Self-Assembled 2D Dipole Clusters made of Magnetic Particles: Experiment, Modeling, and Application for Tunable Photonic Crystals

Abstract

Two-dimensional magnetic dipole cluster is an interesting model system which shows an interplay between continuum and discrete descriptions. It has also potential in the context of tunable photonic crystals. In this work we study experimentally the static properties of confined ordered 2D magnetic clusters and the order-disorder transition in these clusters. We develop continuum model, similar to Thomas-Fermi model for atoms, which accounts fairly well for the smooth part of the dependence of static cluster properties on the number of particles [M. Golosovsky, Y. Saado, D. Davidov, Phys. Rev. E 65, 061405 (2002)]. However, on top of it we observe quasiperiodic fluctuations at “magic” numbers corresponding to particularly symmetric particle configurations. We demonstrate that these fluctuations arise from the discrete nature of clusters.

We fabricated a 3D photonic structure consisting of the stack of 2D dipole clusters. We measure transmission of electromagnetic waves through these structures and demonstrate a tunable photonic stop-band in the microwave range [Y. Saado, M. Golosovsky, D. Davidov, A. Frenkel, Phys. Rev. B 66, 195108 (2002)]. The tunability can be achieved by two ways: (i) compression of the crystal in inhomogeneous magnetic field; (ii) magnetic field tunable order-disorder transition. The theoretical understanding of the electromagnetic properties of these systems is achieved by the combination of the continuumlike effective-medium model and the Einstein theory of fluctuations, which takes into account discrete nature of clusters.