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Radiofrequency-driven resonant spin rotators are routinely used as standardinstruments in polarization experiments in particle and nuclear physics.Maintaining the continuous exact parametric spin-resonance condition of theequality of the spin rotator and the spin precession frequency during operationconstitutes one of the challenges. We present a detailed analytic descriptionof the impact of detuning the exact spin resonance on the vertical and thein-plane precessing components of the polarization. An important part of theformalism presented here is the consideration of experimentally relevantspin-decoherence effects. We discuss applications of the developed formalism tothe interpretation of the experimental data on the novel pilot bunch approachto control the spin-resonance condition during the operation of theradiofrequency-driven Wien filter that is used as a spin rotator in the firstdirect deuteron electric dipole moment measurement at COSY. We emphasize thepotential importance of the hitherto unexplored phase of the envelope of thehorizontal polarization as an indicator of the stability of theradiofrequency-driven spin rotations in storage rings. The work presented hereserves as a satellite publication to the work published concurrently on theproof of principle experiment about the so-called pilot bunch approach that wasdeveloped to provide co-magnetometry for the deuteron electric dipole momentexperiment at COSY.

Spin decoherence and off-resonance behavior of radiofrequency-driven spin rotations in storage rings