Spin wave dispersion in bilayer hybrid systems composed of artificial spin ice and thin film: Brillouin light scattering measurements and simulations

We performed a joint experimental and theoretical study of the spin-wave dispersion in hybrid magnonic structures made of a NiFe artificial spin ice (ASI) layer deposited on top of a continuous (unpatterned) NiFe thin film. The ASI lattice consists of 20 nm thick ellipses with lateral dimensions of 260x90 nm2 either in contact with the 20 nm thick NiFe film, or separated from the NiFe film by a 10 nm thick nonmagnetic spacer. The ASI is defined using electron beam lithography, electron beam deposition, and lift off [1]. We performed Brillouin light scattering measurements as a function of the light incidence angle (symbols in fig. 1 right panel), i.e., by varying the probed spin-wave wavevector, and hence the experimental dispersions omega(kappa) are obtained. Depending on the separation between the underlayer and the ASI nanostructure, we observe a rich mode spectrum that exhibits characteristics both spin waves in the extended film (Damon-Eshbach mode) and higher-order ASI modes. Among the latter, we experimentally reveal a weakly dispersive magnon mode. By means of mumax3 simulations [2], and by performing the space-resolved time Fourier transform, we calculated the spin-wave dispersions omega(kappa) (which we compared to the measured ones), the spatial profile of the spin mode cell functions, and the power spectra (k=0). We found a dynamic interplay between ASI and the film underneath. In particular, the ASI is forcing a nonuniform magnetization in the film layer [3], impressing its periodicity, and the film is found to increase the intensities of the ASI resonances and to alter the mode bandwidth. We finally draw important considerations of having a tuneable system which possesses different spin-wave modes that are either propagating or are stationary, as well as localized or extended.