  The thermal activation of magnetization reversal in magnetic nanoparticles is
controlled by the anisotropy-energy barrier. Using perturbation theory, exact
diagonalization and stability analysis of the ferromagnetic spin-s Heisenberg
model with coupling or single-site anisotropy, we study the effects of quantum
fluctuations on the height of the energy barrier. Opposed to the classical
case, there is no critical anisotropy strength discriminating between reversal
via coherent rotation and via nucleation/domain-wall propagation. Quantum
fluctuations are seen to lower the barrier depending on the anisotropy
strength, dimensionality and system size and shape. In the weak-anisotropy
limit, a macrospin model is shown to emerge as the effective low-energy theory
where the microscopic spins are tightly aligned due to the ferromagnetic
exchange. The calculation provides explicit expressions for the anisotropy
parameter of the effective macrospin. We find a reduction of the
anisotropy-energy barrier as compared to the classical high spin-s limit.
