  Floquet states have been subject of great research interest since
Zel'dovich's pioneering work on the quasienergy of a quantum system subject to
a temporally periodic action. Nowadays periodic modulation of the system
Hamiltonian is mostly achieved by microwaves leading to novel exciting
phenomena in condensed matter physics: Floquet topological insulators, chiral
edge states etc. On the other hand, nonthermal optical control of magnetization
at picosecond time scales is currently a highly appealing research topic for
potential applications in magnetic data storage. Here we combine these two
concepts to investigate Floquet states in the system of exchange-coupled spins
in a ferromagnet. We periodically perturb the magnetization of an iron-garnet
film by a train of circularly-polarized femtosecond laser pulses hitting the
sample at 1 GHz repetition rate and monitor the magnetization dynamics behaving
like a Floquet state. An external magnetic field allows tuning of the Floquet
states leading to a pronounced increase of the precession amplitude by one
order of magnitude at the center of the Brillouin zone, i.e. when the
precession frequency is a multiple of the laser pulse repetition rate. Floquet
states might potentially allow for parametric generation of magnetic
oscillations. The observed phenomena expand the capabilities of coherent
ultrafast optical control of magnetization and pave a way for their application
in quantum computation or data processing.
