  Generating and probing the magnon squeezing is an important challenge in the
field of quantum magnonics. In this work, we propose a cavity magnonics setup
with an easy-axis ferromagnet to address this challenge. To this end, we first
establish a mechanism for the generation of magnon squeezing in the easy-axis
ferromagnet and show that the magnon squeezing can be critically enhanced by
tuning an external magnetic field near the Ising phase transition point. When
the magnet is coupled to the cavity field, the effective cavity-magnon
interaction becomes proportional to the magnon squeezing, allowing one to
enhance the cavity-magnon coupling strength using a static field. We
demonstrate that the magnon squeezing can be probed by measuring the frequency
shift of the cavity field. Moreover, a magnonic superradiant phase transition
can be observed in our setup by tuning the static magnetic field, overcoming
the challenge that the magnetic interaction between the cavity and the magnet
is typically too weak to drive the superradiant transition. Our work paves the
way to develop unique capabilities of cavity magnonics that goes beyond the
conventional cavity QED physics by harnessing the intrinsic property of a
magnet.
