Role of the spin transfer in the ferromagnetic resonance response of thin films

Abstract

We develop a theory to describe the ferromagnetic resonance response of layered structures composed of two ferromagnetic thin films separated by a nonferromagnetic spacer layer, when spin-polarized current emanates from one layer and is injected into the second. The resulting spin torque influences both the frequency and the linewidth of the ferromagnetic resonance response of the film into which the current is injected. We derive explicit formulas that describe such effects, for arbitrary orientations of an external magnetic field and directions of the magnetization of the polarizing ferromagnetic layer. This enables us to calculate the effect of the spin-transfer torque on characteristic quantities such as the high-frequency susceptibility, ferromagnetic resonance linewidth, ferromagnetic resonance frequency, and the equilibrium magnetization orientation. The results demonstrate that ferromagnetic resonance investigations provide access to spin-transfer torque effects by analyzing both the resonance frequency as well as the resonance linewidth. The latter can be used as a very sensitive measure of spin-torque physics in the regime of small current densities, i.e., at the onset of spin-transfer-torque-driven dynamics. The theory is compared quantitatively to experimental results obtained on Py/Cu/Co-trilayer structures.