Magnons in one-dimensional k-component Fibonacci structures

We have studied the magnon transmission through of one-dimensional magnonic k-component Fibonacci structures, where k different materials are arranged in accordance with the following substitution rule: Sn(k)=Sn−1(k)Sn−k(k) (n≥k=0,1,2,…), where Sn(k) is the nth stage of the sequence. The calculations were carried out in exchange dominated regime within the framework of the Heisenberg model and taking into account the RPA approximation. We have considered multilayers composed of simple cubic spin-S Heisenberg ferromagnets, and, by using the powerful transfer-matrix method, the spin wave transmission is obtained. It is demonstrated that the transmission coefficient has a rich and interesting magnonic pass- and stop-bands structures, which depends on the frequency of magnons and the k values.