Anomalous long-distance RKKY interaction in quasicrystals

The Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction is a key mechanism to understand the coupling between localized magnetic moments in the presence of itinerant electrons. Such indirect exchange coupling generally shows the typical oscillation with 2k_F where k_F is the Fermi momentum and the power law decaying as a function of the distance. In this paper, we argue this paradigm is not valid anymore in quasicrystals and discuss anomalous behavior of the RKKY interaction in quasicrystals. Rather than the uniform decaying, the RKKY interaction becomes significant between the moments in non-local region. In other words, it realize a strong couplings between the moments which are far separated, where their distance can be controlled via quasi-periodicity of the systems. It turns out that such anomalous RKKY interaction is originated from the critical states of itinerant electrons, which are neither localized nor extended wave functions and mediate the RKKY interactions on behalf of the extended itinerant electrons. Moreover, the RKKY interaction also shows the fractal structure from the self-similarity of the critical wave functions. Finally, we show that such anomalous RKKY interaction allows quasicrystals as a novel platform for non-local manipulation of the magnetic moments.