  Magnetic nanoparticles with Neel surface anisotropy, different internal
structures, surface arrangements and elongation are modelled as many-spin
systems. The results suggest that the energy of many-spin nanoparticles cut
from cubic lattices can be represented by an effective one-spin potential
containing uniaxial and cubic anisotropies. It is shown that the values and
signs of the corresponding constants depend strongly on the particle's surface
arrangement, internal structure and elongation. Particles cut from a simple
cubic lattice have the opposite sign of the effective cubic term, as compared
to particles cut from the face-centered cubic lattice. Furthermore, other
remarkable phenomena are observed in nanoparticles with relatively strong
surface effects: (i) In elongated particles surface effects can change the sign
of the uniaxial anisotropy. (ii) In symmetric particles (spherical and
truncated octahedral) with cubic core anisotropy surface effects can change its
sign. We also show that the competition between the core and surface
anisotropies leads to a new energy that contributes to both the 2nd- and
4th-order effective anisotropies.
