  The superradiant phase transition (SPT) has been widely studied in cavity
quantum electrodynamics (CQED). However, this SPT is still subject of ongoing
debates due to the no-go theorem induced by the so-called ${\bf A}^2$ term
(AT). We propose a hybrid quantum system, consisting of a single-mode cavity
simultaneously coupled to both a two-level system and yttrium-iron-garnet
sphere supporting magnons with Kerr nonlinearity, to restore the SPT against
the AT. The Kerr magnons here can effectively introduce an additional strong
and tunable AT to counteract the intrinsic AT, via adiabatically eliminating
the degrees of freedom of the magnons. We show that the Kerr magnons induced
SPT can exist in both cases of ignoring and including the intrinsic AT. Without
the intrinsic AT, the critical coupling strength can be dramatically reduced by
introducing the Kerr magnons, which greatly relaxes the experimental conditions
for observing the SPT. With the intrinsic AT, the forbidden SPT can be
recovered with the Kerr magnons in a reversed way. Our work paves a potential
way to manipulate the SPT against the AT in hybrid systems combining CQED and
nonlinear magnonics.
