  Phenomena involving interactions among magnons, phonons, and photons in
cavity magnomechanical systems have attracted considerable attention recently,
owing to their potential applications in the microwave frequency range. One
such important effect is the response of a probe field to such tripartite
interaction between photon-magnon-phonon. In this paper, we study
Goos-H\"{a}nchen shift (GHS) of a reflected probe field in a cavity
magnomechanical system. We consider a YIG sphere positioned within a microwave
cavity. A microwave control field directly drives the magnon mode in YIG
sphere, whereas the cavity is driven via a weak probe field. Our results show
that the GHS can be coherently controlled through magnon-phonon coupling via
the control field. For instance, GHS can be tuned from positive to negative by
tuning the magnon-phonon coupling. Similarly, the effective cavity detuning is
another important controlling parameter for GHS. Furthermore, we observe that
the enhancement of GHS occurs when magnon-phonon coupling is weak at resonance,
and when the magnon-photon coupling is approximately equal to the loss of
microwave photons. Our findings may have potential significance in applications
related to microwave switching and sensing.
