  We study the dynamics of a localized spin-1/2 driven by a time-periodic
magnetic field that undergoes a topological transition. Despite the strongly
non-adiabatic effects dominating the spin dynamics, we find that the field's
topology appears clearly imprinted in the Floquet spin states through an
effective Berry phase emerging in the quasienergy. This has remarkable
consequences on the spin resonance condition suggesting a whole new class of
experiments to spot topological transitions in the dynamics of spins and other
two-level systems, from nuclear magnetic resonance to strongly-driven
superconducting qubits.
