  We study the response of ideal spin systems which are interacting with both a
strong oscillating magnetic field, and a thermal environment, to a weak probing
magnetic field. We demonstrate that even the sign of the resulting mean
magnetization depends on the amplitude of the driving field, and that its
absolute value can be significantly larger than the equilibrium magnetization
in the absence of time-periodic forcing. Since the underlying Floquet-state
occupation probabilities are determined by the precise form of the system-bath
coupling, future measurements of such effects have the potential to establish a
particularly innovative line of research, providing information on
nonequilibrium thermodynamics, and giving access to quantities which usually
remain hidden when probing equilibrium systems.
