Towards 3D Magnonics: spin wave dynamics in geometrically undulated ferromagnetic films

In recent times, the role of three-dimensionality in the propagation properties of spin waves has been increasingly at the center of research interest. We investigate the fundamental properties emerging from a progressive undulation of the film plane, from smooth (2D) to rippled (3D). The geometric undulation (which acts as a constraint for the magnetization texture) is taken along a single direction, is periodic and the period is constant, while the amplitude (which is the differential maximum height with respect to the film thickness) is gradually increased from 0 to 60nm. We find that the undulated systems display at once properties both of a continuous ferromagnetic film and a discretized medium. Depending if the spin wave oscillates parallel or perpendicular to the film undulation direction, and if the external field is applied parallel or perpendicular to the undulation direction, the spin wave dispersion shows peculiar regularities determined by the third dimension (the transverse one), which are tunable through geometric design or magnetization changes. We study the characteristic modification of the internal effective field and link it to the resulting spin wave profile and frequency. We discuss the invariance of the spin wave group velocity with respect to even major changes in the undulation, when the field is applied perpendicular to the undulation direction. Finally we address a potential dual band activity, namely the simultaneous propagation of two independent spin wave signals, with separated frequency bands and disjoint oscillation regions.