  Bistable mechanical vibration is observed in a cavity magnomechanical system,
which consists of a microwave cavity mode, a magnon mode, and a mechanical
vibration mode of a ferrimagnetic yttrium-iron-garnet (YIG) sphere. The
bistability manifests itself in both the mechanical frequency and linewidth
under a strong microwave drive field, which simultaneously activates three
different kinds of nonlinearities, namely, magnetostriction, magnon self-Kerr,
and magnon-phonon cross-Kerr nonlinearities. The magnon-phonon cross-Kerr
nonlinearity is first predicted and measured in magnomechanics. The system
enters a regime where Kerr-type nonlinearities strongly modify the conventional
cavity magnomechanics that possesses only a radiation-pressure-like
magnomechanical coupling. Three different kinds of nonlinearities are
identified and distinguished in the experiment. Our work demonstrates a new
mechanism for achieving mechanical bistability by combining magnetostriction
and Kerr-type nonlinearities, and indicates that such Kerr-modified cavity
magnomechanics provides a unique platform for studying many distinct
nonlinearities in a single experiment.
