Generalized Fibonacci superlattices, dynamical trace maps, and magnetic excitations

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Abstract
Long-wavelength magnetic excitations are investigated in the quasiperiodic layered structures consisting of alternating magnetic and nonmagnetic layers, distributed according to the recently introduced generalized Fibonacci sequences. Both periodic and real boundary conditions are used. Spin-wave spectra for Fibonacci superlattices with copper and nickel mean are compared with those for the golden-mean case. Relations between the spectra and the properties of the dynamical trace maps associated with the generalized Fibonacci sequences are discussed.