Chern numbers for spin models of transition metal nanomagnets

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 nontrivial dependence of a nanoparticle's many-electron wave function 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.