A dilute collection of spins, when driven coherently by crossed magnetic fi
elds of arbitrary and controllable time dependences along the three Cartesi
an directions, is shown to exhibit a striking phenomenon in which the azimu
thal quantum number remains unchanged for certain resonant combinations of
the field intensities and field frequencies. The formalism of dynamic local
ization available for the area of charge transport in crystals is shown to
provide an approximate but highly efficient analytic method for the study o
f this phenomenon. The effect on scattering of probe particles is elucidate
d.