Quasiperiodic spin waves in bi-component magnonic crystal arrays of nanowires

A theoretical analysis is given for the compositional effects of quasiperiodicity on the dipole-exchange spin waves (SWs) in bi-component magnonic arrays. The investigations are applied to lateral arrays of ferromagnetic nanowire stripes of cobalt and permalloy as the two building blocks, separated by nonmagnetic spacers. The growth rule applied to the building blocks is taken to be in accordance with either the Fibonacci or Thue-Morse quasiperiodic sequence, which provide contrasting results for the spin-wave properties. The spectra of the spin-wave bandgaps and allowed bands for the bicomponent arrays are calculated up to high generation numbers of the quasiperiodic sequences using a Hamiltonian-based microscopic method. The fractal-like scaling properties of the SWs in these structures are studied as a function of wave vector, which affects the relative importance of the dipolar and exchange terms in the two magnetic materials. Comparisons are made for the density of spin-wave states for the quasiperiodic structures with those for periodic and random lateral arrays, showing that the quasiperiodic arrays have distinctive characteristics.