6 Effective energy landscapes of elongated nanoparticles

Now we investigate the effect of elongation. As discussed earlier, due to the contribution in Eq. (2.16), even a small elongation may have a strong effect on the energy barrier of the multi-spin particle, and in particular on the effective uniaxial constant $ k_\mathrm {ua}^\mathrm {eff}$, as will be seen below. Fig. 2.9 shows the energy potential of an ellipsoidal multi-spin particle with aspect ratio 2:3, cut from an fcc lattice. Unlike the energy potentials of spherical multi-spin particle, the result here shows that for large surface anisotropy the energy minimum corresponds to $ \theta=\pi/2$, see Fig. 2.9(d). Indeed, due to a large number of local easy axes on the surface pointing perpendicular to the core easy axis, the total effect is to change this point from a saddle for small $ k_s$ to a minimum when $ k_s$ has large values.

Figure 2.9: Energy potentials of an ellipsoidal particle cut from an fcc lattice and with uniaxial anisotropy in the core ( $ k_c = 0.0025$) and NSA with constant (a) $ k_s = 0.0125$, (b) $ k_s = 0.075$, (c) $ k_s = 0.1$ and (d) $ k_s = 0.175$.
Figure 2.10: Effective anisotropy constants against $ k_s$ for an ellipsoidal particle of $ {\cal N} = 2044$ spins on sc and fcc lattices, with uniaxial core anisotropy $ k_c = 0.0025$. The lines are guides.

The effective uniaxial and cubic anisotropy constants are shown in Fig. 2.10, for nanoparticles cut from fcc and sc lattice. As expected, the effective uniaxial constant is linear in $ k_s$ shows a strong variation and even changes sign at some value of $ k_s$, as opposed to the case of a spherical multi-spin particle. On the other hand, as for the latter case, the constant $ k_\mathrm{ca}^\mathrm{eff}$ retains its behavior as a function of $ k_s$, i.e. is proportional $ k_{s}^{2}$. Again, in the case of an sc lattice $ k_{ca}^\mathrm{eff}<0$ and on an fcc lattice $ k_{ca}^\mathrm{eff}>0$.

Rocio Yanes