Fractalized magnon transport on the quasicrystal with enhanced stability

Magnonics has been receiving significant attention in magnetism and spintronics because of its premise for devices using spin current carried by magnons, quanta of spin-wave excitations of a macroscopically ordered magnetic media. Although magnonics has clear energy-wise advantage over conventional electronics due to the absence of the Joule heating, the inherent magnon-magnon interactions give rise to finite lifetime of the magnons which has been hampering the efficient realizations of magnonic devices. To promote magnonics, it is imperative to identify the delocalized magnon modes that are minimally affected by magnon-magnon interactions and thus possess a long lifetime and use them to achieve efficient magnon transport. Here, we suggest that quasicrystals may offer the solution to this problem via the critical magnon modes that are neither extended nor localized. We find that the critical magnon exhibits fractal characteristics that are absent in conventional magnon modes in regular solids such as a unique power-law scaling and a self-similar distribution of distances showing perfect magnon transmission. Moreover, the critical magnons have longer lifetimes compared to the extended ones in a periodic system, by suppressing the magnon-magnon interaction decay rate. Such enhancement of the magnon stability originates from the presence of the quasi-periodicity and intermediate localization behavior of the critical magnons. Thus, we offer the utility of quasicrystals and their critical spin wave functions in magnonics as unique fractal transport characteristics and enhanced stability.