Ground State of Magnetic Dipoles on a Two-Dimensional Lattice: Structural Phases in Complex Plasmas

We study analytically and by molecular dynamics simulations the ground state configuration of a system of magnetic dipoles fixed on a two-dimensional lattice. We find different phases, in close agreement with previous results. Building on this result and on the minimum energy requirement we determine the equilibrium lattice configuration, the magnetic order (ferromagnetic versus antiferromagnetic), and the magnetic polarization direction of a system of charged mesoscopic particles with magnetic dipole moments, in the domain where the strong electrostatic coupling leads to a crystalline ground state. Orders of magnitudes of the parameters of the system relevant to possible future dusty plasma experiments are discussed.