Microstate and geometry influence on dynamic spin wave properties in Artificial Spin Ice

In this work, carried out by means of the GPU accelerated software mumax3 and Fourier analysis, we perform micromagnetic simulations with regard to the spin dynamics at remanence in a periodic square artificial spin ice (ASI). We consider four different microstates characterized by a specific number of magnetic charges at the central vertex of the primitive cell. Each ASI element, which can be regarded as a macrospin, consists of permalloy elliptical dot with fixed long axis and thickness (256 and 5 nm, respectively), variable width and interdot separation, saturation magnetization 800 kA/m and exchange stiffness 13 pJ/m [1, 2]. Equilibrium ground states are computed for each microstate and are excited by applying a uniform sinc pulse perpendicular to the plane. Fourier analysis is performed to obtain frequency spectra and space phase profiles. The results establish a correlation between ASI macrospin orientation at vertices and key dynamic properties: first, we notice a phaseshift in the fundamental and edge mode profiles as a function of the macrospin separation and width as well as of the magnetic charges at vertex. We also register a frequency gap between the edge and fundamental modes that increases for increasing effective charge at a vertex, as a consequence of the more intense demagnetizing fields. Furthermore, we investigate the role of the macrospin density and width in the array; we also focus on the absolute size of a macrospin (in units of the exchange length), which is responsible for the richness of modes and peaks in the spectrum [3]. These findings fully demonstrate the footprints left in the dynamics by the specific orientation of the macrospin magnetization at the ASI vertices. Moreover, our results suggest specific experiments for validation (e.g. how dynamic measurements can be employed to investigate the statics of the system, with special regard to ferromagnetic resonance - FMR - and Brillouin light scattering - BLS - techniques). Finally, we propose applications in interferometric magnonic logic devices and spin waves computing: for example, the aforementioned spin wave phase-shift, which can be properly regulated by triggering specific macrospin reversals.