  We consider a single spin in a constant magnetic field or an anisotropy
field. We show that additional external time-periodic fields with zero mean may
generate nonzero time-averaged spin components which are vanishing for the
time-averaged Hamiltonian. The reason is a lowering of the dynamical symmetry
of the system. A harmonic signal with proper orientation is enough to display
the effect. We analyze the problem both with and without dissipation, both for
quantum spins (s=1/2,1) and classical spins. The results are of importance for
controlling the system's state using high or low frequency fields and for using
new resonance techniques which probe internal system parameters, to name a few.
