We demonstrate the nonreciprocal transmission of magnonic frequency combs (MFCs) in a dissipative cavity-magnonic system. We utilize the recently emerged pump-induced magnon (PIM) mode in YIG spheres to generate an MFC, as the PIM mode exhibits excellent nonlinearity under coherent pumping. Meanwhile, the dissipative cavity magnonic device is prepared to critical bound states in the continuum (BIC), providing clear nonreciprocity. Based on the different absorption efficiencies of the device in two opposite directions, we have demonstrated a clear difference in the number of frequency comb teeth for forward and reverse transmission, showcasing the ability to generate unidirectional combs. The nonreciprocal MFCs can be systematically tuned by modulating the detuning of the pump and BIC, the magnon and cavity modes, as well as the pump and perturbation tone. This research promotes the combination of MFCs and functional non-Hermitian cavity-magnon electronic devices, realizing new applications for nonreciprocal magnonic devices.
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