We present a generic theoretical framework to describe non-reciprocal microwave circulation in a multimode cavity magnonic system and assess the optimal performance of practical circulator devices. We show that high isolation (> 56 dB), extremely low insertion loss (< 0.05 dB), and flexible bandwidth control can be potentially realized in high-quality-factor superconducting cavity based magnonic platforms. These circulation characteristics are analyzed with materials of different spin densities. For high-spin-density materials such as yttrium iron garnet, strong coupling operation regime can be harnessed to obtain a broader circulation bandwidth. We also provide practical design principles for a highly integratible low-spin-density material (vanadium tetracyanoethylene) for narrow-band circulator operation, which could benefit noise-sensitive quantum microwave measurements. This theory can be extended to other coupled systems and provide design guidelines for achieving tunable microwave non-reciprocity for both classical and quantum applications.
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