  Combining field-theoretical methods and ab-initio calculations, we construct
an effective Hamiltonian with a single giant-spin degree of freedom, capable of
the describing the low-energy spin dynamics of ferromagnetic metal nanoclusters
consisting of up to a few tens of atoms. In our procedure, the magnetic moment
direction of the Kohn-Sham SDFT wave-function is constrained by means of a
penalty functional, allowing us to explore the entire parameter space of
directions, and to extract the magnetic anisotropy energy and Berry curvature
functionals. The average of the Berry curvature over all magnetization
directions is a Chern number - a topological invariant that can only take on
values equal to multiples of one half, representing the dimension of the
Hilbert space of the effective spin system. The spin Hamiltonian is obtained by
quantizing the classical anisotropy energy functional, after performing a
change of variables to a constant Berry curvature space. The purpose of this
article is to examine the impact of the topological effect from the Berry
curvature on the low-energy total-spin-system dynamics. To this end, we study
small transition metal clusters: Co$_{n}$ ($n=2,...,5$), Rh$_{2}$, Ni$_{2}$,
Pd$_{2}$, Mn$_{x}$N$_{y}$, Co$_{3}$Fe$_{2}$.
