2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171262The derivation of a new family of magnetic fields inducing exactly solvable spin evolutions is presented. The conditions for which these fields generate the evolution loops (dynamical processes for which any spin state evolves cyclically) are studied. Their natural connection with geometric phases and the corresponding calculation is also elaborated.8 pages, LaTeX file, no figures. To appear in Rep. Math. PhysQuantum Physicstext