  We argue that ferromagnetic transition metal nanoparticles with fewer than
approximately 100 atoms can be described by an effective Hamiltonian with a
single giant spin degree of freedom. The total spin $S$ of the effective
Hamiltonian is specified by a Berry curvature Chern number that characterizes
the topologically non-trivial dependence of a nanoparticle's many-electron
wavefunction on magnetization orientation. The Berry curvatures and associated
Chern numbers have a complex dependence on spin-orbit coupling in the
nanoparticle and influence the semiclassical Landau-Liftshitz equations that
describe magnetization orientation dynamics.
