RF field characterization and rectification effects in spin pumping and spin-torque FMR for spin-orbitronics

Abstract

Quantifying spin-orbital-to-charge conversion efficiency is crucial for spin-orbitronics. Two widely used methods for determining these efficiencies are based on ferromagnetic resonance (FMR), spin pumping FMR for the inverse effect, and spin-torque FMR for the direct effect. A key parameter to achieve accurate quantification, especially for spin-pumping FMR, is the RF field strength, $h_{\mathrm{RF}}$. We present a comprehensive theoretical model and experimental protocol that allow a correct quantification of $h_{\mathrm{RF}}$. It was validated by extensive experimental results and it was rigorously tested across various antennas geometries and ferromagnetic systems. We demonstrate that odd-symmetric Lorentzian voltages-which perfectly mimic spin-pumping or spin-torque FMR signals-can arise purely from rectification effects (due to anisotropic magnetoresistance) when $h_{\mathrm{RF}}$ orientation is parallel to the ferromagnetic surface. Through a systematic study of various 10-nm-thick ferromagnetic layers, such as Ni, NiFe, Fe, and CoFeB, we find that while Fe and CoFeB exhibit minimal rectification, Ni and NiFe generate strong rectified signals that must be corrected. We further demonstrate that these rectification effects become negligible for ferromagnetic thicknesses $\leq$ 6 nm, as validated in NiFe/Pt bilayers, providing an important guideline for the design of future heterostructures.