  We report the first observation of the magnon-polariton bistability in a
cavity magnonics system consisting of cavity photons strongly interacting with
the magnons in a small yttrium iron garnet (YIG) sphere. The bistable behaviors
are emerged as sharp frequency switchings of the cavity magnon-polaritons
(CMPs) and related to the transition between states with large and small number
of polaritons. In our experiment, we align, respectively, the [100] and [110]
crystallographic axes of the YIG sphere parallel to the static magnetic field
and find very different bistable behaviors (e.g., clockwise and
counter-clockwise hysteresis loops) in these two cases. The experimental
results are well fitted and explained as being due to the Kerr nonlinearity
with either positive or negative coefficient. Moreover, when the magnetic field
is tuned away from the anticrossing point of CMPs, we observe simultaneous
bistability of both magnons and cavity photons by applying a drive field on the
lower branch.
