  We performed ab initio computations of the magnetic properties of simple iron
oxide clusters and slabs. We considered an iron oxide cluster functionalized by
a molecule or glued to a gold cluster of the same size. We also considered a
magnetite slab coated by cobalt oxide or a mixture of iron oxide and cobalt
oxide. The changes in magnetic behavior were explored using constrained
magnetic calculations. A possible value for the surface anisotropy was
estimated from the fit of a classical Heisenberg model on ab initio results.
The value was found to be compatible with estimations obtained by other means,
or inferred from experimental results. The addition of a ligand, coating, or of
a metallic nanoparticle to the systems degraded the quality of the description
by the Heisenberg Hamiltonian. Proposing a change in the anisotropies allowing
for the proportion of each transition atom we could get a much better
description of the magnetism of series of hybrid cobalt and iron oxide systems.
