Mean-field modelling of magnetic nanoparticles: The effect of particle size and shape on the Curie temperature

A Heisenberg mean-field model is used to study the effect of size and shape on the Curie temperature of magnetic nanoparticles. Simple cubic, body-centered cubic, and magnetite nanoparticles are modelled as spheres, cubes, and needlelike particles. The Curie temperatures of particles of different shape, but with the same crystal structure and smallest dimension d, are found to differ. The range in the value of the Curie temperature between particles of different shape, Delta T-C, is found to be similar to 20% of the bulk value of T-C in particles where d < 10 atoms. As particle size increases, the value of Delta T-C reduces rapidly and becomes negligible above a threshold size. This threshold size differs between systems and is controlled predominantly by crystal structure. All systems were fit to the finite-size scaling equation, with values of the scaling exponent nu found to lie between 0.46 and 0.55, in good agreement with the expected value of nu = 0.5. No trend in the value of nu due to shape was found.