Coupled spin waves in trilayer films and nanostripes of Permalloy separated by nonmagnetic spacers: Brillouin light scattering and theory

We present a combined experimental and theoretical study of the di-exchange spin waves in layered structures constituted by permalloy(30 nm)/Cu(10 nm)/permalloy (d)/Cu(10 nm)/permalloy (30 nm), which differ by the variable thickness d of the middle permalloy film (with d = 15, 30, 60 nm). Both the plane layered films and two sets of stripes having widths of 150 and 400 nm were studied. The spin-wave dispersions (frequency vs wave vector) were measured by Brillouin light scattering and the experimental data interpreted using a microscopic (Hamiltonian-based) theory that takes into account the magnetic dipole-dipole and exchange interactions within each stripe and the dipole-dipole coupling between stripes of the stack. Overall, good agreement is found, showing that modes of the layered films constituted by surface dipolar and exchange-dominated waves give rise to complicated spectra in the case of layered stripes because of the lateral confinement. The role of the middle-layer thickness d in the determination of the perpendicular profile of the spin modes is analyzed in detail.