7 Conclusions

In summary we have evaluated the energy barriers for multispin magnetic nanoparticles with different underlying lattice, shapes, sizes and with the Néel surface anisotropy model. The main results are summarized as follows:

• The energy barriers evaluated in a multidimensional space are complex functions of the system parameters and multiple saddle points can exist. Only in the case of $\mid\zeta\mid\gg1$, where $\zeta =k_\mathrm {ca}^\mathrm {eff}/k_\mathrm {ua}^\mathrm {eff}$, all energy barriers are simple linear combinations of the two effective anisotropy constants.
• We have found energy barriers larger than $K_{c}\mathcal{N}$ value for all studied symmetric nanoparticles with very large surface anisotropy, $k_{s}\gtrsim 100k_{c}$, or for elongated particles with $k_{s}<0$. This confirms a well-known fact that the surface anisotropy may contribute to the enhancement of the thermal stability of a magnetic particle.
• We have analyzed the behavior of the energy barriers of different magnetic nanoparticles as a function of their sizes. We have observed that the influence of the surface become weaker when the size of the particle is increased. The energy barriers value recovers the full value $K_{c}\mathcal{N}$ when $\mathcal{N}\rightarrow\infty$, with very slow convergence.
• We have found that the effective anisotropy values extracted from the energy barriers measurements are consistent with the formula $\mathcal{K}^{eff}=\mathcal{K}_{\infty}+\frac{6}{D}\mathcal{K}_{S}$ only for elongated nanoparticles. This formula is never fulfilled in perfect spherical or truncated octahedral nanoparticles.
• We have studied Co fcc nanoparticles prepared experimentally in Ref. [10] varing the strength of the surface anisotropy constant. The energy barriers were fitted to the experimentally measured energy barriers values for nanoparticles with different cappings, $Al_{2}O_{3}$, Cu and Au [8,10]. From this comparison we obtained the local surface anisotropy values which are almost of the order of the exchange parameter $k_{s}\sim 0.4 \div0.7 J$.