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We argue that ferromagnetic transition metal nanoparticles with fewer thanapproximately 100 atoms can be described by an effective Hamiltonian with asingle giant spin degree of freedom. The total spin $S$ of the effectiveHamiltonian is specified by a Berry curvature Chern number that characterizesthe topologically non-trivial dependence of a nanoparticle's many-electronwavefunction on magnetization orientation. The Berry curvatures and associatedChern numbers have a complex dependence on spin-orbit coupling in thenanoparticle and influence the semiclassical Landau-Liftshitz equations thatdescribe magnetization orientation dynamics

Chern Numbers for Spin Models of Transition Metal Nanomagnets