  We address the development of geometric phases in classical and quantum
magnetic moments (spin-1/2) precessing in an external magnetic field. We show
that nonadiabatic dynamics lead to a topological phase transition determined by
a change in the driving field topology. The transition is associated with an
effective geometric phase which is identified from the paths of the magnetic
moments in a spherical geometry. The topological transition presents close
similarities between SO(3) and SU(2) cases but features differences in, e.g.,
the adiabatic limits of the geometric phases, being $2\pi$ and $\pi$ in the
classical and the quantum case, respectively. We discuss possible experiments
where the effective geometric phase would be observable.
