Instabilities and melting in a two-dimensional magnetic dipolar system

A monolayer of spherical non-magnetic inclusions in a paramagnetic fluid is known to crystallize in the presence of a perpendicular magnetic field. It is shown, as a function of increasing layer thickness, that an initially stable 2D triangular monolayer becomes unstable with respect to a quasi-2D centered rectangular structure. The latter then becomes unstable with respect to a quasi-2D square lattice. Both transitions are continuous and Ising-like. The order parameter characterizing the initial transition is an out-of-plane distortion mode while that of the second is in-plane. An estimate of the melting temperature of the quasi-2D structures is given—above this temperature, the time-averaged out-of-plane deviation at each site is zero and the 2D triangular structure is stable. Thus only below this lattice-to-lattice melting point would the quasi-2D structures be observable.