Spin wave propagation spectra in Octonacci one-dimensional magnonic quasicrystals

In this paper, we study spin wave propagation in quasiperiodic magnonic superlattices that follow the so-called Octonacci quasiperiodic sequence, where the N-th stage can be obtained through the recurrence rule SN=SN-1SN-2SN-1, for N⩾3, and starting with S1=A and S2=B. The multilayered magnonic nanostructure is composed of two simple cubic ferromagnetic materials, labeled A and B, which interact through bilinear and biquadratic exchange couplings at their interfaces. The ferromagnetic materials are described by the Heisenberg model, and a transfer matrix treatment is employed, with the calculations performed for the exchange-dominated regime, taking the random phase approximation (RPA) into account. The obtained numerical results show the effects of both (i) the Octonacci quasiperiodic sequence and (ii) the biquadratic exchange coupling on the band structure and transmission spectra of spin waves. Comparisons are also performed with the spectra found in other periodic and quasiperiodic structures.