  It is proved that the energy absorption in a periodically driven classical
spin system is exponentially slow in frequency, which results in a two-step
relaxation called the Floquet prethermalization. This result is shown by
establishing the classical limit of the quantum spin dynamics. The Floquet
prethermal state is well described by the Gibbs ensemble with respect to the
static effective Hamiltonian obtained by a truncation of the Floquet-Magnus
expansion. On the other hand, the same effective Hamiltonian does not reproduce
the local dynamics for an exponentially long time. This is due to the
chaoticity of classical dynamics, and in stark contrast to quantum spin
systems, in which the effective Hamiltonian well reproduces the exact quantum
dynamics up to an exponentially long time.
