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We address the development of geometric phases in classical and quantummagnetic moments (spin-1/2) precessing in an external magnetic field. We showthat nonadiabatic dynamics lead to a topological phase transition determined bya change in the driving field topology. The transition is associated with aneffective geometric phase which is identified from the paths of the magneticmoments in a spherical geometry. The topological transition presents closesimilarities 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 theclassical and the quantum case, respectively. We discuss possible experimentswhere the effective geometric phase would be observable.

Effective geometric phases and topological transitions in SO(3) and SU(2) rotations