  A study of spherical maghemite nanoparticles on a two dimensional triangular
array was carried out using a stochastic Landau-Lifshitz-Gilbert (sLLG)
approach. The simulation method was first validated with a triangular array of
simple dipoles, where results show the expected phase transition to a
ferromagnetic state at a finite temperature. The ground state exhibited a
continuous degeneracy that was lifted by an order-from-disorder mechanism at
infinitesimal temperatures with the appearance of a six-fold planar anisotropy.
The nanoparticle array consisted of 7.5 nm diameter maghemite spheres with
bulk-like superexchange interactions between Fe-ions in the core, and weaker
exchange between surface Fe-ions and a radial anisotropy. The triangular
nanoparticle array ordered at the same reduced temperature as the simple dipole
array, but exhibited different behaviour at low temperatures due to the surface
anisotropy. We find that the vacancies on the octahedral sites in the
nanoparticles combine with the surface anisotropy to produce an effective
random temperature-dependent anisotropy for each particle. This leads to a
reduction in the net magnetization of the nanoparticle array at zero
temperature compared to the simple dipole array.
