Spin waves in quasi-periodic magnetic superlattices

A microscopic theory is employed to investigate the spin-wave spectra in structures that exhibit what has been called deterministic disorder. A class of models that has attracted particular attention in this context are the quasi-periodic magnetic multilayers, which are artificial crystals fabricated from the juxtaposition of two (or more) materials obeying a quasi-periodic arrangement of substitutional character forming a Cantor set. These quasi-periodicity can be of the type so-called substitutional sequences, and can be characterized by the nture of their Fourier spectrum, which may be dense pure point (Fibonacci sequences) or singular continuous (Thue-Morse and double-period sequences). The calculations are carried out for the exchange dominated regime within the framework of the Heisenberg model and taking into account the random phase approximation (RPA). We consider that the magnetic material has a ferromagnetic order, and a transfer matrix treatment is applied to simplify the algebra, which can be otherwise quite involved. Comparisons with the spectra found in periodic and complete random structures are also done, with more interesting features to understand the physical properties of these structures.