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In Fig. 5.2 we present the results for the -component of the average restoring torque at for the nanoparticles whose energy landscapes are presented in Figs. 5.1. The shapes of the torque curves are well described by the expression (5.2) for all temperatures with the macroscopic anisotropy constants decreasing with temperature. For relatively small strength of the surface anisotropy (see Fig. 5.2(a)), practically only uniaxial anisotropy is present. For large strength of the anisotropy constant we observed the competition of two anisotropies: uniaxial and additional cubic due to surface effects (see Fig. 5.2(b)). At high temperatures, however, the cubic anisotropy contribution disappears.
The torque curves presented in Figs. 5.2 allow to investigate the temperature dependence of the effective anisotropies in nanoparticles. Fig. 5.3 presents the corresponding temperature dependence of uniaxial and additional cubic anisotropy for the two values of the surface anisotropy constants. The macroscopic uniaxial anisotropy is independent on the surface anisotropy value, as expected. The macroscopic cubic anisotropy, coming from the surface anisotropy, is practically zero for small strength of the surface anisotropy . In the case of strong surface anisotropy this additional cubic anisotropy is negative and its absolute value is decreasing with temperature. As it happens with the bulk cubic anisotropy, the surface-induced cubic anisotropy is decreasing faster with temperature as the uniaxial core contribution. Consequently, at high temperatures the cubic counterpart disappears leaving the uniaxial core anisotropy as the dominant factor. A transition in the magnetic behavior then can take place. It is similar to the observed in thin films with strong surface effects: at low temperatures the surface effects predominate and the magnetization of the film is perpendicular to the thin film plane while at higher temperatures the surface anisotropy vanishes and the magnetization stays in plane, see section 4.3.3 in previous chapter. In the case of nanoparticles a similar effect occurs: at low temperatures the surface effects dominate determining the overall cubic behavior, at high temperatures the surface contribution vanishes and the nanoparticle behaves as a uniaxial one.
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Rocio Yanes