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

TL;DR

This paper critically examines the formulas used to extract current-induced spin-orbit torques from harmonic Hall voltage measurements, clarifying discrepancies and providing the correct fitting formula.

Contribution

It explicitly derives the relations to resolve the factor of two discrepancy and discusses how to determine the sign of the field-like torque accurately.

Findings

Identifies the origin of the factor of two discrepancy.

Provides the correct formula for fitting harmonic Hall signals.

Discusses the sign determination of field-like torque.

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.