Transition from superparamagnetism to ferromagnetic single-domain in a Heisenberg model for nano-cluster magnetic system

The transition behaviour of a magnetic system consisting of numerous nano-sized clusters with a zero external field was studied. We investigated the transition from superparamagnetism (SP) to ferromagnetic single-domain (SD) state due to the increase of cluster size by Monte Carlo simulation of Heisenberg and Ising models which are the two extreme cases in anisotropy of spin exchange. The counter-effect of uniaxial anisotropy energy against thermal activation plays an important role in determining the degree of polarization of magnetic moments along easy axis as well as the total anisotropic energy of the system. Based on the sigmoidal anisotropic energy dependence on cluster size, we studied the relationship of the dynamic growth exponent P and critical cluster size N_C of the transition with reduced temperature t and uniaxial anisotropic constant A. We found that the transitional growth exponent P, exhibiting a maximum at certain temperature, is not a universal constant as some previous investigators suggested.