Recursive evolution of spin-wave multiplets in magnonic crystals of antidot-lattice fractals

We explored spin-wave multiplets excited in a different type of magnonic crystal composed of ferromagnetic antidot-lattice fractals, by means of micromagnetic simulations with a periodic boundary condition. The modeling of antidot-lattice fractals was designed with a series of self-similar antidot-lattices in an integer Hausdorff dimension. As the iteration level increased, multiple splits of the edge and center modes of quantized spin-waves in the antidot-lattices were excited due to the fractals’ inhomogeneous and asymmetric internal magnetic fields. It was found that a recursive development (F(n) = F(n−1) + G(n−1)) of geometrical fractals gives rise to the same recursive evolution of spin-wave multiplets.