Simultaneous nonreciprocal and ultra-strong coupling in cavity magnonics

We demonstrate the simultaneous realization of nonreciprocal coupling and ultra-strong coupling in cavity magnonics. By replacing a copper cylinder with a yttrium iron garnet cylinder within the photonic crystal, we achieve an ultra-strong coupling strength of 1.18 GHz and a coupling efficiency of 10.9%. Nonreciprocal microwave transmission emerges within the photonic bandgap, due to the breaking of time-reversal symmetry through the gyromagnetic and Faraday effects. This work establishes a foundation for advanced nonreciprocal devices in hybrid cavity magnonic systems, with promising applications in quantum information processing and microwave isolation.