Accurate analysis for harmonic Hall voltage measurement for spin-orbit torques

TL;DR

This paper presents a precise analytical method for extracting spin-orbit effective fields from harmonic Hall voltage measurements, accounting for magnetic anisotropy and magnetic field components, validated through macrospin simulations.

Contribution

The paper introduces a detailed analytical approach that improves accuracy in analyzing harmonic Hall voltage data for spin-orbit torque studies, considering additional magnetic effects.

Findings

Excellent agreement with macrospin simulation results.

Superior accuracy compared to conventional methods.

Effective across a wide range of parameters.

Abstract

An accurate method is developed to extract the spin-orbit effective fields through analysis of the results of harmonic Hall voltage measurements by deriving detailed analytical equations, in which both the z-component of the applied magnetic field and the second-order perpendicular magnetic anisotropy are taken into account. The method is tested by analyzing the results of a macrospin simulation. The spin-orbit effective fields extracted from the analysis are found to be in excellent agreement with the input spin-orbit effective fields used for the macrospin simulation over the entire range of the polar magnetization angle and a wide range (0-2) of the ratio of the planar to the anomalous Hall voltage considered in this study. The accuracy of the proposed method is demonstrated more clearly via a systematic study involving a comparison of its results with those of the conventional analytical method.