Dipolar mode localization and spectral gaps in quasi-periodic arrays of ferromagnetic nanoparticles

In this paper we study the spectral, localization and dispersion properties of the ferromagnetic dipolar modes around a stable, saturated and spatially uniform equilibrium, in quasiperiodically modulated arrays of ferromagnetic nanoparticles based on the Fibonacci sequence. The Fibonacci sequence is the chief example of deterministic quasi-periodic order. The problem is reduced to the study of a linear generalized eigenvalue equation for a suitable hermitian operator connected to the micromagnetic effective field, which accounts for the magnetostatic, anisotropy and Zeeman interactions. The coupling with a weak applied magnetic field, varying sinusoidally in time, is dealt with and the role of the losses is highlighted. By calculating the resonance frequencies and eigenmodes of the Fibonacci arrays we demonstrate the presence of large spectral gaps and strongly localized modes and we evaluate the pseudo-dispersion diagrams. The magnetization oscillation modes in quasi-periodic arrays of magnetic nanoparticles show, at microwave frequencies, behaviors that are very similar to those shown, at optical frequencies, by plasmon modes in quasi-periodic arrays of metal nanoparticles. The presence of band-gaps and strongly localized states in magnetic nanoparticle arrays based on quasi-periodic order may have an impact in the design and fabrication of new microwave nanodevices and magnetic nanosensors.