Superferromagnetism on a two-dimensional array of magnetic nanodots: an Ising model approximation

A simple theory, using the differential operator technique with the approximated Van der Waerden identity, was developed to investigate two-dimensional arrays of magnetic nanodots. The calculations were performed using an Ising model for a hexagonal lattice consisting of metallic nanodots deposited onto non-magnetic insulator substrate. The nanodots are assumed to interact with each other via a tunneling exchange coupling. The nanodot magnetic moment was represented by an effective spin which simulates thermal fluctuations. We found that the superferromagnetic ordering temperature increases with the dot-size, magnetic anisotropy, and dot volume fraction, and is strongly dependent upon the substrate parameters.