  A basic result about the dynamics of spinless quantum systems is that the
Maryland model exhibits dynamical localization in any dimension. Here we
implement mathematical spectral theory and numerical experiments to show that
this result does not hold, when the 2-dimensional Maryland model is endowed
with spin 1/2 -- hereafter dubbed spin-Maryland (SM) model. Instead, in a
family of SM models, tuning the (effective) Planck constant drives dynamical
localization{delocalization transitions of topological nature. These
transitions are triggered by the self-duality, a symmetry generated by some
transformation in the parameter -- the inverse Planck constant -- space. This
provides significant insights to new dynamical phenomena such as what occur in
the spinful quantum kicked rotor.
