Characterization of Spin-Orbit Torque Efficiency in Magnetic Heterostructures with Perpendicular Magnetic Anisotropy via Spin-Torque Ferromagnetic Resonance

Abstract

Characterization of spin-orbit torques (SOTs) in the perpendicular magnetic anisotropy (PMA) system is of great importance for fundamental studies and technological applications in spintronic devices. Here, we report a spin Hall magnetoresistance (SMR) based spin-torque ferromagnetic resonance (ST FMR) study of SOT efficiency in perpendicularly magnetized $\mathrm{W}$/${\mathrm{Co}}_{40}{\mathrm{Fe}}_{40}{\mathrm{B}}_{20}$/$\mathrm{Mg}\mathrm{O}$ structures. A full analysis of the ST FMR spectrum is developed for the PMA sample. A typical ST FMR spectrum of the PMA system shows two resonance modes, i.e., in-plane and out-of-plane magnetization precession modes. By performing modulation of the damping measurement for the in-plane mode, the dampinglike torque efficiency is determined to be \ensuremath{-}0.38, which is consistent with the reference value obtained in samples with in-plane magnetic anisotropy. The dampinglike torque efficiency of \ensuremath{-}0.31 is also obtained from the out-of-plane resonance mode, in which the significant contribution of the spin-pumping-induced inverse spin Hall effect is carefully considered. The obtained values of dampinglike torque efficiency by different means are consistent with each other. The present work provides useful insights to determine the dampinglike torque efficiency of the PMA sample via ST FMR measurements.