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 < 1.5nm), an in-plane superparamagnet (1.5 < a < 3nm), and an in-plane ferromagnet (a > 3.0nm) 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.