In this paper a quantitative theoretical formulation of the critical behavior of soft mode frequencies as a function of an applied magnetic field in two-dimensional Permalloy square antidot lattices in the nanometric range is given according to micromagnetic simulations and simple analytical calculations. The degree of softening of the two lowest-frequency modes, namely the edge mode and the fundamental mode, corresponding to the field interval around the critical magnetic field, can be expressed via numerical exponents. For the antidot lattices studied we have found that: a) the ratio between the critical magnetic field and the in-plane geometric aspect ratio and (b) the ratio between the numerical exponents of the frequency power laws of the fundamental mode and of the edge mode do not depend on the geometry. The above definitions could be extended to other types of in-plane magnetized periodic magnetic systems exhibiting soft-mode dynamics and a fourfold anisotropy.
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