Spin Waves in Ferromagnetic Insulators Coupled via a Normal Metal

TL;DR

This paper investigates how spin waves propagate and dissipate in a layered system of ferromagnetic insulators separated by a normal metal, revealing how dynamic coupling and dipolar fields influence resonance and damping.

Contribution

It provides a detailed analysis of spin-wave interactions mediated by spin pumping, spin transfer, and dipolar fields, including effects on resonance frequencies and damping in multilayer systems.

Findings

Long-wavelength modes can couple acoustically or optically.

Spin-pumping damping vanishes for acoustic modes without spin-loss.

Surface waves with anisotropy show greater damping and can couple acoustically or optically.

Abstract

Herein, we study the spin-wave dispersion and dissipation in a ferromagnetic insulator--normal metal--ferromagnetic insulator system. Long-range dynamic coupling because of spin pumping and spin transfer lead to collective magnetic excitations in the two thin-film ferromagnets. In addition, the dynamic dipolar field contributes to the interlayer coupling. By solving the Landau-Lifshitz-Gilbert-Slonczewski equation for macrospin excitations and the exchange-dipole volume as well as surface spin waves, we compute the effect of the dynamic coupling on the resonance frequencies and linewidths of the various modes. The long-wavelength modes may couple acoustically or optically. In the absence of spin-memory loss in the normal metal, the spin-pumping-induced Gilbert damping enhancement of the acoustic mode vanishes, whereas the optical mode acquires a significant Gilbert damping enhancement, comparable to that of a system attached to a perfect spin sink. The dynamic coupling is reduced for short-wavelength spin waves, and there is no synchronization. For intermediate wavelengths, the coupling can be increased by the dipolar field such that the modes in the two ferromagnetic insulators can couple despite possible small frequency asymmetries. The surface waves induced by an easy-axis surface anisotropy exhibit much greater Gilbert damping enhancement. These modes also may acoustically or optically couple, but they are unaffected by thickness asymmetries.