Spin pumping and anisotropic magnetoresistance voltages in magnetic bilayers: Theory and experiment

Abstract

We investigate experimentally and theoretically the dc voltage generated in ferromagnetic and nonmagnetic metal bilayers under ferromagnetic resonance. The voltage is given by a superposition of the contributions from spin pumping (${V}_{\mathrm{SP}}$) and anisotropic magnetoresistance (${V}_{\mathrm{AMR}}$). A theoretical model is presented that separately determines ${V}_{\mathrm{SP}}$ and ${V}_{\mathrm{AMR}}$ as a function of the applied static field intensity as well the in-plane angle. The model is used to interpret a detailed set of data obtained in a series of ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$/Pt samples excited by in-plane ferromagnetic resonance. The results show excellent agreement between theory and the measured voltages as a function of the Permalloy and Pt layer thicknesses. Our findings show that the quantitative separation of both effects is crucial to the interpretation of experiments and the determination of the spin Hall angle and spin-diffusion length.