Spin waves in exchange-coupled double layers in the presence of spin torques

Abstract

Spin-wave spectra of a double magnetic layer are calculated theoretically in the macroscopic limit. Magnetic dynamics is described in terms of the Landau-Lifshitz-Gilbert equation, and both static (of the Ruderman-Kittel-Kasuya-Yosida type) and dynamic (via spin pumping) interlayer couplings are taken into account. The influence of spin pumping and spin transfer torque on the spin-wave spectra (frequency and damping factor) has been studied for both parallel and antiparallel magnetic configurations. The spin-wave spectrum in the parallel magnetic state is reciprocal, while in the antiparallel configuration it is nonreciprocal. In both cases, a substantial reduction of the spin-wave lifetimes due to spin pumping to the nonmagnetic metallic layers has been found. In the parallel configuration, this reduction appears mainly for optical modes, while in the antiparallel configuration, it is remarkable for all modes. In turn, the spin torque due to spin current flowing from a metallic layer, created for instance by the spin Hall effect, gives rise to significant changes in the damping factors as well, but these modifications depend on the sign of spin current. For one spin current orientation, the spin-wave damping becomes reduced and may disappear for some modes at a specific threshold value of the spin current, indicating magnetic instability in the system due to spin transfer torque. For the opposite spin current, the damping is enhanced, which indicates stabilization of the corresponding magnetic state.