Spin waves in ferromagnetic insulators coupled via a normal metal

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-LifshitzGilbert-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.

Chiral excitation of spin waves in ferromagnetic films by magnetic nanowire gratings

“…In ultra-thin films without chiral surface waves, the exchange coupling mixes the Kittel mode almost symmetrically with the spin waves in opposite directions, thereby leading to in-plane standing waves by interference. In the presence of spacer layers, the dynamic exchange interaction competes as well, falling off on the scale of the spin-flip diffusion length, which can be rather long-range when the spacer is a clean simple metal such as copper [50].…”

Spin-Torque Excitation of Perpendicular Standing Spin Waves in Coupled YIG/Co Heterostructures

“…These STs couple the YIG and Co magnetization dynamics by microwave frequency spin currents [12]. Phenomenological modeling of the coupling reveals a combined action of exchange, damping-like and field-like torques that are localized at the YIG/Co interface.…”

Current-induced magnetization dynamics in two magnetic insulators separated by a normal metal

“…This might not be the case in the antiparallel configuration, and results should be viewed with some caution. Spin waves have a wave-number-dependent damping enhancement [13], which implies that the dynamic coupling in spin valves should be mode dependent [23], which cannot be treated by our model. In the nonlinear regime and FIs with dimensions exceeding the exchange length l ex (∼17 nm for YIG), the energy separation between the modes may be coupled by the large-angle dynamics, increasing dissipation and reducing the oscillation amplitude [24], which again is outside the scope of the present study.…”