Magnetic Order in Two-Dimensional Arrays of Nanometer-Sized Superparamagnets

Random two-dimensional island assemblies have three magnetic phases at room temperature as a function of island radius $a$. These magnetic states are a perpendicularly magnetized random antiferromagnet ( $a<\mathrm{}1.5\mathrm{}\mathrm{nm}$), an in-plane superparamagnet ( $1.5<a<\mathrm{}3\mathrm{}\mathrm{nm}$), and an in-plane ferromagnet ( $a>\mathrm{}3.0\mathrm{}\mathrm{nm}$) in a superferromagnetic regime. Mean-field and Monte Carlo methods are used to examine order-disorder transitions in two dimensions, and to set minimum interisland coupling strengths.