  We propose how to achieve nonreciprocal quantum phase transition in a
spinning microwave magnonic system composed of a spinning microwave resonator
coupled with an yttrium iron garnet sphere with magnon Kerr effect.
Sagnac-Fizeau shift caused by the spinning of the resonator brings about a
significant modification in the critical driving strengths for second- and
one-order quantum phase transitions, which means that the highly controllable
quantum phase can be realized by the spinning speed of the resonator. More
importantly, based on the difference in the detunings of the counterclockwise
and clockwise modes induced by spinning direction of the resonator, the phase
transition in this system is nonreciprocal, that is, the quantum phase
transition occurs when the system is driven in one direction but not the other.
Our work offers an alternative path to engineer and design nonreciprocal
magnonic devices.
