Quantitative characterization of the spin-orbit torque using harmonic Hall voltage measurements

TLDR

Current‑induced torques in ultrathin magnetic heterostructures are crucial for voltage‑controlled magnetization dynamics, yet their size and direction must be accurately evaluated by various methods. This study examines the adiabatic harmonic Hall voltage measurement as a tool to probe the effective field. An analytical formula for harmonic Hall voltages is derived to evaluate effective fields in both out‑of‑plane and in‑plane magnetized systems, and applied to Pt|CoFeB|MgO and CuIr|CoFeB|MgO films. The formula agrees with macrospin simulations, the effective field in CuIr|CoFeB|MgO matches prior spin‑torque switching data, and the results confirm the versatile applicability of harmonic Hall voltage measurements for current‑induced torques.

Abstract

Solid understanding of current induced torques is key to the development of current and voltage controlled magnetization dynamics in ultrathin magnetic heterostructures. To evaluate the size and direction of such torques, or effective fields, a number of methods have been employed. Here we examine the adiabatic (low frequency) harmonic Hall voltage measurement that has been used to study the effective field. We derive an analytical formula for the harmonic Hall voltages to evaluate the effective field for both out of plane and in-plane magnetized systems. The formula agrees with numerical calculations based on a macrospin model. Two different in-plane magnetized films, Pt|CoFeB|MgO and CuIr|CoFeB|MgO are studied using the formula developed. The effective field obtained for the latter system shows relatively good agreement with that estimated using a spin torque switching phase diagram measurements reported previously. Our results illustrate the versatile applicability of harmonic Hall voltage measurement for studying current induced torques in magnetic heterostructures.