# 7 Effective energy landscape of an octahedral nanoparticle

In this section we analyze the energy landscape of a magnetic nanoparticle with the so-called truncated octahedral shape. The Co particles are usually reported as having this structure with fcc underlying lattice, see for example Ref. [20,14,8] and image in Figs. 1.1(c-d).

Regular truncated octahedrons having six squares and eight hexagons on the surface have been constructed cutting the ideal fcc lattice in an octahedral (two equal mutually perpendicular pyramids with square bases parallel to XY plane) and subsequent truncation. Equal surface densities in all hexagons and squares can be obtained if the fcc lattice is initially rotated in the XY plane, i.e. when the X axis is taken parallel to the direction and the Z axis to the direction. We perform the same calculations as before for a multi-spin particle cut from an fcc lattice, with cubic single-site anisotropy in the core and NSA.

In Fig. 2.11 we presents the values of the effective uniaxial and cubic anisotropy constants as a function of surface anisotropy value . The results show that the effective uniaxial contribution in this system is practically zero. We can also observe that the effective cubic anisotropy is modified with respect to the core by surface effects. It can be seen that, similarly to the results discussed above for spherical particles, the effective cubic anisotropy constant is again proportional to for small . This is mainly due to the two contributions, one coming from the initial core cubic anisotropy and the other from the surface contribution as in Eq. (2.14). It is interesting to note that the surface contribution can change the sign of the effective cubic anisotropy constant from the initially negative cubic core anisotropy. We can also observe an asymmetric behavior of the effective anisotropy constants with respect to the change of the sign of the surface anisotropy which we found, in general, in all particles with fcc underlying lattice.

If the fcc lattice is initially orientated with crystallographic lattice axes parallel to those of the system of coordinates, then different atomic densities are created on different surfaces. This way the surface density along the XY circumference is different from that along XZ one. In Fig. 2.12 we plot the dependence of the effective cubic constant as a function of for and . It can be seen that, similarly to the results discussed above, the effective cubic constant is again proportional to but now its increase with is slower. The surface contribution can again change the sign of the initially negative cubic core anisotropy. Besides, we clearly see that the multi-spin particle develops a negative uniaxial anisotropy contribution, induced by the surface in the presence of core anisotropy, according to Eq. (2.20).

Rocio Yanes