  Precision experiments, such as the search for electric dipole moments of
charged particles using radiofrequency spin rotators in storage rings, demand
for maintaining the exact spin resonance condition for several thousand
seconds. Synchrotron oscillations in the stored beam modulate the spin tune of
off-central particles, moving it off the perfect resonance condition set for
central particles on the reference orbit. Here we report an analytic
description of how synchrotron oscillations lead to non-exponential decoherence
of the radiofrequency resonance driven up-down spin rotations. This
non-exponential decoherence is shown to be accompanied by a nontrivial walk of
the spin phase. We also comment on sensitivity of the decoherence rate to the
harmonics of the radiofreqency spin rotator and a possibility to check
predictions of decoherence-free magic energies.
