Soft magnonic modes in two-dimensional permalloy antidot lattices

Soft magnonic modes in permalloy antidot lattices with a fixed lattice constant a = 420 nm and circular hole diameters ranging between 140 and 260 nm are investigated both experimentally and theoretically. The frequency dependence of magnonic modes on the magnetic field intensity, applied along the vertical rows of holes, was measured by Brillouin light scattering from thermally excited spin waves. All the detected modes exhibit a monotonic frequency evolution with respect to the applied magnetic field, with the exception of the two lowest frequency modes which become soft at a given critical field and exhibit a finite frequency gap. It has been shown, by means of micromagnetic simulations based on the dynamical matrix method, that the mode softening is strictly related to the rotation of the static magnetization from the hard to the easy axis marking a reorientational and continuous phase transition. In addition, the different frequency trend of the fundamental mode and of the corresponding mode localized along the horizontal rows of holes as a function of the aspect ratio is explained in terms of the opposite demagnetizing field experienced by the two modes.