Abstract
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, $\mathrm{\ensuremath{\Delta}}{T}_{C}$, is found to be $\ensuremath{\sim}20%$ of the bulk value of ${T}_{C}$ in particles where $dl10$ atoms. As particle size increases, the value of $\mathrm{\ensuremath{\Delta}}{T}_{C}$ 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 $\ensuremath{\nu}$ found to lie between 0.46 and 0.55, in good agreement with the expected value of $\ensuremath{\nu}=0.5$. No trend in the value of $\ensuremath{\nu}$ due to shape was found.
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