Static magnetization induced by time-periodic fields with zero mean

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 vanish 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. 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.