss the determination of the sign of the field-like torque from harmonic Hall voltage measurements, which depends on the assumed form of the current-induced torques.